Potential and flux decomposition for dynamical systems and non-equilibrium thermodynamics: Curvature, gauge field, and generalized fluctuation-dissipation theorem

Feng, Haidong; Wang, Jin

doi:10.1063/1.3669448

Cited by 66 publications

(95 citation statements)

References 32 publications

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“…Although the established framework is useful for addressing the global natures of complex systems (2)(3)(4)(5)(6)(7)(8), it has been applied only to a single landscape and is not directly applicable for multiple coupled landscapes. However, the adiabatic and nonadiabatic treatment of multiple energy surfaces taking into account the multiple time scales applies for the Hamiltonian systems where the energy function is a prior known for individual surfaces but does not directly apply to the case where the underlying process is nonequilibrium in nature.…”

mentioning

confidence: 99%

Eddy current and coupled landscapes for nonadiabatic and nonequilibrium complex system dynamics

Zhang

Sasai

Wang

2013

Proc. Natl. Acad. Sci. U.S.A.

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Physical and biological systems are often involved with coupled processes of different time scales. In the system with electronic and atomic motions, for example, the interplay between the atomic motion along the same energy landscape and the electronic hopping between different landscapes is critical: the system behavior largely depends on whether the intralandscape motion is slower (adiabatic) or faster (nonadiabatic) than the interlandscape hopping. For general nonequilibrium dynamics where Hamiltonian or energy function is unknown a priori, the challenge is how to extend the concepts of the intra-and interlandscape dynamics. In this paper we establish a theoretical framework for describing global nonequilibrium and nonadiabatic complex system dynamics by transforming the coupled landscapes into a single landscape but with additional dimensions. On this single landscape, dynamics is driven by gradient of the potential landscape, which is closely related to the steadystate probability distribution of the enlarged dimensions, and the probability flux, which has a curl nature. Through an example of a self-regulating gene circuit, we show that the curl flux has dramatic effects on gene regulatory dynamics. The curl flux and landscape framework developed here are easy to visualize and can be used to guide further investigation of physical and biological nonequilibrium systems.nonequilibrium landscape | adiabaticity | nonadiabaticity H eterogeneity among coupled processes is a hallmark of complex behaviors of physical and biological systems. A photoexcited molecule, for example, may relax into different low-energy states depending on the difference among time scales of electronic and atomic motions. Molecular motors are fueled by ATP hydrolysis and move into the different structural states, where the heterogeneous distribution of time scales of reactions and structural changes should characterize the motor performance. Dynamical complexity owing to the interplay of heterogeneous processes with multiple time scales can give rise to rich phenomena.In a system having multiple time scales, some dynamical quantities may take discrete values whereas others are continuous. An example of such heterogeneity is found in the electron-transfer reaction, in which the electronic state is discrete and atomic motions are continuous (1). Then, the system can be represented by multiple electronic energy surfaces and the change in atomic positions is motion along individual surfaces. Complex behaviors of the system are explained by the combined process of intrasurface motion along the same and intersurface hopping between different electronic energy surface(s). If the intrasurface motion is slower (faster) than the intersurface hopping, the process is called adiabatic (nonadiabatic). We here extend this notion, the significance of adiabatic and nonadiabatic effects, beyond the Hamiltonian systems to general nonequilibrium problems. Indeed, important complex systems such as reaction networks, gene switches, and molecular motors are co...

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confidence: 99%

Eddy current and coupled landscapes for nonadiabatic and nonequilibrium complex system dynamics

Zhang

Sasai

Wang

2013

Proc. Natl. Acad. Sci. U.S.A.

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“…Even at the classical level, the classical master equation (CME) and Fokker-Plank diffusion equation approaches had been already successfully applied to en-ergy transport induced by adenosine triphosphate (ATP) hydrolysis in biochemical systems 30,31 . In particular, a potential and flux landscape theory for non-equilibrium system were developed for studying the global stability and function of the non-equilibrium systems 32,33 . The non-equilibrium systems can be globally quantified by the steady state probability landscape (or population landscape).…”

Section: Introductionmentioning

confidence: 99%

Curl flux, coherence, and population landscape of molecular systems: Nonequilibrium quantum steady state, energy (charge) transport, and thermodynamics

Zhang

Wang

2014

The Journal of Chemical Physics

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We established a theoretical framework in terms of the curl flux, population landscape and coherence for non-equilibrium quantum systems at steady state, through exploring the energy and charge transport in molecular processes. The curl quantum flux plays the key role in determining transport properties and the system reaches equilibrium when flux vanishes. The novel curl quantum flux reflects the degree of nonequilibriumness and the time-irreversibility. We found an analytical expression for the quantum flux and its relationship to the environmental pumping (non-equilibriumness quantified by the voltage away from the equilibrium) and the quantum tunnelling. Furthermore, we investigated another quantum signature, the coherence, quantitatively measured by the non-zero off diagonal element of the density matrix. Populations of states give the probabilities of individual states and therefore quantify the population landscape. Both curl flux and coherence depend on steady state population landscape. Besides the environment-assistance which can give dramatic enhancement of coherence and quantum flux with high voltage at a fixed tunnelling strength, the quantum flux is promoted by the coherence in the regime of small tunnelling while reduced by the coherence in the regime of large tunneling, due to the non-monotonic relationship between the coherence and tunneling. This is in contrast to the previously found linear relationship. For the systems coupled to bosonic (photonic and phononic) reservoirs the flux is significantly promoted at large voltage while for fermionic (electronic) reservoirs the flux reaches a saturation after a significant enhancement at large voltage due to the Pauli exclusion principle. In view of the system as a quantum heat engine, we studied the nonequilibrium thermodynamics and established the analytical connections of curl quantum flux to the transport quantities such as energy (charge) transfer efficiency (ETE or CTE), chemical reaction efficiency (CRE), energy dissipation, heat and electric currents observed in the experiments. We observed a perfect transfer efficiency in chemical reactions at high voltage (chemical potential difference). Our theoretical predicted behavior of the electric current with respect to the voltage is in good agreements with the recent experiments on electron transfer in single molecules.

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“…In equilibrium systems, fluctuations and responses are related by the fluctuation-dissipation theory. In nonequilibrium steady states, however, this relation fails to hold and must be modified [16,[30][31][32][33][34]. Therefore, in order to fully understand the nature of fluctuations in orientation under shear flow, the fluctuations should be observed directly, say, with the dynamic light scattering technique for nematic liquid crystals.…”

Section: Discussionmentioning

confidence: 99%

Influence of shear flow on the linear response of a nematic liquid crystal to external electric fields

et al. 2012

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We have investigated the linear response of shear stress to ac electric fields under shear flow in a nematic liquid crystal. The experimental results were compared with the theoretical results derived from the Ericksen-Leslie theory. Although close agreement was obtained at low shear rates, discrepancies were observed at high shear rates. By introducing a two-mode coupling model the experimental results were well reproduced for the entire range of shear rates, and nonconservative forces were found to play an important role in determining the fluctuation dynamics, which is a characteristic of nonequilibrium steady states.

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Potential and flux decomposition for dynamical systems and non-equilibrium thermodynamics: Curvature, gauge field, and generalized fluctuation-dissipation theorem

Cited by 66 publications

References 32 publications

Eddy current and coupled landscapes for nonadiabatic and nonequilibrium complex system dynamics

Eddy current and coupled landscapes for nonadiabatic and nonequilibrium complex system dynamics

Curl flux, coherence, and population landscape of molecular systems: Nonequilibrium quantum steady state, energy (charge) transport, and thermodynamics

Influence of shear flow on the linear response of a nematic liquid crystal to external electric fields

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