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

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.