Next seminar

Title Super-additivity, generalized concavity and quasi-homogeneity in non-additive systems
Speaker Velimir Ilić (Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade)
Date&time 📅 September 12
🕓 11.00
Location room 138, SISSA + Virtual
Abstract Super-additivity, concavity, and homogeneity of the entropy function set up the basis for the maximum entropy principle, which arises from the second law of thermodynamics. On the other hand, in the case of non-additive systems, which are common in the presence of long-range interactions and in black hole thermodynamics, the entropy is not a homogeneous but a quasi-homogeneous function. Although some fundamental results, such as the zeroth law of thermodynamics and the Gibbs-Duhamel relationship, have already been established for quasi-homogeneous entropies, the relationships between quasi-homogeneity, concavity, and super-additivity for non-additive systems are still unknown. In this talk, we will discuss these relationships and the results will be applied to the characterization of the generalized Landsberg ideal gas, which is an example of a simple system that violates homogeneity (and consequently super-additivity) while being consistent with ideal gas state equations. Possible applications for the characterization of long-range interacting systems will also be discussed.
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