Thermodynamics on Noncommutative Geometry in Coherent State Formalism

TL;DR

This paper explores the thermodynamics of ideal gases in noncommutative geometry using coherent state formalism, revealing residual interactions, finite energy limits, and differences in heat capacity for squeezed states compared to commutative cases.

Contribution

It introduces a novel analysis of ideal gas thermodynamics on noncommutative geometry, including effects of squeezed states and residual interactions, expanding understanding of quantum geometry impacts.

Findings

Residual attraction and repulsion potentials at high temperature

Finite asymptotic energy in noncommutative geometry

Different heat capacities for squeezed coherent states

Abstract

The thermodynamics of ideal gas on the noncommutative geometry in the coherent state formalism is investigated. We first evaluate the statistical interparticle potential and see that there are residual "attraction (repulsion) potential" between boson (fermion) in the high temperature limit. The characters could be traced to the fact that, the particle with mass $m$ in noncommutative thermal geometry with noncommutativity $\theta$ and temperature $T$ will correspond to that in the commutative background with temperature $T(1+kTm\theta)^{-1}$. Such a correspondence implies that the ideal gas energy will asymptotically approach to a finite limiting value as that on commutative geometry at $T_\theta= (km\theta)^{-1}$. We also investigate the squeezed coherent states and see that they could have arbitrary mean energy. The thermal properties of those systems are calculated and compared to each other. We find that the heat capacity of the squeezed coherent states of boson and fermion on the noncommutative geometry have different values, contrast to that on the commutative geometry.