Thermodynamic constraints on fluctuation phenomena

TL;DR

This paper shows that thermal fluctuation phenomena can be integrated into classical thermodynamics, extending its validity and constraining fluctuation spectra without relying on specific microscopic models.

Contribution

It demonstrates how fluctuation phenomena can be incorporated into thermodynamics, leading to constraints on fluctuation spectra and deriving known distributions like Gibbs and Tsallis.

Findings

Fluctuation phenomena extend the validity of the second law.

Constraints on thermal fluctuation spectra are derived.

Gibbs and Tsallis distributions naturally emerge from the framework.

Abstract

The relationships between reversible Carnot cycles, the absence of perpetual motion machines and the existence of a non-decreasing, globally unique entropy function forms the starting point of many textbook presentations of the foundations of thermodynamics. However, the thermal fluctuation phenomena associated with statistical mechanics has been argued to restrict the domain of validity of this basis of the second law of thermodynamics. Here we demonstrate that fluctuation phenomena can be incorporated into the traditional presentation, extending, rather than restricting, the domain of validity of the phenomenologically motivated second law. Consistency conditions lead to constraints upon the possible spectrum of thermal fluctuations. In a special case this uniquely selects the Gibbs canonical distribution and more generally incorporates the Tsallis distributions. No particular model of microscopic dynamics need be assumed.