The Weight of the Past: History-Dependent Structure in Transitions to Sustained Inactivity
Article information
Abstract
Objective
This study aims to evaluate whether short-term behavioral history improves the prediction of transitions into sustained inactivity in continuous rest–activity data beyond the instantaneous activity level alone.
Methods
Minute-level wrist actigraphy data from individuals with major depressive disorder, schizophrenia, attention-deficit/hyperactivity disorder, and healthy controls were analyzed (2.53 million observations). Activity was transformed into trajectory-based features capturing instantaneous level, short-timescale variability, and directional drift memory. The primary outcome, D20_onset, was defined as the onset of ≥20 consecutive minutes of zero recorded activity and treated as an operational marker of transition into sustained inactivity. Logistic regression models with interaction terms evaluated whether recent trajectory features improved prediction beyond memoryless formulations.
Results
Transition probability exhibited a stable and reproducible structure within the behavioral state space. Sustained activity level showed a strong suppressive association with D20_onset probability across diagnostic groups. Variability and drift memory exerted conditional effects, amplifying transition probability primarily within low-activity regimes. A significant three-way interaction among activity level, variability, and drift indicated a nonlinear, history-sensitive structure. Predicted probability surfaces showed concentration of transition probability within a low-activity, high-instability region, consistent with a structured region of the state space.
Conclusion
Transitions into sustained inactivity in naturalistic settings are temporally embedded and depend on short-term behavioral history. Because actigraphy reflects behavior within circadian rest–activity organization, these transitions likely represent a mixture of behavioral disengagement, rest, and phase-related quiescence rather than a single process. The findings support history-aware, state-space modeling of rest–activity dynamics without presupposing a specific underlying mechanism.
INTRODUCTION
Human behavior rarely ceases instantaneously. Across physical, cognitive, and motivational domains, sustained activity is typically followed by gradual slowing, intermittency, and eventual withdrawal rather than abrupt termination. Such progressive decline has been described in contexts ranging from prolonged mental effort and fatigue to everyday goal pursuit, where persistence gives way to reduced behavioral output over time [1-3]. Contemporary theories of cognitive control and effort similarly emphasize that sustained performance reflects dynamic allocation processes rather than fixed capacity limits [4,5]. These observations suggest that behavioral disengagement is not a discrete switch but an evolving process unfolding over time.
In psychiatric populations, alterations in activity persistence CIMand withdrawal are especially pronounced. Major depression, schizophrenia, and attention-deficit/hyperactivity disorder are associated with reduced activity levels, extended inactivity bouts, disrupted engagement patterns, and impaired motivational persistence [2,6,7]. These alterations are observable not only in subjective reports but also in real-world behavioral data, where individuals exhibit prolonged inactivity, fragmented activity, or difficulty sustaining effort across minutes and hours. In depression, for example, prognostic models increasingly rely on longitudinal trajectories rather than static symptom levels to predict relapse and recurrence [8]. Such findings suggest that behavioral withdrawal may depend not only on the current state but also on how that state has been reached.
Wearable actigraphy provides a direct window into these temporal dynamics. Continuous motor activity recordings in naturalistic settings capture sustained behavior, transient fluctuations, and extended periods of low or zero activity without reliance on retrospective reports or laboratory tasks [9]. Unlike experimental paradigms that isolate brief episodes of effort, actigraphy reflects spontaneous rest–activity rhythms unfolding in daily life. Importantly, transitions into sustained inactivity in such data do not uniquely identify a single underlying process. Periods of zero or near-zero activity may reflect behavioral disengagement but may also correspond to rest, sleep onset, or other quiescent states embedded within circadian regulation. Nevertheless, the onset of sustained inactivity remains a meaningful transition event within rest–activity dynamics, providing a tractable empirical target for examining how recent behavioral history shapes entry into inactive states.
Despite this temporal richness, many analytic approaches implicitly adopt memoryless formulations. In such models, the probability of entering an inactive state depends solely on the instantaneous level of activity, without reference to the recent trajectory. This assumption aligns with traditional state-based perspectives in executive attention and control research [5,10,11], but entails a strong simplification: that two moments with identical current activity are equivalent, regardless of whether that state followed sustained exertion, gradual decline, or recent recovery.
There are reasons to question this assumption. Cognitive and motivational literatures consistently indicate that effort costs accumulate over time and that persistence is shaped by prior exertion, opportunity costs, and fatigue history [12-15]. Neuroeconomic and control valuation models similarly emphasize dynamic updating, in which prior investment alters subsequent willingness to continue [16-19]. Experimental studies of mental fatigue demonstrate that prior exertion can reduce persistence even when current task demands remain constant [20-22]. In parallel, chronobiological research highlights inertia and asymmetry in rest–activity regulation, with transitions between active and inactive states influenced by both prior trajectory and circadian phase [23-25]. Together, these findings suggest that entry into sustained inactivity may depend not only on instantaneous activity level but also on short-term behavioral history and trajectory.
