τ-Thermodynamics: A Retrospective Theoretical Framework for Reconstructing Thermal Physics Through Internal Temporal Dynamics

This deposit contains the full manuscript “τ-Thermodynamics: A Retrospective Theoretical Framework for Reconstructing Thermal Physics Through Internal Temporal Dynamics.” The work proposes a foundational reconstruction of thermodynamics based on internal time (τ) rather than external clock time (t). Classical thermodynamics assumes that all systems evolve on the same external time axis; this paper shows that real physical, chemical, biological, and technological systems instead generate their own intrinsic temporal progression, and that thermodynamic laws take their natural form only when written on τ. Using a systematic retrospective analysis of seven decades of published experimental data—including microbial growth, ester hydrolysis, polymer creep, seed germination, Drosophila lifespan, and Li-ion battery discharge—the study demonstrates that trajectories which appear disparate on t collapse onto single master curves on τ, with a mean collapse factor C̄ = 0.926 ± 0.058. This provides quantitative evidence that τ, not t, is the natural temporal variable for thermodynamic processes. On this basis, the paper reformulates the Zeroth, First, Second, and Third Laws of thermodynamics on τ, restores strictly monotonic entropy production, gives Gibbs and Helmholtz free energies true potential behavior, and reveals systematic mis-accounting of energy in rate-varying systems under conventional t-based analysis. The framework points to new design principles for high-efficiency energy systems, τ-optimized batteries, and a deeper connection between thermodynamics, biology, and Union Dipole Theory’s internal-time physics.