Noncommutative spaces and covariant formulation of statistical mechanics

Abstract

We study the statistical mechanics of a general Hamiltonian system in the context of symplectic structure of the corresponding phase space. This covariant formalism reveals some interesting correspondences between properties of the phase space and the associated statistical physics. While topology, as a global property, turns out to be related to the total number of microstates, the invariant measure which assigns {\it a priori} probability distribution over the microstates, is determined by the local form of the symplectic structure. As an example of a model for which the phase space has a nontrivial topology, we apply our formulation on the Snyder noncommutative space-time with de Sitter four-momentum space and analyze the results. Finally, in the framework of such a setup, we examine our formalism by studying the thermodynamical properties of a harmonic oscillator system.

arXiv comment12 two column pages, 2 figures, Final version

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Cited by in corpus (6)

• Generalized Uncertainty Principle Removes The Chandrasekhar Limit
• Non-commutative effects on gravitational measurements
• Compact stars in quantum spacetime
• Photon gas thermodynamics in dS and AdS momentum spaces
• Statistical physics on Euclidean Snyder space: connections with the GUP and cosmological implications
• Thermodynamics Properties of Confined Particles on Noncommutative Plane