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Generalized thermostatistics based on deformed exponential and logarithmic functions

Jan Naudts
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Abstract

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 phi(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 phi(x)=x^q.

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Jan Naudts. 2003-11-19. Generalized thermostatistics based on deformed exponential and logarithmic functions. https://doi.org/10.1016/j.physa.2004.03.074

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