Probability currents and entropy production in nonequilibrium lattice systems

Szabó, György; Tomé, Tânia; Borsos, István

doi:10.1103/physreve.82.011105

Cited by 25 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%

“…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%

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Evolutionary potential games on lattices

2016

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Game theory provides a general mathematical background to study the effect of pair interactions and evolutionary rules on the macroscopic behavior of multi-player games where players with a finite number of strategies may represent a wide scale of biological objects, human individuals, or even their associations. In these systems the interactions are characterized by matrices that can be decomposed into elementary matrices (games) and classified into four types. The concept of decomposition helps the identification of potential games and also the evaluation of the potential that plays a crucial role in the determination of the preferred Nash equilibrium, and defines the Boltzmann distribution towards which these systems evolve for suitable types of dynamical rules. This survey draws parallel between the potential games and the kinetic Ising type models which are investigated for a wide scale of connectivity structures. We discuss briefly the applicability of the tools and concepts of statistical physics and thermodynamics. Additionally the general features of ordering phenomena, phase transitions and slow relaxations are outlined and applied to evolutionary games. The discussion extends to games with three or more strategies. Finally we discuss what happens when the system is weakly driven out of the "equilibrium state" by adding non-potential components representing games of cyclic dominance.

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Section: Effects Of Matching Penniesmentioning

confidence: 97%

Section: Pure Nash Equilibia In Multi-player Gamesmentioning

confidence: 99%

Evolutionary potential games on lattices

2016

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“…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%

Entropy production and entropy extraction rates for a Brownian particle that walks in underdamped medium

Taye

2020

Phys. Rev. E

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The expressions for entropy production, free energy, and entropy extraction rates are derived for a Brownian particle that walks in an underdamped medium. Our analysis indicates that as long as the system is driven out of equilibrium, it constantly produces entropy at the same time it extracts entropy out of the system. At steady state, the rate of entropy productionėp balances the rate of entropy extractionḣ d. At equilibrium both entropy production and extraction rates become zero. The entropy production and entropy extraction rates are also sensitive to time. As time progresses, both entropy production and extraction rates increase in time and saturate to constant values. Moreover employing microscopic stochastic approach, several thermodynamic relations for different model systems are explored analytically and via numerical simulations by considering a Brownian particle that moves in overdamped medium. Our analysis indicates that the results obtained for underdamped cases quantitatively agree with overdamped cases at steady state. The fluctuation theorem is also discussed in detailed.

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“…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%