Second law of thermodynamics for relativistic fluids formulated with relative entropy

• URL: http://arxiv.org/abs/2008.02706v2
• Date: Fri, 6 Nov 2020 17:23:29 GMT
• Title: Second law of thermodynamics for relativistic fluids formulated with relative entropy
• Authors: Neil Dowling and Stefan Floerchinger and Tobias Haas
• Abstract summary: The second law of thermodynamics is discussed and reformulated from a quantum information theoretic perspective. We discuss this first for generic quantum systems in contact with a thermal bath and then turn to a formulation suitable for the description of local dynamics. 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.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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