Exact four-vector work distribution and covariant fluctuation theorems of work for a relativistic particle in an expanding piston

TL;DR

This paper derives the exact four-vector work distribution for a relativistic particle in an expanding piston, demonstrating covariant fluctuation theorems and introducing a new geometric analysis method for relativistic collisions.

Contribution

It provides the first exact work distribution in a relativistic piston model and establishes covariant fluctuation theorems, with a novel geometric approach for collision dynamics.

Findings

Work distribution concentrates on the origin and specific curves in (W^0, W^1) space.

Model recovers non-relativistic dynamics in the appropriate limit.

Momentum component of work remains significant in relativistic frameworks.

Abstract

We investigate the non-equilibrium four-vector work in an expanding relativistic piston. We derive the exact work distribution in this pedagogical model and find that the joint distribution of four-vector work $(W^0, W^1)$ concentrates on the origin and some curves in the $(W^0, W^1)$ space, rather than being smoothly distributed. In the non-relativistic limit, our model consistently recovers the non-relativistic dynamics. We further demonstrate that the momentum component of four-vector work remains significant in both the Lorentz-relativistic and Galilean-relativistic frameworks. On top of the work distribution, we verify a family of covariant fluctuation theorems of work. In addition, we introduce a novel geometrical technique for analyzing the dynamics of relativistic collision processes, which can be straightforwardly extended to multi-dimensional piston models.