The nonextensive gas: a kinetic approach

We discuss a kinetic nonextensive generalization of the Maxwellian ideal gas. The analysis rests on two basic assumptions: (i) instead of the standard Gaussian form, the q-gas is described by a power-law velocity distribution as suggested in the nonextensive Tsallis' framework (ii) the q-nonextensive generalization of the Boltzmann entropy formula governs the behavior of the q-gas. In this context, we show that the pressure and the internal energy are kinetically modified, but the general equation of state, PV=2U/3, remains valid. The adiabatic index is now a function of the nonextensive parameter, γ=Cp/CV=5/3q. However, the standard expression relating the specific heats (at constant pressure and volume) with the coefficient of expansion and the isothermal compressibility, CP−CV=TVα2/κT, is not modified.