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CATEGORIES:Information Theory Seminar
SUMMARY:Group Entropies: functionals on probability spaces
 \, state space growth rates\, energy\, and connect
 ions to thermodynamics - Prof. Henrik Jeldtoft Jen
 sen\, Imperial College London
DTSTART;TZID=Europe/London:20260211T140000
DTEND;TZID=Europe/London:20260211T150000
UID:TALK239707AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/239707
DESCRIPTION:The group entropies introduced by Piergiulio Tempe
 sta [1] offer a systematic axiomatic\napproach to 
 entropies\, considered as functionals on probabili
 ty spaces. Beside of satisfying\nthe axiomatic gro
 up structure functionals are also required to be e
 xtensive for the relevant\nasymptotic behaviour of
  W(N)\, the number of allowed microstates of the s
 ystem consisting\nof N constituents. In this way e
 ntropies fall into different classes determined by
  W(N). For\nexponential W(N) ~ exp(N)\, the group 
 entropies reduce to either the Boltzmann or the Ré
 nyi\nentropy. Sub-exponential W(N) leads to the Ts
 allis q-entropy and super-exponential to new\nentr
 opies. The latter case has\, e.g.\, been suggested
  to be relevant to the thermodynamics of\nblack ho
 les [2]. It is interesting to note that the maximu
 m entropy principle leads to q-\nexponential proba
 bility distributions for all cases of W(N)\, even 
 when the entropy is different\nfrom the Tsallis en
 tropy[3].\nThe group entropies are directly releva
 nt to information theory for instance when applyin
 g\nthe approach of permutation entropies to time s
 eries where the number of patterns easily\ngrows f
 aster than exponential as a function of the length
  of the time series [4].\nTurning to thermodynamic
 s\, we will want to relate the group entropies to 
 Clausius entropy\n(defined in terms of heat exchan
 ge) and to derive the first law of thermodynamics.
  We will\nfurther discuss thermodynamics equilibri
 um conditions for systems described by group\nentr
 opies.\nReferences\n[1] P. Tempesta\, Group entrop
 ies\, correlation laws\, and zeta functions. Phys.
  Rev. E 84\,\n021121 (2011).\n[2] H.J. Jensen and 
 P. Tempesta\, Group Entropies as a Foundation for 
 Entropies\, Entropy\n26\, 266 (2024).\n[3] Constan
 tino Tsallis\, Henrik Jeldtoft Jensen\, Extensive 
 composable entropy for the\nanalysis of cosmologic
 al data. Phys. Lett. B\, 861\, 139238 (2025).\n[4]
  J M Amigó\, R Dale and Piergiulio Tempesta\, Perm
 utation group entropy: A new route to\ncomplexity 
 for real-valued processes\, Chaos 32\, 112101 (202
 2).
LOCATION:MR5\, CMS Pavilion A
CONTACT:Prof. Ramji Venkataramanan
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