Detecting temperature fluctuations at equilibrium

TL;DR

This paper proposes a new framework for understanding temperature fluctuations in small systems at equilibrium, revealing their effects on system properties and extending statistical mechanics beyond the macroscopic limit.

Contribution

It introduces a stochastic temperature model for small systems, providing a generalized statistical mechanics framework applicable to biophysics and nanotechnology.

Findings

Temperature fluctuations can be detected in equilibrium properties.

The model accurately describes dynamics of small systems.

Generalizes statistical mechanics to finite-sized systems.

Abstract

Gibbs and Boltzmann definitions of temperature agree only in the macroscopic limit. The ambiguity in identifying the equilibrium temperature of a finite sized `small' system exchanging energy with a bath is usually understood as a limitation of conventional statistical mechanics. We interpret this ambiguity as resulting from a stochastically fluctuating temperature coupled with the phase space variables giving rise to a broad temperature distribution. With this ansatz, we develop the equilibrium statistics and dynamics of small systems. Numerical evidence using an analytically tractable model shows that the effects of temperature fluctuations can be detected in equilibrium and dynamical properties of the phase space of the small system. Our theory generalizes statistical mechanics to small systems relevant to biophysics and nanotechnology.