On the foundations of thermodynamics

TL;DR

This paper presents a concise, self-contained foundation for thermodynamics, deriving its core laws and relations from basic assumptions applicable across different equilibrium types, without relying on subjective or microscopic assumptions.

Contribution

It offers a new, minimalistic approach to thermodynamics foundations that is accessible and applicable to classical and quantum systems without statistical or mechanical assumptions.

Findings

Derivation of the four laws of thermodynamics from basic principles

Unified treatment of thermodynamic relations across equilibrium types

Framework applicable to classical and quantum statistical mechanics

Abstract

On the basis of new, concise foundations, this paper establishes the four laws of thermodynamics, the Maxwell relations, and the stability requirements for response functions, in a form applicable to global (homogeneous), local (hydrodynamic) and microlocal (kinetic) equilibrium. The present, self-contained treatment needs very little formal machinery and stays very close to the formulas as they are applied by the practicing physicist, chemist, or engineer. From a few basic assumptions, the full structure of phenomenological thermodynamics and of classical and quantum statistical mechanics is recovered. Care has been taken to keep the foundations free of subjective aspects (which traditionally creep in through information or probability). One might describe the paper as a uniform treatment of the nondynamical part of classical and quantum statistical mechanics ``without statistics'' (i.e., suitable for the definite descriptions of single objects) and ``without mechanics'' (i.e., independent of microscopic assumptions). When enriched by the traditional examples and applications, this paper may serve as the basis for a course on thermal physics.