The postulates of gravitational thermodynamics

TL;DR

This paper develops a thermodynamic formalism for strongly self-gravitating systems, generalizing classical thermodynamics to account for gravitational effects, non-additivity, and inhomogeneous equilibrium states.

Contribution

It introduces a set of postulates for gravitational thermodynamics that resolve fundamental issues like non-additivity and inhomogeneity, extending classical thermodynamic principles.

Findings

Formal resolution of gravitational thermodynamics problem

Inhomogeneous equilibrium states identified

Reformulation of Euler equation and absence of Gibbs-Duhem relation

Abstract

The general principles and logical structure of a thermodynamic formalism that incorporates strongly self-gravitating systems are presented. This framework generalizes and simplifies the formulation of thermodynamics developed by Callen. The definition of extensive variables, the homogeneity properties of intensive parameters, and the fundamental problem of gravitational thermodynamics are discussed in detail. In particular, extensive parameters include quasilocal quantities and are naturally incorporated into a set of basic general postulates for thermodynamics. These include additivity of entropies (Massieu functions) and the generalized second law. Fundamental equations are no longer homogeneous first-order functions of their extensive variables. It is shown that the postulates lead to a formal resolution of the fundamental problem despite non-additivity of extensive parameters and thermodynamic potentials. Therefore, all the results of (gravitational) thermodynamics are an outgrowth of these postulates. The origin and nature of the differences with ordinary thermodynamics are analyzed. Consequences of the formalism include the (spatially) inhomogeneous character of thermodynamic equilibrium states, a reformulation of the Euler equation, and the absence of a Gibbs-Duhem relation.