Detecting temperature fluctuations at equilibrium

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.

References in corpus (8)

• Interpretation of the nonextensitivity parameter $q$ in some applications of Tsallis statistics and Lévy distributions
• Stochastic thermodynamics: Principles and perspectives
• Inconsistent thermostatistics and negative absolute temperatures
• Generalized entropies and the transformation group of superstatistics
• Maximum Entropy and Bayesian Data Analysis: Entropic Priors
• Beyond Boltzmann-Gibbs statistics: Maximum entropy hyperensembles out-of-equilibrium
• A maximum entropy framework for non-exponential distributions
• Quantifying extrinsic noise in gene expression using the maximum entropy framework