Work statistics in slow thermodynamic processes

TL;DR

This paper derives the full counting statistics of work in slow thermodynamic processes using the adiabatic approximation, revealing the roles of free energy change, dissipated work, and geometric phases, and relates these to thermodynamic geometry.

Contribution

It provides a novel analytical framework for understanding work statistics in slow thermodynamic processes, including explicit expressions for the friction tensor and phase relations.

Findings

Full counting statistics of work derived for slow processes

Identification of dynamical and geometric phases in work

Relation between phases via fluctuation-dissipation theorem

Abstract

We apply the adiabatic approximation to slow but finite-time thermodynamic processes and obtain the full counting statistics of work. The average work consists of change in free energy and the dissipated work, and we identify each term as a dynamical- and geometric-phase-like quantity. An expression for the friction tensor, the key quantity in thermodynamic geometry, is explicitly given. The dynamical and geometric phases are proved to be related to each other via the fluctuation-dissipation relation.