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Docta Complutense author Tempesta, Piergiulio 2023-06-17T21:51:12Z 2023-06-17T21:51:12Z 2016-11-01 1364-5021 10.1098/rspa.2016.0143 https://hdl.handle.net/20.500.14352/17652 http://dx.doi.org/10.1098/rspa.2016.0143 http://rspa.royalsocietypublishing.orghttps://arxiv.org/abs/1507.07436 We shall prove that the celebrated Renyi entropy is the first example of a new family of infinitely many multi-parametric entropies. We shall call them the Z-entropies. Each of them, under suitable hypotheses, generalizes the celebrated entropies of Boltzmann and Renyi. A rucial aspect is that every Z-entropy is composable (Tempesta 2016 Ann. Phys. 365, 180-197. (doi: 10.1016/j.aop.2015.08.013)). This property means that the entropy of a system which is composed of two or more independent systems depends, in all the associated probability space, on the choice of the two systems only. Further properties are also required to describe the composition process in terms of a group law. The composability axiom, introduced as a generalization of the fourth Shannon-Khinchin axiom (postulating additivity), is a highly non- trivial requirement. Indeed, in the trace-form class, the Boltzmann entropy and Tsallis entropy are the only known composable cases. However, in the non-trace form class, the Z-entropies arise as new entropic functions possessing the mathematical properties necessary for information-theoretical applications, in both classical and quantum contexts. From a mathematical point of view, composability is intimately related to formal group theory of algebraic topology. The underlying group-theoretical structure determines crucially the statistical properties of the corresponding entropies. eng Formal groups and Z-entropies journal article URL https://docta.ucm.es/bitstreams/c0815a40-bf22-47c1-9646-4e989e914458/download File MD5 9db7acabff4d4c49016db2ae16e0d8b5 271681 application/pdf tempesta27preprint.pdf