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.Comment: 12 two column pages, 2 figures, Final versio

Generalized uncertainty principle and the maximum mass of ideal white dwarfs

“…This means that the one-particle phase space measure is given by h −3 and therefore each integral on the phase space will be of the form d 3 xd 3 ph −3 ( ). For a system obeying the GUP, the volume of phase space cells can be derived in several ways [19,21,22,23,41]. All of them show that the phase space should be divided into cells of volume h 3 (1 + λ 2 p 2 ) 3 and thus phase space integrals are…”

Thermodynamics Properties of Confined Particles on Noncommutative Plane

“…showing another way to measure the parameter θ in terms of the field B. We conclude that particles moving in a noncommutative plane can be envisaged as the usual motion of particles experiencing an effective magnetic field (15).…”

“…[9−13] On the other hand, the noncommutative geometry has been employed to study different thermodynamics systems, one may see Refs. [14][15][16]. The main outcome is that modification of different thermodynamics quantities were obtained in terms of the noncommutative parameter θ.…”

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