The Photonic Foundation of Temperature: Mechanisms of Thermal Equilibrium and Entropy Production

TL;DR

The paper argues that photons establish and maintain the energy scale $E_c = k_B T$ in ordinary matter, providing the microscopic mechanism behind temperature and thermal equilibrium. It derives the Boltzmann distribution from a minimal differential scaling premise and shows continuous photon exchange is required to counter radiative losses, with the average photon energy $igl⟨hν⟩ igr) ≈ 2.701 E_c$. Entropy production arises from inelastic photon scattering that cascades high-energy quanta into many lower-energy ones, increasing microstate count and driving irreversibility. The work distinguishes genuine thermal equilibrium from formal temperature assignments and emphasizes a hierarchical structure of photon baths, where infinite reservoirs are idealizations and temperature emerges from sustained energy exchange across scales.

Abstract

I examine the physical foundations of temperature and thermal equilibrium by identifying photons as the fundamental agents that establish and maintain the characteristic energy scale $E_c = k_B T$ in ordinary matter. While classical thermodynamics successfully describes equilibrium phenomenologically, the realization of thermal distributions requires concrete microscopic mechanisms provided by quantum electrodynamics. We derive the Boltzmann distribution from a minimal differential scaling postulate and show that sustaining thermal equilibrium demands continuous photon exchange with average energy $\langle hν\rangle = 2.701\,E_c$, quantifying the energetic throughput necessary to counter radiative losses. Entropy production is shown to arise naturally from inelastic photon scattering that converts high-energy photons into many lower-energy quanta, thereby increasing accessible microstates and driving irreversible evolution toward equilibrium. We establish physical criteria distinguishing genuine thermal equilibrium from purely formal temperature assignments and demonstrate that the classical notion of an infinite thermal reservoir emerges as an effective idealization within a hierarchy of dynamically maintained photon baths. This photonic framework complements phenomenological thermodynamics by providing its microscopic foundation and clarifies the physical meaning of temperature as an emergent collective property of photon-mediated energy exchange.