This motivates a concrete empirical question: Does short-term behavioral history alter the probability of entering sustained inactivity in real-world activity data, even when instantaneous activity is matched?
To address this question, the present study adopts a resistance-based operationalization inspired by Lagun’s Law [26]. In this context, resistance is treated strictly as an analytically derived feature of behavioral time series, capturing trajectory-dependent constraints on continued activity. It does not represent a directly observed biological, psychological, or mechanistic variable. Instead, it functions as a formal summary of how recent changes in activity level and direction relate to the likelihood of transitioning into sustained inactivity. When applied to actigraphy, such features can be interpreted in chronobiological terms as reflecting constraints on transitions within rest–activity rhythms, without presupposing a specific underlying mechanism.
Importantly, the present study does not test Lagun’s Law as a comprehensive theory of effort or motivation. Rather, it uses a resistance-derived feature framework as an analytic tool to evaluate whether short-term behavioral history improves the prediction of sustained inactivity onset beyond memoryless formulations. This allows the results to be interpreted alongside alternative accounts, including motivational fatigue, opportunity cost models, and dynamic control valuation frameworks [16-18], without privileging a single explanatory mechanism.
Using continuous motor activity data from individuals with major depression, schizophrenia, attention-deficit/hyperactivity disorder, and healthy controls [9,27], we examine whether the probability of entering sustained inactivity depends on recent trajectory features, even when instantaneous activity levels are held constant. The primary outcome is defined as the onset of sustained inactivity (≥20 consecutive minutes of zero recorded activity), which is treated as a transition within rest–activity dynamics rather than a direct measure of motivational disengagement. We further examine whether divergence emerges between different recent trajectories leading into similar instantaneous states, consistent with path-dependent transition structures.
Rather than proposing a new biological law, this work evaluates whether real-world rest–activity behavior exhibits empirically detectable short-term history dependence that cannot be reduced to memoryless state models. By formalizing transitions into sustained inactivity as a function of local activity level, short-timescale variability, and recent directional history, the study aims to clarify how persistence and withdrawal should be modeled in naturalistic behavioral systems, particularly within the context of temporally embedded and circadian-influenced activity patterns.
Conceptual scope: resistance as a formal constraint
The present study treats resistance strictly as a formal, analytically defined construct rather than as a mechanistic, biological, or psychological entity. In this context, resistance refers to a derived feature of behavioral time series that modulates the probability of continued activity versus transition into sustained inactivity. It is introduced as a modeling construct, not as a claim about a specific neural, physiological, or psychological substrate. This distinction is fundamental to the scope of the study. Throughout the manuscript, resistance should be understood solely as an operational descriptor of trajectory-dependent constraints within observable behavior, rather than as a directly measured latent mechanism.
Within this framework, resistance is operationalized as a scalar signal derived from observable activity trajectories. It summarizes how recent patterns of activity level and directional change relate to the likelihood of transitioning into sustained inactivity. Importantly, resistance is not equated with fatigue, motivation, effort, arousal, or any single psychological construct. Rather, it functions as a composite descriptor that may reflect the combined influence of multiple processes evolving over time. These processes may include, but are not limited to, motivational dynamics, environmental constraints, sleep-related processes, and circadian regulation.
This modeling choice is particularly important in the context of naturalistic actigraphy data. Actigraphy measures motor output, not internal states. Any derived signal, including resistance, necessarily reflects the interaction of multiple underlying influences rather than a single identifiable factor. Similarly, the primary outcome examined in this study, the onset of sustained inactivity, does not uniquely correspond to behavioral disengagement. Such periods may reflect disengagement but may also arise from rest, sleep onset, or other quiescent states embedded within circadian organization. Accordingly, resistance should be interpreted as a formal descriptor of transition structure within rest–activity dynamics, not as a direct proxy for a specific internal state or process.
From a dynamical perspective, resistance can be viewed as a constraint on transitions within rest–activity regulation. Biological rhythms exhibit inertia, delayed recovery, and asymmetry between activation and deactivation phases [24,25]. These properties imply that transitions into sustained inactivity may depend on recent trajectory as well as current activity level. By framing resistance as a formal constraint on such transitions, the present study aligns with state-dependent approaches in chronobiology while remaining explicitly agnostic about underlying mechanisms.
