Thermodynamic length, geometric efficiency and Legendre invariance

TL;DR

This paper explores thermodynamic length as a measure of dissipation in thermodynamic systems, comparing ideal and real gases within geometric frameworks, and introduces a geometric efficiency concept to distinguish ideal from non-ideal behaviors.

Contribution

It introduces a novel geometric efficiency measure based on thermodynamic length, applicable to both Ruppeiner and geometrothermodynamic formalisms, to quantify deviations from ideality.

Findings

Geometric efficiency is higher for geometrothermodynamic fluids.

The efficiency measure can distinguish ideal from non-ideal gases.

The approach provides a geometric perspective on thermodynamic behavior.

Abstract

Thermodynamic length is a metric distance between equilibrium thermodynamic states that asymptotically bounds the dissipation induced by a finite time transformation of a thermodynamic system. By means of thermodynamic length, we first evaluate the departures from ideal to real gases in geometric thermodynamics with and without Legendre invariance. In particular, we investigate ideal and real gases in the Ruppeiner and geometrothermodynamic formalisms. Afterwards, we formulate a strategy to relate thermodynamic lengths to efficiency of thermodynamic systems in both the aforementioned frameworks in the working assumption of small deviations from ideality. In this respect, we propose a geometric efficiency definition built up in analogy to quantum thermodynamic systems. We show the result that this efficiency is higher for geometrothermodynamic fluids. Moreover, we stress this efficiency could be used as a novel geometric way to distinguish ideal from non-ideal thermal behaviors. In such a way, it could be useful to quantify deviations from ideality for a variety of real gases. Finally, we discuss the corresponding applications of our recipe to classical thermodynamic systems, noticing that our findings could help geometrically grasping the nature of different metrizations on manifolds of equilibrium thermal states.