τ-Thermodynamics & τ-Kinetics: Reparameterized Thermodynamic and Kinetic Laws with an Internal Clock-Rate Field χ = dt/dτ

Classical thermodynamics and chemical kinetics parameterize energy flow, entropy production, and reaction rates by external laboratory time t. Yet diverse systems—from biochemical pathways to solid-state transformations—exhibit persistent heterogeneity in measured timescales even under nominally identical external conditions. Reaction rates vary by orders of magnitude despite fixed temperature and concentration; aging materials show nonlinear fatigue accumulation; biological metabolic clocks diverge from chronological time; and the second law’s irreversibility arrow appears contingent on the choice of time coordinate. This paper reparameterizes thermodynamic and kinetic laws using an internal time coordinate τ and introduces a measurable clock-rate field χ(τ)=dt/dτ (with generalization to spatial dependence χ(x,τ)). We derive: (1) τ-form first and second laws with explicit clock-rate dependence; (2) τ-reparameterized entropy production as the fundamental measure of irreversibility; (3) τ-Arrhenius equation with activation ‘energy’ reinterpreted as temporal threshold; (4) Master equations and Markov processes in τ-space; (5) Fluctuation theorems (Jarzynski, Crooks) in reparameterization-invariant form; (6) Falsifiable tests using published calorimetry, reaction kinetics, and materials aging datasets. Central operational claim: When experimental heterogeneity arises primarily from condition-dependent clock-rate fields χ(τ) rather than distinct physical mechanisms, external time t becomes a shadow coordinate of thermodynamic progress while τ provides a universal parameterization that collapses disparate observations onto single master curves. Key results: (i) τ-entropy collapse with variance reduction ΔC/Ct≈85–98%; (ii) Arrhenius universality; (iii) Aging master curves. Validation is specified at three levels … with reproducible Python code (Appendix B).