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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.