The resistance construct used here is inspired by Lagun’s Law [26], but the present work does not test that framework in its entirety. Instead, it adopts a minimal operationalization sufficient to evaluate a narrow empirical question: whether short-term behavioral history alters the probability of entering sustained inactivity, even when instantaneous activity levels are matched. The same empirical structure could, in principle, be described using alternative trajectory-based feature representations; the resistance formulation is used here as a compact and interpretable way to summarize such information, rather than as a uniquely privileged construct.
Accordingly, the claims of this study are intentionally limited. Evidence of history dependence in transitions into sustained inactivity does not establish a universal law of effort, nor does it identify a specific biological or psychological mechanism. Rather, it indicates that memoryless formulations are insufficient to capture certain features of real-world rest–activity dynamics and that short-term trajectory information contributes meaningfully to predicting transitions into inactive states.
By constraining resistance to a model-level role, this work separates structural inference from mechanistic speculation. The aim is to determine whether transitions into sustained inactivity exhibit path dependence in naturalistic behavior and to clarify how such dependence should inform the modeling of rest–activity dynamics and their temporal organization.
METHODS
Operationalizing resistance from actigraphy
Resistance was operationalized directly from continuous motor activity time series obtained via actigraphy [9]. The objective of this operationalization was not to infer internal psychological states but to construct a mathematically explicit set of features that encode attenuation of activity and its recent temporal evolution. Consistent with the conceptual framework outlined above, this operationalization should be interpreted as a transformation of observable behavior designed to capture trajectory-dependent structure relevant to transitions into sustained inactivity.
Let A(t) denote recorded motor activity at time t, measured as activity counts per minute. Raw activity values exhibit a heavy-tailed distribution, with large outliers and strong heteroskedasticity. To stabilize variance and increase resolution in low-activity regimes, instantaneous resistance was defined as a monotonic transformation of activity:
This transformation preserves ordinal relationships between activity levels while compressing extreme values and expanding resolution near zero. Under this mapping, lower motor activity corresponds to higher values of G(t). Importantly, G(t) depends only on activity at the time t and contains no explicit information about prior behavior.
To capture short-term trajectory dynamics, a discrete temporal difference of the transformed signal was defined as follows:
Positive increments in ΔG(t) correspond to decreases in activity (i.e., increasing values of the transformed signal), whereas negative increments correspond to increases in activity. To isolate directional changes, rectified components of the derivative were constructed, separating increases from decreases in the transformed signal.
Short-term trajectory history was then operationalized as a rolling accumulation of recent directional changes. Specifically, for a window of length τ, we defined:
where ΔG+ denotes positive increments only. This term captures recent upward shifts in the transformed signal over the preceding τ minutes. By excluding the current time point, the history term reflects the trajectory leading into the present state rather than incorporating contemporaneous information.
In parallel, a complementary directional memory term was constructed from negative increments, capturing accumulated downward shifts in activity over the same temporal window. This term quantifies short-term drift in the opposite direction and enables examination of asymmetries between increasing and decreasing trajectories.
Together, these operators define two components: 1) an instantaneous level, G(t), reflecting current activity attenuation; and 2) a short-term directional memory term, Hτ(t), reflecting the recent trajectory.
This decomposition allows comparison between moments with matched instantaneous levels but differing recent histories. Two time points may exhibit identical G(t) values yet differ substantially in whether activity has been decreasing, increasing, or stable in the preceding window.
The operationalization is intentionally minimal and does not assume that the transformed signal corresponds uniquely to fatigue, motivation, arousal, or sleep pressure, nor that it accumulates as a persistent internal quantity. Rather, it provides a compact representation of local trajectory structure within observable behavior. Although described in resistance terms, the same construction can equivalently be interpreted as encoding short-term changes in activity level and direction, independent of any specific theoretical framework.
This feature construction enables direct evaluation of whether incorporating recent trajectory improves the prediction of transitions into sustained inactivity beyond instantaneous activity level alone, without presupposing a specific underlying mechanism.
Dataset and study design
This study uses continuous wrist-worn actigraphy data from the OBF-Psychiatric dataset, a publicly available collection of motor activity recordings from individuals diagnosed with major depressive disorder, schizophrenia, attention-deficit/hyperactivity disorder (ADHD), and matched healthy controls [9,27]. Full details of recruitment procedures, diagnostic assessment, and data acquisition are provided in the original dataset publication. The present work constitutes a secondary reanalysis; no new data were collected.
The original dataset received ethical approval from the relevant institutional review board as described in the data descriptor [9]. The present study involved secondary analysis of fully de-identified publicly available data and therefore did not require additional ethical approval under applicable guidelines.
