Theoretical self-consistency in nonextensive statistical mechanics with parameter transformation

Self-consistency in nonextensive statistical mechanics is studied as a recourse to parameter transformation, where different nonextensive parameters are presented for various theoretical branches. The unification between the first and third choices of the average definition and that between the normal and escort distributions are both examined. The problem of parameter inversion in the generalized H theorem is also investigated. The inconsistency between the statistical ensemble pressure and molecular dynamics pressure can be eliminated. This work also verifies the equivalence of physical temperature and gravitational temperature in nonextensive statistical mechanics. In these parameter transformations, the Tsallis entropy form is observed to remain invariant.