The Legendre Transform in Non-additive Thermodynamics and Complexity

Abstract

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".

23 pages. LaTeX2e. No figures

References in corpus (4)

• Phase transitions and configuration space topology
• Sharp geometric and functional inequalities in metric measure spaces with lower Ricci curvature bounds
• Approach of complexity in nature: Entropic nonuniqueness
• Ricci curvature, isoperimetry and a non-additive entropy

Cited by in corpus (2)

• The ${\tau }_q$-Fourier transform: covariance and uniqueness
• Power-law entropies for continuous systems and generalized operations