A new entropy based on a group-theoretical structure |
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Authors: | Evaldo MF Curado Piergiulio Tempesta Constantino Tsallis |
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Institution: | 1. Centro Brasileiro de Pesquisas Fisicas, Rua Xavier Sigaud 150, 22290–180 Rio de Janeiro–RJ, Brazil;2. National Institute of Science Technology for Complex Systems, Rua Xavier Sigaud 150, 22290–180 Rio de Janeiro–RJ, Brazil;3. Departamento de Física Teórica II (Métodos Matemáticos de la Física), Facultad de Físicas, Universidad Complutense, 28040–Madrid, Spain;4. Instituto de Ciencias Matemáticas, C/ Nicolás Cabrera, No 13–15, 28049 Madrid, Spain;5. Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA |
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Abstract: | A multi-parametric version of the nonadditive entropy Sq is introduced. This new entropic form, denoted by Sa,b,r, possesses many interesting statistical properties, and it reduces to the entropy Sq for b=0, a=r:=1−q (hence Boltzmann–Gibbs entropy SBG for b=0, a=r→0). The construction of the entropy Sa,b,r is based on a general group-theoretical approach recently proposed by one of us, Tempesta (2016). Indeed, essentially all the properties of this new entropy are obtained as a consequence of the existence of a rational group law, which expresses the structure of Sa,b,r with respect to the composition of statistically independent subsystems. Depending on the choice of the parameters, the entropy Sa,b,r can be used to cover a wide range of physical situations, in which the measure of the accessible phase space increases say exponentially with the number of particles N of the system, or even stabilizes, by increasing N, to a limiting value. |
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Keywords: | Generalized entropies Group theory Statistical mechanics |
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