Maxwell relation between entropy and atom-atom pair correlation

TL;DR

This paper derives a Maxwell relation linking entropy and atom-atom pair correlation in 1D Bose gases, enabling entropy estimation from measurable correlations using computational and potential experimental methods.

Contribution

It introduces a thermodynamic Maxwell relation between entropy and pair correlation in 1D Bose gases and demonstrates its application using the SPGPE formalism.

Findings

Derived a Maxwell relation between entropy and pair correlation.

Showed how to compute entropy from pair correlations numerically.

Proposed a method for experimental entropy measurement via atom-atom correlations.

Abstract

For many-particle systems with short-range interactions the local (same point) particle-particle pair correlation function represents a thermodynamic quantity that can be calculated using the Hellmann-Feynman theorem. Here we exploit this property to derive a thermodynamic Maxwell relation between the local pair correlation and the entropy of an ultracold Bose gas in one dimension (1D). To demonstrate the utility of this Maxwell relation, we apply it to the computational formalism of the stochastic projected Gross-Pitaevskii equation (SPGPE) to determine the entropy of a finite-temperature 1D Bose gas from its atom-atom pair correlation function. Such a correlation function is easy to compute numerically within the SPGPE and other formalisms, which is unlike computing the entropy itself. Our calculations can be viewed as a numerical experiment that serves as a proof-of-principle demonstration of an experimental method to deduce the entropy of a quantum gas from the measured atom-atom correlations.