Stochastic mechanics of nonequilibrium systems

Tomé, Tânia; Oliveira, Mário J. de

doi:10.1590/s0103-97331997000400016

Cited by 6 publications

(8 citation statements)

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“…This expression has been obtained before [15] by means of a similar reasoning. Using a reasoning similar to those used before we can write this expression as…”

Section: U(t) = E(x)p(xt)dxmentioning

confidence: 83%

Entropy production in nonequilibrium systems described by a Fokker-Planck equation

Tomé¹

2006

Braz. J. Phys.

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163

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We study the entropy production in nonequilibrium systems described by a Fokker-Planck equation. We have devised an expression for the entropy flux in the stationary state. We have found that the entropy flux can be written as an ensemble average of an expression containing the force and its derivative. This result is similar to the one used by Lebowitz and Spohn for system following a Markovian process in discrete space. We have also been able to obtain a fluctuation-dissipation type relation between the dissipated power, which was written as an ensemble average, and the production of entropy for the case of systems in contact with one heat bath. We have applied the results for a simple model for particles subjected to dissipative forces.

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“…This expression has been obtained before [15] by means of a similar reasoning. Using a reasoning similar to those used before we can write this expression as…”

Section: U(t) = E(x)p(xt)dxmentioning

confidence: 83%

Entropy production in nonequilibrium systems described by a Fokker-Planck equation

Tomé¹

2006

Braz. J. Phys.

Self Cite

100

163

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“…(see Supplementary Information) [68][69][70], where we replaced time averages [...] = 1/t t 0 dt... by ensemble averages . .…”

Section: Simplified Maxepp For Nonequilibrium Steady Statesmentioning

confidence: 99%

Entropy production selects nonequilibrium states in multistable systems

Endres

2017

Sci Rep

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Far-from-equilibrium thermodynamics underpins the emergence of life, but how has been a long-outstanding puzzle. Best candidate theories based on the maximum entropy production principle could not be unequivocally proven, in part due to complicated physics, unintuitive stochastic thermodynamics, and the existence of alternative theories such as the minimum entropy production principle. Here, we use a simple, analytically solvable, one-dimensional bistable chemical system to demonstrate the validity of the maximum entropy production principle. To generalize to multistable stochastic system, we use the stochastic least-action principle to derive the entropy production and its role in the stability of nonequilibrium steady states. This shows that in a multistable system, all else being equal, the steady state with the highest entropy production is favored, with a number of implications for the evolution of biological, physical, and geological systems.

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“…(14), (15), (16), and (17), we deduce the joint transition probabilities w(σ i ; τ i |σ i−i , σ i+1 ; τ i−1 , τ i+1 ) that the site i of the system and the replica assume the values σ i and τ i , respectively. The resultant joint transition probabilities are displayed in Table 2 and are valid for 0 ≤ a ≤ p. For p < a ≤ 1, the algorithm yields a joint transition probability which is independent of a and is the one that results by formally replacing, in Table 2, a by p. The joint transition probability fulfill the following properties…”

Section: Coupled Systemmentioning

confidence: 99%

“…The update was done in a synchronized way by using the algorithm defined by Eqs. (14), (15), (16), and (17), with the same random number for both lattices. The density of damages Ψ(t), obtained by taking the averages over 2000 samples, were collected from t = 1 to t = 1500 Monte Carlo steps.…”

Section: Numerical Simulationsmentioning

confidence: 99%

Stochastic dynamics of coupled systems and damage spreading

et al. 2003

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We study the damage spreading in the one-dimensional Ising model by means of the stochastic dynamics resulting from coupling the system and its replica by a family of algorithms that interpolate between the heat bath and the Hinrichsen-Domany algorithms. At high temperatures the dynamics is exactly mapped to the DomanyKinzel probabilistic cellular automaton. Using a mean-field approximation and Monte Carlo simulations we find the critical line that separates the phase where the damage spreads from the one where it does not.

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Stochastic mechanics of nonequilibrium systems

Cited by 6 publications

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Entropy production in nonequilibrium systems described by a Fokker-Planck equation

Entropy production in nonequilibrium systems described by a Fokker-Planck equation

Entropy production selects nonequilibrium states in multistable systems

Stochastic dynamics of coupled systems and damage spreading

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