The dataset and code are publicly available via the Open Science Framework (OSF; at https://doi.org/10.17605/OSF.IO/6MVBX). All preprocessing scripts and analysis code used in this study are provided in the same repository for full reproducibility.
Participants contributed multi-day to multi-week recordings with minute-level temporal resolution. All analyses adopt a within-subject, time-resolved design. Diagnostic labels are used solely for stratified analysis and robustness evaluation; no diagnostic classification or symptom prediction is performed.
Preprocessing and behavioral time-series construction
Raw data consisted of minute-by-minute activity counts recorded from the non-dominant wrist. Preprocessing proceeded as follows: 1) timestamp parsing and ordering: records were sorted by subject and time; 2) duplicate resolution: duplicate subject-minute entries were collapsed using a maximum-activity rule; 3) nonwear removal: periods of ≥90 consecutive zero-activity minutes were classified as probable non-wear and excluded; and 4) temporal continuity checks: inter-minute spacing was verified to ensure consistent resolution.
No explicit sleep–wake classification was imposed. Periods of zero recorded activity may reflect sleep, quiet wakefulness, rest, or other forms of behavioral quiescence. Rather than attempting to disambiguate these states a priori, the analysis focuses on the structure and predictability of transitions into sustained inactivity within the observed rest–activity signal.
Because circadian phase and clock time were not explicitly modeled, all estimates should be interpreted as aggregated across circadian contexts. Accordingly, the resulting transition structure reflects phase-averaged dynamics rather than phase-specific effects.
Construction of resistance and trajectory features
Instantaneous transformation
Let A(t) denote motor activity at time t. To stabilize the heavy-tailed distribution of activity counts and emphasize low-activity regimes, a monotonic transformation was applied:
This transformation compresses high values and expands resolution near zero while preserving ordinal relationships. Higher values of G(t) correspond to lower activity.
Directional derivatives and short-term memory
The first temporal difference was computed as:
Positive increments indicate decreases in activity, whereas negative increments indicate increases.
Two finite-memory operators were constructed over trailing windows (5–60 minutes; primary analyses using 20 minutes):
• Escalation memory:
• Negative drift memory:
The 20-minute window was selected as the primary timescale to capture sustained short-term behavioral evolution while remaining within the range of typical activity bout durations observed in actigraphy data. Sensitivity analyses across alternative window lengths (5-60 minutes) yielded qualitatively similar interaction structure, indicating that findings are not dependent on a specific temporal scale.
Both operators exclude the current minute, ensuring that all trajectory features reflect prior dynamics only.
Local activity level and variability
To characterize the immediate dynamical regime, rolling window statistics were computed over 20-minute windows, including rolling mean activity and rolling standard deviation of activity. These quantities capture sustained activity level and short-timescale variability. Together with directional memory terms, they define a local behavioral state in terms of level, variability, and recent trajectory.
Definition of sustained inactivity events
Transitions into sustained inactivity were defined using runlength encoding of zero-activity intervals within each subject. Two operational definitions were constructed: D5, defined as the onset of at least 5 consecutive zero-activity minutes, and D20_onset, defined as the onset of at least 20 consecutive zero-activity minutes. The primary analyses focus on D20_onset, which captures entry into sustained inactivity rather than transient pauses.
Importantly, D20_onset should be interpreted as an operational marker of transition into sustained inactivity within actigraphy data, not as a direct or validated measure of motivational disengagement. Such episodes may correspond to sleep onset, rest, sedentary wakefulness, or behavioral withdrawal. Accordingly, the analysis focuses on the structure and predictability of entry into sustained inactivity, with disengagement treated as one possible interpretation among several, rather than an exclusive label.
Outcome labels were defined prospectively: features at time t were used to predict the onset occurring at time t.
Empirical binning and transition zone analysis
To examine nonparametric structure, rolling mean activity, rolling variability, and negative drift memory were discretized into quintile bins within each diagnostic group. Transition probability (D20_onset rate) was evaluated across mean activity bins, variability bins, negative drift bins, and joint mean–variability bins. A high-risk transition region was defined as the combination of low mean activity and elevated variability. This region was used to evaluate the concentration of transition probability within the joint low-level/high-instability regime.
Multivariate interaction model
To formally evaluate joint structure, a logistic regression model was estimated at the minute level:
predictors were standardized prior to interaction construction. The model included mean×std, mean×hneg, std×hneg, and mean×std×hneg. This specification allows evaluation of higher-order interaction structure in the relationship between local state variables and transition probability.
