# 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.

## Key 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.

---
Source: https://tomesphere.com/paper/1907.09604