2014/07/14 by Piergiulio Tempesta, Tempesta, Piergiulio · 4 citations
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Complex Network Analysis Techniques #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.1407.3807
openalex publication_date 2014/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The notion of entropy is ubiquitous both in natural and social sciences. In\nthe last two decades, a considerable effort has been devoted to the study of\nnew entropic forms, which generalize the standard Boltzmann-Gibbs (BG) entropy\nand are widely applicable in thermodynamics, quantum mechanics and information\ntheory. In [23], by extending previous ideas of Shannon [38], [39], Khinchin\nproposed an axiomatic definition of the BG entropy, based on four requirements,\nnowadays known as the Shannon-Khinchin (SK) axioms.\n The purpose of this paper is twofold. First, we show that there exists an\nintrinsic group-theoretical structure behind the notion of entropy. It comes\nfrom the requirement of composability of an entropy with respect to the union\nof two statistically independent subsystems, that we propose in an axiomatic\nformulation. Second, we show that there exists a simple universal class of\nadmissible entropies. This class contains many well known examples of entropies\nand infinitely many new ones, a priori multi-parametric. Due to its specific\nrelation with the universal formal group, the new family of entropies\nintroduced in this work will be called the universal-group entropy. A new\nexample of multi-parametric entropy is explicitly constructed.\n