Group-stratified robustness
The same model specification was estimated separately within each diagnostic group to assess structural stability. No hyperparameters or model structures were altered across groups.
Probability surface visualization
Predicted log-odds were projected across standardized grids of rolling mean activity and rolling variability at fixed levels of negative drift memory (–1 SD, mean, +1 SD). These surfaces illustrate how transition probability varies across local dynamical regimes.
Model stability and validation strategy
To assess structural stability and guard against overfitting, the logistic specification was estimated both in the full dataset and within diagnostic subgroups. Consistency of coefficient signs, relative magnitudes, and interaction structure across independent fits was used as a primary robustness criterion.
Sensitivity analyses across alternative temporal windows (5–60 minutes) confirmed that the interaction structure among activity level, variability, and trajectory features was preserved across timescales.
Given the large sample size (>2.5 million minute-level observations) and the study’s focus on structural inference rather than individual-level prediction, formal cross-validation was not the primary objective. However, comparisons against reduced models (excluding interaction terms) indicated improved fit when interaction structure was included.
Model fit was quantified using pseudo-R2 and likelihood ratio statistics. Convergence of results across subgroup analyses, temporal resolutions, and model specifications supports the stability of the identified interaction structure.
RESULTS
Across 2,534,645 time-indexed observations, D20_onset events were infrequent but systematically distributed across the behavioral state space. Transition probability did not vary randomly over time; instead, it exhibited structured gradients across sustained activity levels, short-timescale variability, and accumulated negative drift memory. These gradients were numerically consistent across diagnostic groups and preserved under multivariate modeling, indicating that transitions into sustained inactivity are structured within a constrained region of the observed rest–activity state space rather than arising from purely stochastic fluctuation.
Distribution of transition risk across mean activity levels
We first characterized the distribution of rolling mean activity computed over the preceding 20 time steps. As summarized in Table 1, rolling mean activity was highly skewed, with a mean of 178.45 and a standard deviation of 264.96, a median of 45.75, and values ranging from 0.00 to 6,140.95, indicating substantial heterogeneity in sustained activity levels across time despite the presence of extremely high-activity outliers.
Descriptive statistics of rolling activity metrics (20-step window)
Transition probability was strongly concentrated at the lower extreme of sustained activity. Binned analyses shown in Table 2 demonstrate a pronounced monotonic suppression gradient across all diagnostic categories. In ADHD, the lowest rolling mean bin (mean activity=2.79) exhibited a D20_onset rate of 0.00668, whereas the highest bin (mean activity=708.94) exhibited a rate of 0.00045, corresponding to an approximately 15-fold reduction across the activity spectrum.
D20 onset rate by binned rolling mean activity
Control participants exhibited a comparable but smaller gradient, with rates declining from 0.00189 to 0.00043 (4.4-fold reduction). In depression, rates decreased from 0.00395 to 0.00045 (8.8-fold reduction), and in schizophrenia from 0.00656 to 0.00051 (12.9-fold reduction). Across all groups, once rolling mean activity exceeded moderate levels, transition probability approached near-zero values.
The suppression pattern was continuous rather than threshold-based, indicating graded scaling of transition probability with sustained activity level. These gradients identify rolling mean activity as the dominant univariate structural determinant of transitions into sustained inactivity.
Negative drift memory and historical modulation
Negative drift memory, operationalized as H_neg_20, exhibited substantial dispersion across 2,536,963 observations. As shown in Table 3, the mean was 7.48 with a standard deviation of 6.44, the median was 6.60, and values ranged from 0.00 to 43.05, indicating that accumulated short-term downward shifts in activity were common rather than exceptional.
Descriptive statistics of negative drift memory (H_neg_20)
Binned analyses of transition probability by drift memory are presented in Table 4. In the control group, D20_onset rates increased from 0.00062 in the lowest drift bin to 0.00499 in the highest bin, corresponding to approximately an eightfold increase. In ADHD, rates increased from 0.00239 to 0.00414 (1.7-fold), in schizophrenia from 0.00321 to 0.00752 (2.3-fold), and in depression from 0.00074 to 0.00568 (>7-fold in intermediate bins).
D20 onset rate by binned negative drift memory (H_neg_20)
Importantly, elevated drift memory did not independently produce high transition probability in high sustained-activity regimes. In bins where rolling mean activity was high, transition probability remained low even under elevated drift. This indicates that drift memory operates as a conditional modulator within already susceptible regions of the state space rather than as an independent driver of transitions.
