2 2 A pr 2 01 4 Non - equilibrium Lyapunov function and a fluctuation relation for stochastic systems : Poisson representation approach
نویسنده
چکیده
We present a statistical physics framework for description of nonlinear non-equilibrium stochastic processes, modeled via chemical master equation, in the weak-noise limit. Using the Poisson representation approach and applying the large-deviation principle we first solve the master equation. Then we use the notion of the non-equilibrium free energy to derive an integral fluctuation relation for nonlinear non-equilibrium systems under feedback control. We point out that the free energy as well as some functionals can serve as non-equilibrium Lyapunov function which has an important property to decay to its minimal value monotonously at all times. The Poisson representation technique is illustrated via exact stochastic treatment of biophysical processes, such as bacterial chemosensing and molecular evolution.
منابع مشابه
Extension of Higher Order Derivatives of Lyapunov Functions in Stability Analysis of Nonlinear Systems
The Lyapunov stability method is the most popular and applicable stability analysis tool of nonlinear dynamic systems. However, there are some bottlenecks in the Lyapunov method, such as need for negative definiteness of the Lyapunov function derivative in the direction of the system’s solutions. In this paper, we develop a new theorem to dispense the need for negative definite-ness of Lyapunov...
متن کامل[hal-00782034, v1] Learning Equilibria in Games by Stochastic Distributed Algorithms
We consider a class of fully stochastic and fully distributed algorithms, that we prove to learn equilibria in games. Indeed, we consider a family of stochastic distributed dynamics that we prove to converge weakly (in the sense of weak convergence for probabilistic processes) towards their mean-field limit, i.e an ordinary differential equation (ODE) in the general case. We focus then on a cla...
متن کاملThe Impact of Monetary and Exchange Policies on the Country’s Trade balance Fluctuation with the Approach of Dynamic Stochastic General Equilibrium (DSGE) models
This paper uses the framework of new Keynesian school and the literature of the Dynamic Stochastic General Equilibrium (DSGE) model to build a general model that can be estimated for Iran economy. By simulating this model, the effects of the implementation of monetary and foreign exchange policies through policy instruments including bank interest rate, central bank international reserves and t...
متن کاملDesign of Observer-based H∞ Controller for Robust Stabilization of Networked Systems Using Switched Lyapunov Functions
In this paper, H∞ controller is synthesized for networked systems subject to random transmission delays with known upper bound and different occurrence probabilities in the both of feedback (sensor to controller) and forward (controller to actuator) channels. A remote observer is employed to improve the performance of the system by computing non-delayed estimates of the sates. The closed-loop s...
متن کاملDesign of A No-chatter Fractional Sliding Mode Control Approach for Stabilization of Non-Integer Chaotic Systems
A nonlinear chattering-free sliding mode control method is designed to stabilize fractional chaotic systems with model uncertainties and external disturbances. The main feature of this controller is rapid convergence to equilibrium point, minimize chattering and resistance against uncertainties. The frequency distributed model is used to prove the stability of the controlled system based on dir...
متن کامل