Open Access
Research Article
Weighted Equilibrium States at Zero Temperature
*ALEJANDRO MESÓNCorresponding authormeson@iflysib.unlp.edu.arConicet–Unlp and Grupo De Aplicaciones Matemáticas Y Estadísticas, De La Facultad De Ingeniería (Gamefi) UnlpInstituto De Física De Líquidos Y Sistemas Biológicos (IFLYSIB)La Plata, ArgentinaView full profile → , FERNANDO VERICATvericat@iflysib.unlp.edu.arConicet–Unlp and Grupo De Aplicaciones Matemáticas Y Estadísticas, De La Facultad De Ingeniería (Gamefi) UnlpInstituto De Física De Líquidos Y Sistemas Biológicos (IFLYSIB)La Plata, ArgentinaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 05 Sep 2020
- Accepted:
- 03 Nov 2020
- Published Online:
- 07 Jan 2021
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- 1726037X.2020.1856340
- Pages:
- 241–259
Abstract
Weighted thermodynamic and multifractal formalism for finite alphabet subshifts have been presented by Barral and Feng (Asian J. Math, 16, 319–352, 2012). Here we analyze the problem of finding weighted equilibrium states for infinite countable shifts. Also we study the problem of ”zero temperature” which consists into consider a sequence of equilibrium states depending of a parameter, interpreted in a Statistical Mechanics context as ”the inverse of the temperature”, and prove the existence of accumulation points of such a sequence.
Keywords
Subject Classifications
37D3537B1037A35
References
- J.Barral and D.J.Feng, Weighted thermodynamic formalism on subshifts and applications . , , 319 – 352 ( 2012 ). doi: 10.4310/AJM.2012.v16.n2.a8
- P.Billingsley, Convergence of Probability Measures ( John Wiley & Sons , New York, 1999 ).
- R.Bowen, Topological entropy for non-compact sets , ., , 125 - 136 ( 1973 ). doi: 10.1090/S0002-9947-1973-0338317-X
- D. J.Feng and W.Huang, Variational principle for the weighted topological pressure . . , 411 – 452 ( 2016 ). doi: 10.1016/j.matpur.2016.02.016
- D. J.Feng, Equilibrium states for factor maps between subshifts , ., , 2470 – 2502 ( 2011 ). doi: 10.1016/j.aim.2010.09.012
- R.Freire and V.Vargas, Equilibrium states and zero temperature limits topologically transitive countable Markov shifts, , , , 8451 – 8465 ( 2018 ).
- B. M.Gurevich, Topological entropy for denumerable Markov chains , Dokl. Akad. Nauk SSSR , , 715 – 718 , ( 1969 ) in Russian. English translation: Soviet Math. Dokl, , 911–915, (1969) .
- O.Jenkinson, R. D.Mauldin and M.Urbanski, Zero temperature limits of Gibbs-equilibrium states for countable alphabet subshifts of finite type,11 . , 765 – 776 ( 2005 ). doi: 10.1007/s10955-005-3035-z
- T.Kempton, Zero temperature limits of Gibbs equilibrium states for countable Markov shifts , . , 795 – 806 ( 2011 ). doi: 10.1007/s10955-011-0195-x
- R.Leplaideur, A dynamical proof for the convergence of Gibbs measures at temperature zero , Nonlinearity , 2847 – 2880 ( 2005 ). doi: 10.1088/0951-7715/18/6/023
- R. DMauldin and MUrbanski, Gibbs states on the symbolic space over an infinite alphabet , Israel J. Math . , 93 – 130 ( 2001 ). doi: 10.1007/BF02773377
- A.M.Mesón and F.Vericat, Weighted multifractal spectrum of statistics , (in the press).
- I. D.Morris, Entropy for zero-temperature limits of Gibbs-equilibrium states for countablealphabet subshifts of finite type , . , 315 – 324 ( 2007 ). doi: 10.1007/s10955-006-9215-7
- O. M.Sarig, Thermodynamic formalism for countable Markov shifts, . , 1565 – 1593 ( 1999 ).
- C.Zhao, E.Chen, X.Zhou and X.Yin, Weighted Topological Entropy of the Set of Generic Points in Topological Dynamical Systems , , 937 – 955 ( 2018 ). doi: 10.1007/s10884-017-9575-5
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