Short-timescale variability and the empirical high-risk region
Rolling activity variability displayed a mean of 144.01 and a standard deviation of 176.53, with a median of 77.92 and values extending to 3,403.02 (Table 1). The relationship between variability and transition probability was context-dependent. As shown in Table 5, in the control group, D20_onset rates increased from 0.00107 in the lowest variability bin to 0.00960 in a moderate variability bin, representing nearly a 9-fold increase. Similar patterns were observed in depression and schizophrenia.
D20 onset rate by binned rolling activity variability
At extreme variability levels, transition probability declined in some groups, indicating non-monotonic structure. To isolate joint vulnerability, an empirical high-risk region was defined by low rolling mean activity and elevated variability. Transition rates within this region are summarized in Table 6. In ADHD, D20_onset rates increased from 0.00342 outside the region to 0.01130 within it, representing a 3.3-fold increase. In controls, rates increased from 0.00265 to 0.01174 (4.4-fold), in depression from 0.00363 to 0.01378, and in schizophrenia from 0.00528 to 0.01787.
High-risk transition region analysis (low mean+high variability)
Across groups, amplification factors ranged between approximately 3.3 and 4.4, indicating a strong and consistent concentration of transition probability within the joint low-mean, high-variability regime. These findings demonstrate that transition probability does not increase independently along single dimensions but instead concentrates within a constrained region of state space defined by sustained low activity and instability.
Multivariate interaction structure
To formally evaluate joint structure, a logistic regression model including standardized rolling mean activity, rolling variability, negative drift memory, all two-way interactions, and a three-way interaction term was estimated. Model estimates are presented in Table 7.
Multivariate logistic dynamical basin model
Rolling mean activity exerted a large negative association with transition probability (β=-3.6963, z=-51.39). Rolling variability exhibited a positive association (β=1.3664, z=39.73). Negative drift memory exhibited a negative main effect (β=-0.5157, z=-13.69).
Two-way interactions were also significant, including mean×std (0.0685) and mean×hneg (-1.5791). Critically, the three-way interaction among mean activity, variability, and drift memory was positive and highly significant (β=0.1457, z=16.38).
These results indicate that transition probability cannot be explained by additive linear contributions alone. Instead, variability and drift effects depend on the level of sustained activity. In particular, variability exerts its strongest influence in low-activity regimes, and the effect of drift is conditional on both activity level and variability. This pattern is consistent with a structured interaction topology in which transition probability is shaped by the joint configuration of local state variables.
Robustness across diagnostic groups
To assess structural stability, the same logistic specification was fit separately within each diagnostic group. Results are summarized in Table 8.
Group-specific logistic model parameters and model fit
Across all groups, rolling mean activity retained a strongly negative coefficient, rolling variability retained a positive coefficient, and the three-way interaction remained positive. Although effect magnitudes varied moderately across groups, the direction and interaction structure were preserved.
This consistency indicates that the observed interaction structure reflects a shared pattern in rest–activity dynamics rather than a disorder-specific effect.
Predicted transition probability surface and structural geometry
Probability surfaces were generated by projecting model predictions across standardized grids of rolling mean activity and rolling variability at three fixed levels of negative drift memory, corresponding to one standard deviation below the mean (hneg=-1), the mean level (hneg=0), and one standard deviation above the mean (hneg=+1). The resulting log-odds surfaces are shown in Figures 1-3.
Predicted transition probability surface at low negative drift memory (hneg=-1). Predicted log-odds of D20 onset as a function of standardized rolling mean activity and rolling variability with negative drift memory fixed at one standard deviation below the mean. Risk increases sharply as sustained activity decreases, with variability amplifying risk primarily in low-mean regimes.
Predicted transition probability surface at average negative drift memory (hneg=0). Predicted log-odds of D20 onset across standardized rolling mean activity and variability at mean drift level. The surface exhibits a curved basin geometry, with minimal risk at moderate-to-high mean activity and amplification under low-mean, higher-variability conditions.
Predicted transition probability surface at elevated negative drift memory (hneg=+1). Predicted log-odds of D20 onset with negative drift memory fixed at one standard deviation above the mean. Elevated drift shifts the surface upward, expanding the highrisk region while preserving interaction topology between sustained activity and variability.
Across all drift conditions, the dominant structural gradient runs along the sustained activity axis. At moderate to high rolling mean activity (mean_z > 0), predicted log-odds of D20_onset remain strongly negative across the full variability range, indicating near-zero transition probability. As mean activity decreases, predicted risk increases sharply.
Variability exerts a conditional amplification effect. In regions of low sustained activity (mean_z < 0), increasing variability shifts predicted log-odds upward, steepening the risk gradient. In contrast, when mean activity is high, variability has minimal impact on predicted risk.
