On the thermodynamics of fermions at any temperature based on parametrized partition function

TL;DR

This paper introduces a novel approach using a parametrized partition function to infer the thermodynamic properties of fermions from bosonic and distinguishable particle simulations across all temperatures, enhancing computational efficiency.

Contribution

The work presents a new method to determine fermionic energies and thermodynamics at any temperature by mapping from bosonic and distinguishable particle data using a parametrized partition function.

Findings

Successfully mapped bosonic energies to fermionic energies in three-dimensional space.

Accurately computed energies and heat capacities for noninteracting and interacting fermions.

Good agreement with analytical results for noninteracting fermions.

Abstract

In this work we study the recently developed parametrized partition function formulation and show how we can infer the thermodynamic properties of fermions based on numerical simulation of bosons and distinguishable particles at various temperatures. In particular, we show that in the three dimensional space defined by energy, temperature and the parameter characterizing parametrized partition function, we can map the energies of bosons and distinguishable particles to fermionic energies through constant-energy contours. We apply this idea to both noninteracting and interacting Fermi systems and show it is possible to infer the fermionic energies at all temperatures, thus providing a practical and efficient approach to obtain thermodynamic properties of Fermi systems with numerical simulation. As an example, we present energies and heat capacities for 10 noninteracting fermions and 10 interacting fermions (more fermions are provided in the appendix) and show good agreement with the analytical result for noninteracting case.