Jeans’ criterion in nonextensive statistical mechanics

The Jeans’ gravitational instability in nonextensive statistical mechanics is studied and a general form of the generalized Jeans’ criterion is obtained that is related to the q-function cq=∑ipiq. In this approach, the nonextensive model of classical ideal gas is applied to the Jeans’ problem instead of the ordinary one in extensive statistical mechanics and the generalized critical wavelength to describe the gravitational instability is deduced. This nonextensive modification of the Jeans’ criterion leads to a new critical length that depends not only on the nonextensive parameter q but also on the dimension D and the total particle numbers N of the system. When q→1−, the Jeans’ length is perfectly recovered. We also give the nonextensive parameter q a physical interpretation that q=1 represents an isothermal process of the gas, corresponding to the state of complete mixing, but 0<q<1 is nonisothermal, corresponding to the state of incomplete mixing, it measures the degree of mixing.