Negative drift memory modulates the vertical position of the surface without altering its topology. Increasing drift shifts the entire surface upward in log-odds space, expanding the region of elevated transition probability while preserving curvature and interaction structure.
The resulting geometry indicates that transitions into sustained inactivity are concentrated within a low-activity, high-instability region of the state space. Entry into this region is associated with a sharp increase in transition probability, while trajectory-dependent features modulate the extent and position of this region. This pattern is consistent with a structured region of the state space of transition probability, without requiring interpretation in terms of a specific underlying mechanism.
DISCUSSION
The present study examined whether transitions into sustained inactivity in naturalistic settings reflect a purely instantaneous process or whether they are structured by short-term behavioral history. Across more than 2.5 million minute-level observations, D20_onset events were not randomly distributed in time. Instead, transition probability exhibited a stable and reproducible structure within a three-dimensional behavioral state space defined by sustained activity level, short-timescale variability, and accumulated negative drift.
The dominant structural determinant of transition probability was sustained activity level. Across all diagnostic groups, rolling mean activity exerted a large suppressive effect, with D20_onset probability declining by approximately 4–15-fold across the activity spectrum. Once sustained activity exceeded moderate levels, transition probability approached near-zero values regardless of variability or drift. This pattern indicates that entry into sustained inactivity occurs primarily within low-activity regimes rather than emerging from isolated short-term fluctuations.
However, low sustained activity alone was not sufficient to account for the observed structure. Variability exerted a conditional amplification effect. Within low-mean regimes, increasing short-timescale instability steepened the transition gradient, concentrating probability within a restricted region of the state space. Outside these regimes, variability had minimal influence. This pattern was observed both in nonparametric analyses and in the interaction structure of the multivariate model, indicating that variability contributes to transition probability in a context-dependent manner rather than as an independent driver.
Negative drift memory further modulated this structure. Rather than acting as a uniform destabilizing factor, drift shifted the transition surface upward, expanding the region in which transitions become more likely while preserving the overall interaction geometry. The significant three-way interaction among sustained activity, variability, and drift indicates that the recent trajectory alters the boundary conditions under which transitions occur. In practical terms, short-term history does not uniformly increase transition probability; instead, it reshapes the regions of the state space in which transitions are more likely.
Taken together, these findings support a structured state-space interpretation in which transition probability is concentrated within a low-activity, high-instability region, with trajectory-dependent modulation of its extent. This organization is consistent with a basin-like structure in the probability surface, in the sense that transitions are more likely within a bounded region defined by joint conditions on activity level, variability, and recent history. Importantly, this interpretation is descriptive of the observed interaction topology and does not require the existence of a literal dynamical basin or a specific underlying mechanism.
From a chronobiological perspective, these results are consistent with the view that rest–activity behavior is embedded within circadian and sleep–wake regulatory systems. Transitions into sustained inactivity may therefore reflect a mixture of processes, including behavioral disengagement, rest behavior, circadian phase-dependent quiescence, and sleep onset. Because the present analysis does not explicitly model clock time or circadian phase, the estimated transition structure should be interpreted as aggregated across these contexts. The observed history sensitivity may thus reflect an interaction between local behavioral trajectory and broader chronobiological regulation, including phase-dependent variation in inactivity propensity and inertia in rest–activity transitions [24,25].
This interpretation aligns with broader theoretical frameworks that emphasize temporal embedding in behavioral regulation. Models of effort and control allocation suggest that prior activity influences subsequent decision thresholds and behavioral persistence [12,16-18]. Similarly, chronobiological systems exhibit asymmetries between activation and deactivation phases, as well as inertia effects that depend on prior states [24,25]. The present findings extend these principles to continuous actigraphic data, showing that even minute-level activity transitions are structured by recent trajectory within a broader state-space configuration.
Importantly, the analysis does not require a specific biological or psychological interpretation of resistance. In the present study, resistance refers only to an operational, analytically derived feature family constructed from activity trajectories. It is not treated as a directly observed latent variable or a validated internal mechanism. The resistance-based formulation provides a compact way to encode trajectory-dependent constraints within observable behavior, but the empirical results can equivalently be interpreted in terms of local state variables and short-term changes in activity. The observed interaction structure, therefore, reflects properties of the data representation rather than evidence for a specific underlying construct.
Structural stability across diagnostic groups further supports this interpretation. Although effect magnitudes varied moderately, the direction of effects and the interaction topology were preserved across ADHD, depression, schizophrenia, and control participants. This consistency indicates that the identified transition structure reflects a general property of rest–activity dynamics rather than a pattern specific to any single diagnostic category. Differences in magnitude, such as the stronger interaction effects observed in schizophrenia, may reflect variation in system sensitivity rather than qualitatively different underlying processes.
