# $ \dfrac{1}{c^2} $ Correction to Thermodynamics

## TL;DR

This paper derives the first relativistic correction to thermodynamics using a Hamiltonian expanded in powers of 1/c^2, and applies it to particles with harmonic interactions to illustrate the corrections.

## Contribution

It provides a general formalism for calculating relativistic corrections to thermodynamics and applies it to a specific N-particle harmonic oscillator system.

## Key findings

- Explicit expressions for relativistic thermodynamic corrections
- Application to N particles with harmonic interactions
- Framework for future relativistic thermodynamics studies

## Abstract

I work out the general expressions for the first relativistic correction of order $ \dfrac{1}{c^2} $ to thermodynamics. The starting point is the relativistic Hamiltonian that I derived in a previous paper, which I expanded to powers of $ \dfrac{1}{c^2} $ to derive a local (in time) Hamiltonian. Limiting to the first relativistic correction, I worked out in general how the relativistic corrections to thermodynamics arise. I then applied the formalism to the problem of N particles with harmonic oscillator interaction in 3D to see the explicit expressions for relativistic corrections.