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  Covariant Momentum Map Thermodynamics for Parametrized Field Theories

Chirco, G., Laudato, M., & Mele, F. M. (2019). Covariant Momentum Map Thermodynamics for Parametrized Field Theories. In Geometric Science of Information. Series: Lecture Notes in Computer Science (pp. 55-65).

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Item Permalink: http://hdl.handle.net/21.11116/0000-0005-4D29-8 Version Permalink: http://hdl.handle.net/21.11116/0000-0006-8621-D
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Chirco, Goffredo1, Author              
Laudato , Marco, Author
Mele , Fabio M., Author
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1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014              

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Free keywords: Mathematical Physics, math-ph,General Relativity and Quantum Cosmology, gr-qc,High Energy Physics - Theory, hep-th,Mathematics, Mathematical Physics, math.MP
 Abstract: Inspired by Souriau's symplectic generalization of the Maxwell-Boltzmann-Gibbs equilibrium in Lie group thermodynamics, we investigate a spacetime-covariant formalism for statistical mechanics and thermodynamics in the multi-symplectic framework for relativistic field theories. A general-covariant Gibbs state is derived, via a maximal entropy principle approach, in terms of the covariant momentum map associated with the lifted action of the diffeomorphisms group on the extended phase space of the fields. Such an equilibrium distribution induces a canonical spacetime foliation, with a Lie algebra-valued generalized notion of temperature associated to the covariant choice of a reference frame, and it describes a system of fields allowed to have non-vanishing probabilities of occupying states different from the diffeomorphism invariant configuration. We focus on the case of parametrized first-order field theories, as a concrete simplified model for fully constrained field theories sharing fundamental general covariant features with canonical general relativity. In this setting, we investigate how physical equilibrium, hence time evolution, emerge from such a state via a gauge-fixing of the diffeomorphism symmetry.

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 Dates: 2019-11-142019
 Publication Status: Published in print
 Pages: 46 pages, 1 figure
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 Identifiers: arXiv: 1911.06224
URI: http://arxiv.org/abs/1911.06224
DOI: 10.1007/978-3-030-26980-7_7
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Title: Geometric Science of Information. Series: Lecture Notes in Computer Science
Source Genre: Book
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Pages: - Volume / Issue: 11712 Sequence Number: - Start / End Page: 55 - 65 Identifier: -