How does pressure fluctuate in equilibrium?

TL;DR

This paper investigates pressure fluctuations in classical particle systems at equilibrium, revealing differences between mechanical and thermodynamic pressure variances and proposing a way to experimentally detect these differences.

Contribution

It demonstrates that mechanical pressure variance exceeds thermodynamic pressure variance in equilibrium and provides conditions for experimental detection.

Findings

Mechanical pressure variance is generally larger than thermodynamic pressure variance.

Both pressure definitions converge to the same mean value in the thermodynamic limit.

A condition is proposed for experimentally distinguishing the two pressure measurements.

Abstract

We study fluctuations of pressure in equilibrium for classical particle systems. In equilibrium statistical mechanics, pressure for a microscopic state is defined by the derivative of a thermodynamic function or, more mechanically, through the momentum current. We show that although the two expectation values converge to the same equilibrium value in the thermodynamic limit, the variance of the mechanical pressure is in general greater than that of the pressure defined through the thermodynamic relation. We also present a condition for experimentally detecting the difference between them in an idealized measurement of momentum transfer.