Generalized thermostatistics and mean-field theory

The present paper studies a large class of temperature-dependent probability distributions and shows that entropy and energy can be defined in such a way that these probability distributions are the equilibrium states of a generalized thermostatistics, which is obtained from the standard formalism by deformation of exponential and logarithmic functions. Since this procedure is non-unique, specific choices are motivated by showing that the resulting theory is well-behaved. In particular, with the choices made in the present paper, the equilibrium state of any system with a finite number of degrees of freedom is, automatically, thermodynamically stable and satisfies the variational principle.