Limitations
Several limitations should be considered. First, D20_onset operationalizes the onset of sustained inactivity rather than a direct measure of motivational disengagement. Periods of inactivity may reflect sleep, rest, or other quiescent states, and the present analysis does not disambiguate among these possibilities. Accordingly, the findings should be interpreted as describing the structure of transitions into sustained inactivity, with behavioral disengagement representing one possible interpretation rather than an exclusive definition. Second, circadian phase and time-of-day effects were not explicitly modeled, and phase-dependent modulation may contribute to the observed patterns. Third, analyses were conducted on a single publicly available dataset; replication in independent cohorts and extension to other behavioral modalities will be necessary to establish generality. Finally, while the feature construction used here is deliberately minimal, alternative representations of trajectory history may capture additional structure.
Despite these limitations, the results provide evidence that transitions into sustained inactivity exhibit structured, history-sensitive organization within rest–activity data. Transition probability is not uniformly distributed across behavioral states but concentrates within a constrained region defined by low sustained activity and elevated instability, with recent trajectory modulating the extent of this region. Models that treat inactivity onset as a memoryless threshold on instantaneous activity, therefore, omit important structural features of behavioral dynamics.
Rather than establishing a specific mechanistic account, the present study demonstrates the importance of temporally embedded modeling for understanding rest–activity transitions. By representing sustained activity, variability, and short-term trajectory within a unified state-space framework, the analysis identifies a structured interaction topology governing transitions into sustained inactivity. This framework provides a basis for future work examining how behavioral, circadian, and physiological factors jointly shape rest–activity regulation in naturalistic settings.
Conclusion
This study examined whether transitions into sustained inactivity in naturalistic settings can be characterized as a purely instantaneous process or whether they reflect short-term history dependence. Using continuous actigraphy data, we show that D20_onset events, defined as the onset of sustained inactivity, are not randomly distributed in time but tend to occur more frequently within a region of the behavioral state space characterized by low sustained activity, elevated short-timescale variability, and accumulated directional drift.
Sustained activity level emerged as the dominant structural determinant of transition probability, exerting strong suppressive effects across diagnostic groups. However, variability and negative drift memory conditionally reshaped the boundary of elevated transition probability, expanding risk within low-activity regimes. The resulting probability surfaces exhibited a structured geometry consistent with a structured region of the state space of transition probability, in which entry into sustained inactivity depends on the joint configuration of local state variables and recent trajectory.
These findings indicate that transitions into sustained inactivity within rest–activity data are temporally embedded and structured by short-term behavioral history rather than governed solely by instantaneous activity levels. Because actigraphy reflects behavior embedded within circadian rest–activity organization, such transitions likely represent a mixture of behavioral disengagement, rest, and phase-dependent quiescent states rather than a single, uniquely identifiable process.
The resistance-based operationalization used in this study provides a compact feature representation of trajectory-dependent structure within observable behavior. In this context, resistance refers only to an analytically derived description of local state and recent activity changes, not to a directly observed biological or psychological mechanism. The empirical findings can therefore be interpreted more generally as evidence for history-sensitive transition structure in rest–activity dynamics.
Taken together, the results support the use of temporally informed, state-space approaches for modeling transitions into sustained inactivity. Models that treat such transitions as memoryless thresholds on instantaneous activity overlook key structural features arising from short-term trajectory and local instability. Future work incorporating explicit circadian phase, time-of-day structure, and independent datasets will be necessary to further clarify how behavioral, physiological, and chronobiological factors jointly shape these transitions.
Notes
The author has no potential conflicts of interest to disclose.
Availability of Data and Material
The data analyzed in this study were obtained from the publicly available OBF-Psychiatric dataset [9,27], which includes continuous wrist-worn actigraphy recordings from individuals diagnosed with major depressive disorder, schizophrenia, attentiondeficit/hyperactivity disorder, and matched healthy controls. The dataset is openly accessible via Zenodo at https://doi.org/10.5281/zenodo.13754984. All analysis code and preprocessing scripts are available via the Open Science Framework (OSF) repository associated with this manuscript (https://doi.org/10.17605/OSF.IO/6MVBX).
Funding Statement
None
Acknowledgments
This study is a secondary analysis of publicly available, fully deidentified data and did not require additional institutional ethical approval. The original OBF-Psychiatric dataset was collected in accordance with the Declaration of Helsinki and approved by the Norwegian Regional Medical Research Ethics Committee West (approval numbers: 150.01 and 251.08), with written informed consent obtained from all participants, as reported in the original dataset publication [9].