[en] The majority vote model is one of the simplest opinion systems yielding distinct phase transitions and has garnered significant interest in recent years. This model, as well as many other stochastic lattice models, are formulated in terms of stochastic rules with no connection to thermodynamics, precluding the achievement of quantities such as power and heat, as well as their behaviors at phase transition regimes. Here, we circumvent this limitation by introducing the idea of a distinct and well-defined thermal reservoir associated to each local configuration. Thermodynamic properties are derived for a generic majority vote model, irrespective of its neighborhood and lattice topology. The behavior of energy/heat fluxes at phase transitions, whether continuous or discontinuous, in regular and complex topologies, is investigated in detail. Unraveling the contribution of each local configuration explains the nature of the phase diagram and reveals how dissipation arises from the dynamics.
Disciplines :
Physics
Author, co-author :
Hawthorne, Felipe; Instituto de Física, Universidade de São Paulo, Rua do Matão, 1371, São Paulo 05508-090, SP, Brazil
HARUNARI, Pedro ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS)
de Oliveira, Mário J; Instituto de Física, Universidade de São Paulo, Rua do Matão, 1371, São Paulo 05508-090, SP, Brazil
Fiore, Carlos E; Instituto de Física, Universidade de São Paulo, Rua do Matão, 1371, São Paulo 05508-090, SP, Brazil
External co-authors :
yes
Language :
English
Title :
Nonequilibrium Thermodynamics of the Majority Vote Model.
Publication date :
18 August 2023
Journal title :
Entropy
eISSN :
1099-4300
Publisher :
Multidisciplinary Digital Publishing Institute (MDPI), Switzerland
This work has received the financial support from FAPESP under grant 2021/03372-2. The financial supports from Brazilian agencies CAPES and CNPq are also acknowledged.
Castellano C. Fortunato S. Loreto V. Statistical physics of social dynamics Rev. Mod. Phys. 2009 81 591 10.1103/RevModPhys.81.591
de Oliveira M.J. Isotropic majority-vote model on a square lattice J. Stat. Phys. 1992 66 273 281 10.1007/BF01060069
Pereira L.F. Moreira F.B. Majority-vote model on random graphs Phys. Rev. E 2005 71 016123 10.1103/PhysRevE.71.016123 15697674
Chen H. Shen C. He G. Zhang H. Hou Z. Critical noise of majority-vote model on complex networks Phys. Rev. E 2015 91 022816 10.1103/PhysRevE.91.022816
Vieira A.R. Crokidakis N. Phase transitions in the majority-vote model with two types of noises Phys. A Stat. Mech. Its Appl. 2016 450 30 36 10.1016/j.physa.2016.01.013
Encinas J. Chen H. de Oliveira M.M. Fiore C.E. Majority vote model with ancillary noise in complex networks Phys. A Stat. Mech. Its Appl. 2019 516 563 570 10.1016/j.physa.2018.10.055
Brunstein A. Tomé T. Universal behavior in an irreversible model with C3v symmetry Phys. Rev. E 1999 60 3666 3669 10.1103/PhysRevE.60.3666
Chen H. Shen C. Zhang H. Li G. Hou Z. Kurths J. First-order phase transition in a majority-vote model with inertia Phys. Rev. E 2017 95 042304 10.1103/PhysRevE.95.042304
Harunari P.E. de Oliveira M. Fiore C.E. Partial inertia induces additional phase transition in the majority vote model Phys. Rev. E 2017 96 042305 10.1103/PhysRevE.96.042305
Encinas J.M. Harunari P.E. de Oliveira M. Fiore C.E. Fundamental ingredients for discontinuous phase transitions in the inertial majority vote model Sci. Rep. 2018 8 9338 10.1038/s41598-018-27240-4
Encinas J.M. Fiore C.E. Influence of distinct kinds of temporal disorder in discontinuous phase transitions Phys. Rev. E 2021 103 032124 10.1103/PhysRevE.103.032124 33862793
