 Entropy density

For a homogeneous extensive system in thermodynamic equilibrium, the entropy density is entropy per physical volume, $s=S/V$. The thermodynamic Euler relation giveswhere $\rho =U/V$ is energy density, $P$ is pressure, $\mu$ is chemical potential, $n=N/V$ is number density and $T$ is absolute temperature. Here $\rho$ denotes energy density, not mass density; in a relativistic application the energy convention must consistently include the rest-energy paired with the chemical potential.

With several conserved particle numbers, replace $\mu n$ by ${\sum }_i{\mu }_i{n}_i$. The Euler form assumes extensivity and negligible surface terms; it is not an automatic identity for a finite interacting system with appreciable boundary contributions. For a photon gas at equilibrium, $\mu =0$ and $P=\rho /3$, yielding $s=4\rho /(3T)$.