Variation on the theme of Jarzynski's inequality

TL;DR

This paper explores extensions of Jarzynski's inequality beyond its original derivation, applying to quantum field systems and non-linear thermodynamics, and discusses its connections to other thermodynamic principles.

Contribution

It introduces new extensions of Jarzynski's inequality applicable to quantum many-body systems and non-linear regimes, expanding its theoretical scope.

Findings

Extended Jarzynski's inequality to quantum field systems

Analyzed relations with maximum work theorem and fluctuation theory

Applied functional-integral techniques to many-body systems

Abstract

The Jarzynski equality, which relates equilibrium free-energy difference to an average of non-equilibrium work, plays a central role in modern non-equilibrium statistical thermodynamics. In this paper, we study a weaker consequence of this relation, known as Jarzynski's inequality, which can be formally obtained from the Jarzynski equality via Jensen's inequality. We identify and analyze several extensions of Jarzynski's inequality that go beyond its direct derivation from the Jarzynski equality. In particular, we consider chemical systems both in the linear-response regime and away from linear thermodynamics. Furthermore, by employing functional-integral techniques, we extend Jarzynski's inequality to many-body statistical systems described by quantum field theory. Salient issues, such as connections of the Jarzynski inequality with the maximum work theorem and the Landau--Lifshitz theory of fluctuations, are also discussed.