Entropy current in relativistic quantum statistical mechanics

TL;DR

This thesis develops a rigorous framework for defining and calculating the entropy current in relativistic quantum statistical mechanics, applying it to systems related to quark-gluon plasma and out-of-equilibrium quantum fluids.

Contribution

It introduces a general method to compute the entropy current at local thermodynamic equilibrium within relativistic quantum statistical mechanics.

Findings

Entropy current defined rigorously in relativistic quantum systems.

Calculated entropy current for relativistic quantum fluids at equilibrium and out-of-equilibrium.

Discussed renormalization of energy-momentum tensor and entropy current.

Abstract

In this thesis, we present and discuss the quantum statistical foundations of relativistic hydrodynamics with special emphasis on the entropy current. We show that it is possible to provide a rigorous definition for this quantity in the framework of relativistic quantum statistical mechanics and we put forward a general method to calculate it at local thermodynamic equilibrium. The method is based on the proof of existence of the thermodynamic potential current, a usually tacitly understood hypothesis. We then apply the method for the entropy current to the study of two different systems. The first system is a relativistic quantum fluid at global thermodynamic equilibrium, phenomenologically related to the quark-gluon plasma and, from a quantum field theoretical standpoint, to the Unruh effect. The second systems is a relativistic quantum fluid with boost invariance, also related to the quark-gluon plasma and of great interest as the first solvable system out of equilibrium. The thermal expectation value of the energy-momentum tensor as well as the entropy current are calculated for both systems, and renormalization is discussed.