# Introduction

Differential expression of the first principle of thermodynamics:

${\displaystyle dE=TdS-pdV}$

Boltzmann relation between entropy ${\displaystyle S}$ and number of microstates at a given energy ${\displaystyle g(E)}$:

${\displaystyle S=k\log(g(E))}$

The above defines an extensive property of the system, i.e. if we have two subsystems at ${\displaystyle S_{1},S_{2}}$ then ${\displaystyle S=S_{1}+S_{2}=k\log(g_{1}g_{2})=k\log(g)}$.