Fluctuation relations and strong inequalities for thermally isolated systems

TL;DR

This paper derives new fluctuation relations and inequalities for thermally isolated systems undergoing adiabatic processes, strengthening the understanding of work bounds in classical and quantum thermodynamics.

Contribution

It introduces an integral fluctuation relation specific to adiabatic processes and derives related inequalities for the strong work bound, extending previous thermodynamic results.

Findings

Derived an integral fluctuation relation for adiabatic processes

Established inequalities related to the strong work bound

Provided classical and quantum derivations of the results

Abstract

For processes during which a macroscopic system exchanges no heat with its surroundings, the second law of thermodynamics places two lower bounds on the amount of work performed on the system: a weak bound, expressed in terms of a fixed-temperature free energy difference, $W \ge \Delta F_T$ , and a strong bound, given by a fixed-entropy internal energy difference, $W \ge \Delta E_S$ . It is known that statistical inequalities related to the weak bound can be obtained from the nonequilibrium work relation, $\langle\exp (-\beta W)\rangle = \exp(-\beta\Delta F_T)$ . Here we derive an integral fluctuation relation $\langle\exp(-\beta X) \rangle = 1 $ that is constructed specifically for adiabatic processes, and we use this result to obtain inequalities related to the strong bound, $W \ge \Delta E_S$ . We provide both classical and quantum derivations of these results.