How Energy, Entropy, and Coherence Sustain the Flow of Life

Time perception, attention, and fatigue are usually studied separately. This paper proposes a unified flow model: life is a system that must continuously sustain flows of energy and information. The system state is described by energy E, entropy S, and coherence C, and the state space is their Cartesian product V = E × S × C. Coherence is the order parameter, defined as the degree of connection between the internal space (physiological state, sensory weighting) and the external space (information supplied by the environment), measured by their mutual information. Together with energy and entropy, it determines whether the flow is in a solid (frozen), liquid (flowing), or gaseous (dispersed) state. The model defines prediction error as the mismatch between internal and external information rates, treats alertness as the concentration of attention, and uses thermodynamics and statistical mechanics to describe energy budgets, entropy production, and recovery. Gibbs free energy sets the upper bound on available work, and coherence determines the fraction actually converted into effective flow: W = C·(−ΔG). The supplementary material gives a formal derivation embedding this state space in relativistic thermodynamics. The model accounts for several phenomena at once: both boredom and overload lengthen subjective time; automatization drives prediction error toward zero with minimal dissipation; time dilation in crowds decays only to a nonzero floor; load does not fall on its own after leaving a stressor and can be cleared only through recovery; and once synchrony is lost, re-establishing it requires a larger intervention than maintaining it. The paper offers falsifiable predictions, including a numerical prediction written down in advance and an experimental design that uses reward to break a circular definition. The model's most critical untested parameter is the constant converting prediction error into energy.