Thermodynamics of a non-commutative fermion gas

TL;DR

This paper analyzes the thermodynamics of a non-commutative fermion gas confined in a two-dimensional well, revealing deviations from classical behavior at high densities and identifying extremal states with unique entropy properties.

Contribution

It provides the first detailed thermodynamic analysis of a non-commutative fermion gas, highlighting non-extensive features and extremal states due to non-commutativity.

Findings

Thermodynamics matches commutative gas at low densities.

Strong deviations occur at high densities due to excluded area.

Existence of extremal states with zero entropy.

Abstract

Building on the recent solution for the spectrum of the non-commutative well in two dimensions, the thermodynamics that follows from it is computed. In particular the focus is put on an ideal fermion gas confined to such a well. At low densities the thermodynamics is the same as for the commutative gas. However, at high densities the thermodynamics deviate strongly from the commutative gas due to the implied excluded area resulting from the non-commutativity. In particular there are extremal macroscopic states, characterized by area, number of particles and angular momentum, that correspond to a single microscopic state and thus have vanishing entropy. When the system size and excluded area are comparable, thermodynamic quantities, such as entropy, exhibit non-extensive features.