Isometries and embedding of the thermodynamic phase space of an ideal gas

TL;DR

This paper investigates the symmetries of the thermodynamic phase space of an ideal gas, identifying its isometry group as Euclidean and providing an explicit embedding into Euclidean space.

Contribution

It characterizes the isometry group of the thermodynamic phase space of an ideal gas and constructs its embedding into Euclidean space.

Findings

Isometry group is homomorphic to Euclidean group E(2)

Explicit embedding of phase space submanifolds into R^3

Identification of Killing vector fields in the thermodynamic manifold

Abstract

In this work we find the Killing vector fields of the riemannian submanifolds of the thermodynamic phase space of an ideal gas and show that the isometry group corresponding to them is homomorphic to the euclidean group $E(2)$. We also give the embedding of these submanifolds in the euclidean space $(R^{3},\ delta)$.