The Zeroth Law and the Heat Chain: From Structural Equilibrium to Threshold Emission
Year: 2025
Type: preprint
Abstract: This theoretical work derives the thermodynamics implied by the cymalogical framework (DOI:10.5281/zenodo.21828306), in which the observable content of a physical system is the projection into our spacetime sheet of discrete causal impulses (khrons) issuing from an external causal space, the sheets forming nested layers of a spiral along which proper time thins by the geometric coupling β. No statistical primitive is assumed at any point: temperature and heat are obtained from structure alone.The paper joins two results previously derived apart into a single chain: Zeroth law: mutual equilibrium is shown to be an equivalence relation whose criterion is commensurate frequencies with locked phase, temperature being the label of its classes. Transitivity follows from the closure of ℚ under multiplication; phase opposition alone fails it twice over. This supplies the physical content that the axiomatic tradition (Carathéodory; Lieb–Yngvason) leaves open. Threshold law: heat is emitted when a configuration driven above a structural threshold sheds its surplus as a photon, by phase opposition between layers of different time density. The chain: dissonance raises an electron's internal frequency — by mechanical friction or radiative absorption — and threshold emission is the exit, giving heat as the inexact path functional δQ = Σ(ν − ν₀). The threshold ν₀ is an interface quantity of order unity, not the negligible absolute value of β. The account is falsifiable at a named point: a temperature-independent infrared floor, retaining residual harmonic structure at sufficiently clean interfaces where a Planck fit predicts a featureless tail.This paper is the thermodynamic foundation of a corpus developed independently (ORCID:0009-0005-9510-5335), and the companion to which the applied papers of that corpus refer. ------- Keywords: Cymalogy • Structural Thermodynamics • Zeroth Law • Zeroth Law of Thermodynamics • Temperature • Equivalence Relation • Commensurability • Threshold Emission • Infrared Floor • Blackbody Radiation • Khron • Causal Geometry • Non-Statistical Thermodynamics • Theoretical Physics • Foundations of Physics • Open Science •
Author: Régent, Xavier J.
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7079016433
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