Thermodynamics of absolute stiff matter

TL;DR

This paper investigates the thermodynamic properties of 'absolute stiff' matter, characterized by pressure equal to energy density, focusing on its behavior at finite temperatures for fermionic and bosonic cases in three-dimensional space.

Contribution

It provides analytical expressions for pressure, particle density, and heat capacity of 'absolute stiff' matter, highlighting differences between fermionic and bosonic behaviors at finite temperatures.

Findings

Heat capacity is linear in temperature at low T.

Fermionic 'absolute stiff' matter has pressure proportional to density squared.

Bose 'absolute stiff' gas does not undergo Bose-Einstein condensation.

Abstract

The 'absolute stiff' matter ($P=E$) can be a Fermi or Bose gas of particles with the energy spectrum $\epsilon_p \sim p^q$ in $q$-dimensional space, particularly $\epsilon_p =p^3/m^2$ in 3-dimensional space. We obtain its pressure, particle number density and heat capacity at finite temperature. The behavior of 'absolute stiff' medium is determined by characteristic temperature $T_c=6\pi ^2n/(\gamma m^2)$. At low temperature the heat capacity obeys the linear law $C_V\sim T$ for both fermionic and bosonic matter, the pressure of 'absolute stiff' fermions $P\sim n^2+O(T^2)$, while the 'absolute stiff' Bose gas never reveals Bose-Einstein condensation.