Relativistic Quantum Thermodynamics of Moving Systems

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.

arXiv comment24 pages, 4 figures; minor changes, references added, to appear in PRD

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• Quantum and Relativistic corrections to Maxwell-Boltzmann ideal gas model from a Quantum Phase Space approach
• Disjointness of inertial KMS states and the role of Lorentz symmetry in thermalization
• A Note on the Relativistic Transformation Properties of Quantum Stochastic Calculus
• Entangled states dynamics of moving two-level atoms in a thermal field bath
• Probing non-equilibrium steady states of the Klein-Gordon field with Unruh-DeWitt detectors
• Study on relativistic transformations for thermodynamic quantities: Boltzmann-Gibbs and Tsallis blast-wave models
• Dynamics of a two-level atom in the presence of a medium-assisted thermal field
• Thermodynamic uncertainty relations for relativistic quantum thermal machines