2010
DOI: 10.1103/physreve.82.011105
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Probability currents and entropy production in nonequilibrium lattice systems

Abstract: The structure of probability currents is studied for the dynamical network after consecutive contraction on two-state, nonequilibrium lattice systems. This procedure allows us to investigate the transition rates between configurations on small clusters and highlights some relevant effects of lattice symmetries on the elementary transitions that are responsible for entropy production. A method is suggested to estimate the entropy production for different levels of approximations (cluster sizes) as demonstrated … Show more

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Cited by 26 publications
(22 citation statements)
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“…In this way we can deduce two approximate results for the specific entropy production (I/N ) and comparison of them indicates the relevance of the second neighbors although they do not influence directly the transition in the present models. Evidently, the larger the neighborhood, the more accurate is the present approach (for a more detailed description of this approach see [92]). Figure 37 shows the Monte Carlo results for the specific entropy production when varying the noise level for different strengths of the matching pennies component.…”
Section: Effects Of Matching Penniesmentioning
confidence: 97%
See 1 more Smart Citation
“…In this way we can deduce two approximate results for the specific entropy production (I/N ) and comparison of them indicates the relevance of the second neighbors although they do not influence directly the transition in the present models. Evidently, the larger the neighborhood, the more accurate is the present approach (for a more detailed description of this approach see [92]). Figure 37 shows the Monte Carlo results for the specific entropy production when varying the noise level for different strengths of the matching pennies component.…”
Section: Effects Of Matching Penniesmentioning
confidence: 97%
“…Regardless of the connectivity structure, the multi-agent systems have 2 N microscopic states (s) if all the pair interactions are characterized by a 2 × 2 game. Furthermore, if the possible transitions between two microscopic states are limited to those s → s ′ where only one player modifies her strategy (e.g., s x → s ′ x ) then the dynamical graph can be represented by an N -dimensional hypercube [41,92]. Such a dynamical graph is shown (for N = 4) in Fig.…”
Section: Pure Nash Equilibia In Multi-player Gamesmentioning
confidence: 99%
“…In the next sections we show that indeed Eqs. (8) and (16) as well Eqs. (9) and (15) agree as long as a periodic boundary condition is imposed.…”
Section: Free Energy and Entropy Productionmentioning
confidence: 98%
“…an expression that has been considered by several authors [10][11][12][13][14][15][16][17][18][19][20][21][22] and has a close relationship with the fluctuation theorems of Gallavotti and Cohen [23] and with the Jarzynski equality [24,25]. It is nonnegative because each term in the summation is of the form ðx À yÞ lnðx=yÞ and vanishes in equilibrium, that is, when microscopic reversibility or detailed balance condition is obeyed.…”
Section: Entropy Production In Nonequilibrium Systems At Stationary Smentioning
confidence: 99%