Metabolic–Attentional Dynamics as a Minimal Generative Mechanism for Subjective Time

Background: Subjective time is commonly modeled as the output of an internal clock or accumulator. However, empirical phenomena such as Weber-like timing, affect-dependent distortions (e.g., depression, flow, crisis), and the dissolution of time during attentional shifts suggest that temporal experience may not arise from a dedicated pacemaker, but from intrinsic neural dynamics governing internal state updates.Objectives: We propose a minimal stochastic dynamical framework in which subjective time emerges from the interaction between metabolic throughput and self-referential attention. The goal is to unify classical psychophysical regularities and affect-dependent temporal distortions within a single, clock-free generative mechanism.Methods: We formulate a low-dimensional stochastic differential equation describing metabolic throughput M(t)M(t), self-referential attention Aself(t)A self (t), and an arousal-dependent sampling resolution R(M)R(M). These variables jointly determine a bounded internal self-update velocity v(t)v(t), which is nonlinearly transformed into an instantaneous subjective-time rate dτself/dt=f(v)dτ self /dt=f(v). Model behavior was analyzed through phase-space geometry, interval-timing simulations, robustness tests across alternative nonlinearities and saturation functions, and noise generalization. Parameters were constrained by biological plausibility; no behavioral data were fitted.Results: Subjective time emerges as a structural property of metabolic–attentional coupling. Interval-timing simulations exhibited Weber-like scaling (log–log slope ≈ 0.9) and approximately constant coefficients of variation when slow across-trial gain variability was present, consistent with requirements for scalar timing under continuous-time integration. Distinct affective regimes (depression-like, normal, flow-like, and crisis-like) occupied separable regions of the (M,Aself)(M,A self ) state space and showed characteristic distributional signatures in vv and dτself/dtdτ self /dt. Crisis-like regimes produced sustained temporal dilation, depression-like regimes produced compression, and flow-like regimes showed elevated but stable accumulation. These qualitative patterns were robust across broad families of nonlinear mappings and noise models.Conclusions: A minimal metabolic–attentional stochastic dynamical system is sufficient to generate subjective time and its distortions without invoking an internal clock. The results suggest that subjective time reflects the rate of self-update in a metabolically constrained attentional system. This framework provides a structurally grounded basis for integrating psychophysics, computational neuroscience, and affective phenomenology, and offers testable predictions for future empirical and clinical work.