# Thermodynamical Properties of Bosons and Fermions for a Lattice Motivated Dispersion Relationship

## TL;DR

This paper investigates the thermodynamical properties of bosonic and fermionic oscillators with a dispersion relation inspired by relativity and condensed matter physics, revealing phenomena like negative temperatures and negative pressure below critical temperatures.

## Contribution

It introduces a novel dispersion relationship for oscillators and analyzes their thermodynamics, highlighting unique behaviors such as negative temperatures and pressure.

## Key findings

- Negative temperatures observed in fermionic oscillators
- Pressure becomes negative for temperatures below a critical point
- Oscillators exhibit a single effective vibrational frequency

## Abstract

In this paper we calculate the basic thermodynamical quantities for a system of bosonic simple harmonic oscillators (BSHOs) and the corresponding system of fermionic simple harmonic oscillators (FSHOs) using a dispersion relationship similar to cases in general relativity and condensed matter physics. In the FSHO we see negative temperatures in both cases we obtain finally a system of oscillators with only one effective frequency of vibration. Also we see that pressure is less than zero for T < Tc where Tc is a critical temperature for bosons.