Crochik L. Tomé T. Entropy production in the majority-vote model Phys. Rev. E 2005 72 057103 10.1103/PhysRevE.72.057103 16383793
Noa C.F. Harunari P.E. de Oliveira M. Fiore C. Entropy production as a tool for characterizing nonequilibrium phase transitions Phys. Rev. E 2019 100 012104 10.1103/PhysRevE.100.012104
Tomé T. de Oliveira M.J. Entropy production in irreversible systems described by a Fokker-Planck equation Phys. Rev. E 2010 82 021120 10.1103/PhysRevE.82.021120
Esposito M. Stochastic thermodynamics under coarse graining Phys. Rev. E 2012 85 041125 10.1103/PhysRevE.85.041125 22680437
Seifert U. Stochastic thermodynamics, fluctuation theorems and molecular machines Rep. Prog. Phys. 2012 75 126001 10.1088/0034-4885/75/12/126001
Tomé T. de Oliveira M.J. Stochastic approach to equilibrium and nonequilibrium thermodynamics Phys. Rev. E 2015 91 042140 10.1103/PhysRevE.91.042140
Schnakenberg J. Network theory of microscopic and macroscopic behavior of master equation systems Rev. Mod. Phys. 1976 48 571 10.1103/RevModPhys.48.571
Tomé T. Fiore C.E. de Oliveira M.J. Stochastic thermodynamics of opinion dynamics Phys. Rev. E 2023 107 064135 10.1103/PhysRevE.107.064135
Landau D. Binder K. A Guide to Monte Carlo Simulations in Statistical Physics Cambridge University Press Cambridge, UK 2021
Fiore C.E. Carneiro C.E.I. Obtaining pressure versus concentration phase diagrams in spin systems from Monte Carlo simulations Phys. Rev. E 2008 76 021118 10.1103/PhysRevE.76.021118
de Oliveira M.M. da Luz M.G.E. Fiore C.E. Generic finite size scaling for discontinuous nonequilibrium phase transitions into absorbing states Phys. Rev. E 2015 92 062126 10.1103/PhysRevE.92.062126 26764651
de Oliveira M.M. da Luz M.G.E. Fiore C.E. Finite-size scaling for discontinuous nonequilibrium phase transitions Phys. Rev. E 2018 97 060101 10.1103/PhysRevE.97.060101 30011570
Goes B.O. Fiore C.E. Landi G.T. Quantum features of entropy production in driven-dissipative transitions Phys. Rev. Res. 2020 2 013136 10.1103/PhysRevResearch.2.013136
Seara D.S. Machta B.B. Murrell M.P. Irreversibility in dynamical phases and transitions Nat. Commun. 2021 12 392 10.1038/s41467-020-20281-2 33452238
Martynec T. Klapp S.H. Loos S.A. Entropy production at criticality in a nonequilibrium Potts model New J. Phys. 2020 22 093069 10.1088/1367-2630/abb5f0
Aguilera M. Moosavi S.A. Shimazaki H. A unifying framework for mean-field theories of asymmetric kinetic Ising systems Nat. Commun. 2021 12 1197 10.1038/s41467-021-20890-5
Hanggi P. Grabert H. Talkner P. Thomas H. Bistable systems: Master equation versus Fokker-Planck modeling Phys. Rev. A 1984 29 371 10.1103/PhysRevA.29.371
Fiore C.E. Harunari P.E. Noa C.E.F. Landi G.T. Current fluctuations in nonequilibrium discontinuous phase transitions Phys. Rev. E 2021 104 064123 10.1103/PhysRevE.104.064123
Nguyen B. Seifert U. Exponential volume dependence of entropy-current fluctuations at first-order phase transitions in chemical reaction networks Phys. Rev. E 2020 102 022101 10.1103/PhysRevE.102.022101
Herpich T. Thingna J. Esposito M. Collective Power: Minimal Model for Thermodynamics of Nonequilibrium Phase Transitions Phys. Rev. X 2018 8 031056 10.1103/PhysRevX.8.031056
Van den Broeck C. Esposito M. Ensemble and trajectory thermodynamics: A brief introduction Phys. A Stat. Mech. Its Appl. 2015 418 6 16 10.1016/j.physa.2014.04.035
Yeomans J.M. Statistical Mechanics of Phase Transitions Clarendon Press Oxford, UK 1992
Jarzynski C. Nonequilibrium equality for free energy differences Phys. Rev. Lett. 1997 78 2690 10.1103/PhysRevLett.78.2690
