Inequalities for non-equilibrium fluctuations of work

TL;DR

This paper derives five new inequalities linking equilibrium free energy differences with non-equilibrium work fluctuations, enhancing understanding of free-energy estimators from experimental data across various scientific fields.

Contribution

It introduces five novel inequalities based on the Jarzynski equality and Weyl's scheme, providing a new theoretical framework for analyzing non-equilibrium fluctuations.

Findings

Derived five new inequalities relating free energy and work fluctuations.

Presented a general method for deriving similar inequalities.

Potentially improves analysis of experimental free-energy data.

Abstract

Five previously unknown inequalities relating equilibrium free energy differences and non-equilibrium work fluctuations are derived, and lucid path to derivation of many similar inequalities is presented. These results are based upon combined exploitation of the Jarzynski equality and the generalization of the scheme for producing uncertainty-type inequalities due to H. Weyl. The inequalities may possibly lead to better understanding of behavior of the equilibrium free-energy estimators from non-equilibrium experimental data in many important applications concerning biological, chemical, and physical molecular processes.