Thermodynamic parameters of fluids on conformally connected spacetimes

TL;DR

This paper explores how thermodynamic variables of a fluid relate between conformally connected spacetimes under thermal equilibrium, revealing consistent scaling relations and geometric structures that generalize previous results.

Contribution

It derives general relations between thermodynamic variables on conformally connected spacetimes, extending previous analyses and preserving geometrothermodynamics structures.

Findings

Scaling relations are consistent with Dicke's heuristic argument.

Satisfaction of Klein's law on one spacetime implies its validity on the other.

Thermodynamic geometric structures are conformally related on the two spacetimes.

Abstract

Local thermal equilibrium generally implies the absence of heat flux within a fluid. We find the relations between a set of thermodynamic variables of a fluid on a general spacetime and those defined on a conformally connected spacetime, assuming both descriptions are at thermal equilibrium. The scaling relations appear to be consistent with Dicke's heuristic argument and the previous analysis done on the basis of various restrictions. Within the present framework, it is observed that the satisfaction of Klein's law on one of the spacetimes implies its validity on the other one. Moreover, our analysis bypasses some of the imposed restrictions and thereby reveals the generality of the earlier predictions. These relations are further shown to preserve the geometric structure of thermodynamics, known as geometrothermodynamics, such that the associated metrics on two conformally connected spacetimes are themselves conformally related. This provides an alternative consistency check as well as a distinct geometric interpretation of the relations.