Entropy Production and the Operational Realization of Time in Physical Clocks

This preprint proposes a thermodynamic framework for understanding how physical clocks realize elapsed duration through irreversible entropy-producing processes. While general relativity defines proper time geometrically along a worldline, any real clock that measures duration must instantiate that parameter through physical transitions, stabilization, readout, and memory. The manuscript therefore examines entropy production as an operational substrate of time measurement in real systems. The central proposal is expressed through the functional: τirr=1κ∫S˙prod (t) dt, ₈ₑₑ=1 Ṡ₏ₑ₎₃ (t) \, dt, τirr=κ1∫S˙prod (t) dt, where S˙prodṠ₏ₑ₎₃S˙prod is the entropy production rate and κκ is a system-dependent calibration constant. The framework emphasizes that this relation does not replace geometric proper time; rather, it describes how physical systems may operationally accumulate duration through irreversible change. The article discusses the structural requirements for a physical time parameter, including additivity, monotonicity, and robustness, and applies the framework to physical clocks, chemical oscillators, biological timing systems, and entropy-producing metabolic processes. A qualitative boundary case involving constrained phase-space accessibility in degenerate matter is also considered. A biological extension is outlined through the hypothesis that metabolic turnover may influence biological timing by changing the density of irreversible biochemical transitions. The manuscript proposes NADH/NAD⁺ redox dynamics, including Peredox-type biosensors, as possible experimental proxies for entropy-production-related metabolic turnover. This biological direction is presented as a testable extension rather than as a completed theory of subjective time perception. The work is conceptual and exploratory. Its purpose is to establish a physically grounded correspondence between irreversible entropy production and operational time accumulation, while identifying experimental routes by which the framework may be refined or falsified.