Title: Landscape and Flux Theory of Nonequilibrium Physical and Biological Systems
Abstract: We will review our recent efforts on establishing a landscape and flux theory for nonequilibrium open systems. We pointed out that equilibrium dynamics is determined by one driving force which is the gradient of the equilibrium interaction potential energy while nonequilibrium dynamics is determined by a dual force pair of gradient of gradient of the nonequilibrium potential landscape and the steady state probability flux. The steady state probability flux has a rotational curl nature and gives the measure of the nonequilibriumness in terms of the degree of detailed balance breaking. An analogy of the equilibrium dynamics is as electrons moving in an electric field while nonequilibrium dynamics is as an electron moving in an electric and a magnetic field. The additional flux force for nonequilibrium dynamics also makes significant modifications the transition state theory, optimal kinetic paths, thermodynamics, fluctuation-dissipation and statistical fluctuations. The landscape and flux theory has many physical and biological applications including: single molecule enzyme dynamics, genetic switch, signal transduction, cell cycle, stem cell differentiation and development, cancer, immune systems, ageing, brain function and neural network dynamics, ecology, evolution, game theory, economy, chaos, turbulence, information systems, nonequilibrium quantum dynamics and transport, long quantum coherence of the photosynthetic energy transfer. The landscape and flux theory has recently been tested in the experiments.
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