Generalized thermostatistics based on deformed exponential and logarithmic functions

Jan Naudts

Physica A: Statistical Mechanics and its Applications, 2004, vol. 340, issue 1, 32-40

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 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.

Keywords: Generalized thermostatistics; Equipartition theorem; Density of states; Deformed logarithmic and exponential functions; Tsallis’ thermostatistics; Duality (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:340:y:2004:i:1:p:32-40

DOI: 10.1016/j.physa.2004.03.074

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