Thermodynamics of absolute stiff matter

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.