Thermostatistics of the Polymeric Ideal Gas

TL;DR

This paper develops a statistical mechanics framework for polymeric systems, revealing how polymer effects modify microstate counts and thermodynamics, aligning with quantum results at high temperatures and classical limits at low temperatures.

Contribution

It introduces a noncanonical coordinate system on the polymeric symplectic manifold that encapsulates polymer effects through a modified density of states.

Findings

Polymeric effects reduce the number of microstates due to an upper momentum bound.

The derived partition function accurately describes thermodynamics in the polymer framework.

Results agree with quantum predictions at high temperature and classical results at low temperature.

Abstract

In this paper, we formulate statistical mechanics of the polymerized systems in the semiclassical regime. On the corresponding polymeric symplectic manifold, we set up a noncanonical coordinate system in which all of the polymeric effects are summarized in the density of states. Since we show that the polymeric effects only change the number of microstates of a statistical system, working in this coordinate is quite reasonable from the statistical point of view. The results show that the number of microstates decreases due to existence of an upper bound for the momentum of the test particles in the polymer framework. We obtain a corresponding canonical partition function by means of the deformed density of states. By using the partition function, we study thermodynamics of the ideal gas in the polymer framework and show that our results are in good agreement with those that arise from the full quantum consideration at high temperature, and they coincide with their usual counterpart in the limit of low temperature.