Relativisticlike structure of classical thermodynamics

TL;DR

This paper explores a geometric framework for classical thermodynamics using concepts inspired by relativity, introducing thermodynamic geodesics and adiabatic cones to analyze equilibrium states and quasi-static processes.

Contribution

It develops a Legendre invariant geometric structure for thermodynamics, revealing a causal-like structure in the equilibrium space similar to relativity.

Findings

Thermodynamic geodesics split the equilibrium space into two regions.

Adiabatic geodesics form boundaries analogous to causal horizons.

The structure suggests a deep link between thermodynamics and relativistic physics.

Abstract

We analyze in the context of geometrothermodynamics a Legendre invariant metric structure in the equilibrium space of an ideal gas. We introduce the concept of thermodynamic geodesic as a succession of points, each corresponding to a state of equilibrium, so that the resulting curve represents a quasi-static process. A rigorous geometric structure is derived in which the thermodynamic geodesics at a given point split the equilibrium space into two disconnected regions separated by adiabatic geodesics. This resembles the causal structure of special relativity, which we use to introduce the concept of adiabatic cone for thermodynamic systems. This result might be interpreted as an alternative indication of the inter-relationship between relativistic physics and classical thermodynamics.