Variation on the theme of Jarzynski's inequality
Dani R. Castellanos, Petr Jizba
TL;DR
This work analyzes variations of Jarzynski's inequality beyond its standard derivation from the Jarzynski equality, with a focus on chemical systems and quantum-field contexts. It presents a path-integral derivation of JE, connects JE-derived inequalities to the maximum work theorem, and extends the framework to both linear and nonlinear regimes, including isothermal-isobaric and isothermal-isochoric processes. By employing entropy-production arguments (linear response) and Bogoliubov–Feynman functional-integral techniques (QFT), the authors derive bound forms relating free-energy changes to average work in a broad set of thermodynamic settings. The results broaden the applicability of Jarzynski-type relations and offer a unified perspective for connecting non-equilibrium work to equilibrium free energies across classical chemistry and quantum-field theories, suggesting avenues for incorporating influence-functionals and Keldysh-type formalisms in future work.
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.