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Lebowitz, Joel L.; Spohn, Herbert

doi:10.1023/a:1004589714161

Cited by 1,335 publications

(1,788 citation statements)

References 43 publications

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“…Open, driven chemical and molecular systems far from chemical equilibrium have been studied from several different points of view in statistical physics. In terms of stochastic processes, these investigations include "nonequilibrium potentials" [1,4,5], "dissipative structures" [36], "cycle kinetics" [16,37,38], "Brownian motors" [39,16], "stochastic resonance" [40], and "fluctuation theorems" [11,12,15,18]. The result we obtain in this work, in terms of a Jarzynski-type equality, clearly demonstrates an intimate connection between the fluctuation theorems and the nonequilibrium potentials.…”

Section: Discussionsupporting

confidence: 62%

“…FTs were first developed in the context of microcanonical chaotic dynamical systems [9,10]. It has also been studied in parallel for stochastic canonical dynamics [11,12]. In this paper, we first present our results via a simple example: a 3-state, driven cyclic reaction widely found in biochemistry.…”

Section: Introductionmentioning

confidence: 99%

“…(Though seldomly it has been presented in this way.) To introduce the new results from the recent work on FTs [11,12,15], we first define the irreversible heat dissipation following a stochastic trajectory in a NESS, Q irr (t).…”

Section: Introductionmentioning

confidence: 99%

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Nonequilibrium Potential Function of Chemically Driven Single Macromolecules via Jarzynski-Type Log-Mean-Exponential Heat

Qian

2005

J. Phys. Chem. B

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Applying the method from recently developed fluctuation theorems to the stochastic dynamics of single macromolecules in ambient fluid at constant temperature, we establish two Jarzynski-type equalities: (1) between the log-mean-exponential (LME) of the irreversible heat dissiption of a driven molecule in nonequilibrium steady-state (NESS) and ln P ness (x), and (2) between the LME of the work done by the internal force of the molecule and nonequilibrium chemical potential function µ ness (x) ≡ U(x) + k B T ln P ness (x), where P ness (x) is the NESS probability density in the phase space of the macromolecule and U(x) is its internal potential function. Ψ = µ ness (x)P ness (x)dx is shown to be a nonequilibrium generalization of the Helmholtz free energy and ∆Ψ = ∆U−T ∆S for nonequilibrium processes, where S = −k B P (x) ln P (x)dx is the Gibbs entropy associated with P (x). LME of heat dissipation generalizes the concept of entropy, and the equalities define thermodynamic potential functions for open systems far from equilibrium.

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Section: Discussionsupporting

confidence: 62%

Section: Introductionmentioning

confidence: 99%

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Nonequilibrium Potential Function of Chemically Driven Single Macromolecules via Jarzynski-Type Log-Mean-Exponential Heat

Qian

2005

J. Phys. Chem. B

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“…These intriguing "symmetries" appear as a consequence of the invariance under time reversal of the underlying microscopic dynamics. These and other recent results [5][6][7][8][9][10][11][12][13][14] are however restricted to nonequilibrium "conservative" systems characterized by currents.…”

Section: Introductionmentioning

confidence: 64%

“…A classical example is the fluctuation-dissipation theorem, which relates the linear response of a system to an external perturbation to the fluctuation properties of the system in thermal equilibrium [2,3]. More recently, the investigation of general properties of fluctuations in nonequilibrium steady states is opening new paths for understanding physics far from equilibrium [4][5][6][7][8][9][10][11][12][13][14]. The study of fluctuation statistics of macroscopic observables provides an alternative path to obtain thermodynamic potentials, a complementary approach to the usual ensemble description.…”

Section: Introductionmentioning

confidence: 99%

Renormalized time scale for anticipating and lagging synchronization

2016

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We consider fluctuations of the dissipated energy in nonlinear driven diffusive systems subject to bulk dissipation and boundary driving. With this aim, we extend the recently-introduced macroscopic fluctuation theory to nonlinear driven dissipative media, starting from the fluctuating hydrodynamic equations describing the system mesoscopic evolution. Interestingly, the action associated to a path in mesoscopic phase-space, from which large-deviation functions for macroscopic observables can be derived, has the same simple form as in non-dissipative systems. This is a consequence of the quasi-elasticity of microscopic dynamics, required in order to have a nontrivial competition between diffusion and dissipation at the mesoscale. Euler-Lagrange equations for the optimal density and current fields that sustain an arbitrary dissipation fluctuation are also derived. A perturbative solution thereof shows that the probability distribution of small fluctuations is always gaussian, as expected from the central limit theorem. On the other hand, strong separation from the gaussian behavior is observed for large fluctuations, with a distribution which shows no negative branch, thus violating the Gallavotti-Cohen fluctuation theorem as expected from the irreversibility of the dynamics. The dissipation large-deviation function exhibits simple and general scaling forms for weakly and strongly dissipative systems, with large fluctuations favored in the former case but heavily supressed in the latter. We apply our results to a general class of diffusive lattice models for which dissipation, nonlinear diffusion and driving are the key ingredients. The theoretical predictions are compared to extensive numerical simulations of the microscopic models, and excellent agreement is found. Interestingly, the large-deviation function is in some cases non-convex beyond some dissipation. These results show that a suitable generalization of macroscopic fluctuation theory is capable of describing in detail the fluctuating behavior of nonlinear driven dissipative media.

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Entangled signal pathways can both control expression stability and induce stochastic focusing

Wang

Liu

2018

FEBS Letters

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Gene transcription is often controlled by multiple interacting signal pathways, but how these pathways impact gene expression is not fully understood. Here, we refine a mechanic model based on experiments in murine embryonic stem cells and analyze the influence of pathway-pathway cross-talk strength (CTS) on mRNA expression stability. We find that the CTS can tune this stability, depending on the manner of regulation. Furthermore, there is an optimal CTS such that the expression pattern is most stable but free energy consumption is at its highest; the CTS can induce stochastic focusing of the mRNA level but this is at the cost of energy. In both cases, there is a cross-talk-mediated trade-off, implying that entangled signal pathways can control both expression stability and energy dissipation.

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Cited by 1,335 publications

References 43 publications

Nonequilibrium Potential Function of Chemically Driven Single Macromolecules via Jarzynski-Type Log-Mean-Exponential Heat

Nonequilibrium Potential Function of Chemically Driven Single Macromolecules via Jarzynski-Type Log-Mean-Exponential Heat

Renormalized time scale for anticipating and lagging synchronization

Entangled signal pathways can both control expression stability and induce stochastic focusing

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