Thermodynamics of exotic matter with constant w=P/E

Abstract: We consider a substance with equation of state $P=wE$ at constant $w$ and find that it is an ideal gas of quasi-particles with the energy spectrum $\epsilon_p\sim p^{wq}$ that can constitute either regular matter (when $w>0$) or exotic matter (when $w<0$) in a $q$-dimensional space. Particularly, an ideal gas of fermions or bosons with the energy spectrum $\epsilon_p=m^4/p^3$ in 3-dimensional space will have the pressure $P=-E$. Exotic material, associated with the dark energy at $E+P<0$, is also included in analysis. We determine the properties of regular and exotic ideal Fermi gas at zero temperature and derive a low-temperature expansion of its thermodynamical functions at finite temperature. The Fermi level of exotic matter is shifted below the Fermi energy at zero temperature, while the Fermi level of regular matter is always above it. The heat capacity of any fermionic substance is always linear dependent on temperature, but exotic matter has negative entropy and negative heat capacity.