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SUMMARY:Group Entropies: functionals on probability spaces\, state space g
 rowth rates\, energy\, and connections to thermodynamics - Prof. Henrik Je
 ldtoft Jensen\, Imperial College London
DTSTART:20260211T140000Z
DTEND:20260211T150000Z
UID:TALK239707@talks.cam.ac.uk
CONTACT:Ramji Venkataramanan
DESCRIPTION:The group entropies introduced by Piergiulio Tempesta [1] offe
 r a systematic axiomatic\napproach to entropies\, considered as functional
 s on probability spaces. Beside of satisfying\nthe axiomatic group structu
 re functionals are also required to be extensive for the relevant\nasympto
 tic behaviour of W(N)\, the number of allowed microstates of the system co
 nsisting\nof N constituents. In this way entropies fall into different cla
 sses determined by W(N). For\nexponential W(N) ~ exp(N)\, the group entrop
 ies reduce to either the Boltzmann or the Rényi\nentropy. Sub-exponential
  W(N) leads to the Tsallis q-entropy and super-exponential to new\nentropi
 es. The latter case has\, e.g.\, been suggested to be relevant to the ther
 modynamics of\nblack holes [2]. It is interesting to note that the maximum
  entropy principle leads to q-\nexponential probability distributions for 
 all cases of W(N)\, even when the entropy is different\nfrom the Tsallis e
 ntropy[3].\nThe group entropies are directly relevant to information theor
 y for instance when applying\nthe approach of permutation entropies to tim
 e series where the number of patterns easily\ngrows faster than exponentia
 l as a function of the length of the time series [4].\nTurning to thermody
 namics\, we will want to relate the group entropies to Clausius entropy\n(
 defined in terms of heat exchange) and to derive the first law of thermody
 namics. We will\nfurther discuss thermodynamics equilibrium conditions for
  systems described by group\nentropies.\nReferences\n[1] P. Tempesta\, Gro
 up entropies\, correlation laws\, and zeta functions. Phys. Rev. E 84\,\n0
 21121 (2011).\n[2] H.J. Jensen and P. Tempesta\, Group Entropies as a Foun
 dation for Entropies\, Entropy\n26\, 266 (2024).\n[3] Constantino Tsallis\
 , Henrik Jeldtoft Jensen\, Extensive composable entropy for the\nanalysis 
 of cosmological data. Phys. Lett. B\, 861\, 139238 (2025).\n[4] J M Amigó
 \, R Dale and Piergiulio Tempesta\, Permutation group entropy: A new route
  to\ncomplexity for real-valued processes\, Chaos 32\, 112101 (2022).
LOCATION:MR5\, CMS Pavilion A
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