Relativistic Quantum Thermodynamics of Moving Systems

TL;DR

This paper investigates the thermodynamics of a quantum system moving at constant velocity interacting with a thermal bath, deriving a velocity-dependent master equation and exploring the implications for relativistic temperature transformations.

Contribution

It derives a velocity-dependent quantum master equation for a moving system and proposes a new framework for Lorentz transformations of thermodynamic states.

Findings

Moving heat bath is equivalent to a mixture of rest heat baths at different temperatures.

The derived master equation has a form similar to quantum optical master equations but with velocity-dependent coefficients.

There is no unique Lorentz transformation rule for temperature; a convex hull approach is proposed.

Abstract

We analyse the thermodynamics of a quantum system in a trajectory of constant velocity that interacts with a static thermal bath. The latter is modeled by a massless scalar field in a thermal state. We consider two different couplings of the moving system to the heat bath, a coupling of the Unruh-DeWitt type and a coupling that involves the time derivative of the field. We derive the master equation for the reduced dynamics of the moving quantum system. It has the same form with the quantum optical master equation, but with different coefficients that depend on velocity. This master equation has a unique asymptotic state for each type of coupling, and it is characterized by a well-defined notion of heat-flow. Our analysis of the second law of thermodynamics leads to a surprising equivalence: a moving heat bath is physically equivalent to a mixture of heat baths at rest, each with a different temperature. There is no unique rule for the Lorentz transformation of temperature. We propose that Lorentz transformations of thermodynamic states are well defined in an extended thermodynamic space that is obtained as a convex hull of the standard thermodynamic space.