Generalized thermostatistics based on deformed exponential and logarithmic functions

The equipartition theorem states that inverse temperature equals the log-derivative of the density of states. This relation can be generalized by introducing a proportionality factor involving an increasing positive function φ(x). It is shown that this assumption leads to an equilibrium distribution of the Boltzmann–Gibbs form with the exponential function replaced by a deformed exponential function. In this way one obtains a formalism of generalized thermostatistics introduced previously by the author. It is shown that Tsallis’ thermostatistics, with a slight modification, is the most obvious example of this formalism and corresponds with the choice φ(x)=xq.