Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Covariant Momentum Map Thermodynamics for Parametrized Field Theories   A general-covariant statistical framework capable of describing classical
fluctuations of the gravitational field is a thorny open problem in theoretical
physics, yet ultimately necessary to understand the nature of the gravitational
interaction and a key to quantum gravity. Inspired by Souriau's symplectic
generalization of the Maxwell-Boltzmann-Gibbs equilibrium in Lie group
thermodynamics, we investigate a spacetime-covariant formulation of statistical
mechanics for parametrized first-order field theories, as a simplified model
sharing essential general covariant features with canonical general relativity.
Starting from a covariant multi-symplectic phase space formulation, we define a
general-covariant notion of Gibbs state in terms of the covariant momentum map
associated with the lifted action of the diffeomorphisms group on the extended
phase space. We show how such a covariant notion of equilibrium encodes the
whole information about symmetry, gauge and dynamics carried by the theory,
associated to a canonical spacetime foliation, where the covariant choice of a
reference frame reflects in a Lie algebra-valued notion of local temperature.
We investigate how physical equilibrium, hence time evolution, emerges from
such a state and the role of the gauge symmetry in the thermodynamic
description.

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The categories of this paper are: nlin
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
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The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph