Density operators that extremize Tsallis entropy and thermal stability effects |
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| Institution: | 1. E.E.C.S., University of Michigan, USA;2. L.I.S., Grenoble, France;3. National University La Plata and Argentina''s CONICET C. C. 727, 1900 La Plata, Argentina;1. Department of Mathematical Sciences, University of Bath, Claverton Down, Bath, BA2 7AY, UK;2. Numerical Analysis and Applied Mathematics Section, KU Leuven, Celestijnenlaan 200a, Box 2402, 3001 Heverlee, Leuven, Belgium;1. School of Mathematics, Cardiff University, Senghennydd Road, Cardiff CF244AG, UK;2. Department of Mathematics, J.J. Strossmayer University of Osijek, Trg Ljudevita Gaja 6, HR-31000 Osijek, Croatia;3. 619 Red Cedar Road, Department of Statistics and Probability, Michigan State University East Lansing, MI 48824, USA;1. College of Economics, Hangzhou Dianzi University, Hangzhou, 310018, China;2. Department of Mathematics, Zhejiang University, Hangzhou, 310027, China |
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| Abstract: | Quite general, analytical (both exact and approximate) forms for discrete probability distributions (PDs) that maximize Tsallis entropy for a fixed variance are here investigated. They apply, for instance, in a wide variety of scenarios in which the system is characterized by a series of discrete eigenstates of the Hamiltonian. Using these discrete PDs as “weights” leads to density operators of a rather general character. The present study allows one to vividly exhibit the effects of non-extensivity. Varying Tsallis’ non-extensivity index q one is seen to pass from unstable to stable systems and even to unphysical situations of infinite energy. |
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