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• W2000356308 abstract "Superstatistics describes statistical systems that behave like superpositions of different inverse temperatures $beta$, so that the probability distribution is $p(epsilon_i) propto int_{0}^{infty} f(beta) e^{-beta epsilon_i}dbeta$, where the `kernel' $f(beta)$ is nonnegative and normalized ($int f(beta)d beta =1$). We discuss the relation between this distribution and the generalized entropic form $S=sum_i s(p_i)$. The first three Shannon-Khinchin axioms are assumed to hold. It then turns out that for a given distribution there are two different ways to construct the entropy. One approach uses escort probabilities and the other does not; the question of which to use must be decided empirically. The two approaches are related by a duality. The thermodynamic properties of the system can be quite different for the two approaches. In that connection we present the transformation laws for the superstatistical distributions under macroscopic state changes. The transformation group is the Euclidean group in one dimension." @default.
• W2000356308 created "2016-06-24" @default.
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• W2000356308 date "2011-04-04" @default.
• W2000356308 modified "2023-10-09" @default.
• W2000356308 title "Generalized entropies and the transformation group of superstatistics" @default.
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• W2000356308 doi "https://doi.org/10.1073/pnas.1103539108" @default.
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