Second law of thermodynamics for relativistic fluids formulated with relative entropy

TL;DR

This paper reformulates the second law of thermodynamics for relativistic quantum fluids using relative entropy, connecting quantum information theory with relativistic fluid dynamics and exploring implications for entanglement and local dynamics.

Contribution

It introduces a local second law formulation for relativistic quantum field theories based on relative entropy, bridging quantum information and relativistic fluid dynamics.

Findings

Monotonicity of relative entropy leads to second law-like inequalities.

A local second law can be formulated in relativistic quantum field theory.

Discussion of entanglement's role in relativistic fluid dynamics.

Abstract

The second law of thermodynamics is discussed and reformulated from a quantum information theoretic perspective for open quantum systems using relative entropy. Specifically, the relative entropy of a quantum state with respect to equilibrium states is considered and its monotonicity property with respect to an open quantum system evolution is used to obtain second law-like inequalities. We discuss this first for generic quantum systems in contact with a thermal bath and subsequently turn to a formulation suitable for the description of local dynamics in a relativistic quantum field theory. A local version of the second law similar to the one used in relativistic fluid dynamics can be formulated with relative entropy or even relative entanglement entropy in a space-time region bounded by two light cones. We also give an outlook towards isolated quantum field theories and discuss the role of entanglement for relativistic fluid dynamics.