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Entropy 2017, 19(7), 298; doi:10.3390/e19070298

The Legendre Transform in Non-Additive Thermodynamics and Complexity

Carnegie Mellon University in Qatar Education City, Doha 24866, Qatar
Received: 27 April 2017 / Revised: 20 June 2017 / Accepted: 20 June 2017 / Published: 23 June 2017
(This article belongs to the Special Issue Geometry in Thermodynamics II)
View Full-Text   |   Download PDF [282 KB, uploaded 26 June 2017]


We present an argument which purports to show that the use of the standard Legendre transform in non-additive Statistical Mechanics is not appropriate. For concreteness, we use as paradigm, the case of systems which are conjecturally described by the (non-additive) Tsallis entropy. We point out the form of the modified Legendre transform that should be used, instead, in the non-additive thermodynamics induced by the Tsallis entropy. We comment on more general implications of this proposal for the thermodynamics of “complex systems”. View Full-Text
Keywords: Legendre transform; statistical mechanics; complex systems; Tsallis entropy; convexity Legendre transform; statistical mechanics; complex systems; Tsallis entropy; convexity
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Kalogeropoulos, N. The Legendre Transform in Non-Additive Thermodynamics and Complexity. Entropy 2017, 19, 298.

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