Non-equilibrium Statistical Theory For Complex Multi-body System And A Number Of Issues

Equilibrium is a special state of the matter. In the nature, non-equilibrium is the ubiquitous state of the matter. In order to study the law of the thermodynamics in further step, it is necessary to study the nonequilibrium theories of statistical mechanics. It's more difficult to set up a series of the nonequilibrium theories of statistical mechanics than the equilibrium theories of statistical mechanics. But nonequilibrium theories of statistical mechanics are more prevalent and more profound than the equilibrium theories of statistical mechanics. The generalized Langevin equations and the Fokker-Plank equation are proving to act as the main theory tool for studying the nonequilibruim theories of statistical mechanics. We have done some work on the basis of the work of others. The main content of this paper is summarized as follows:1. The recent experiments on the dynamics of a common biological network motif, p53 and Mdm2 feedback loop, in population and individual cells have shown the two different kinds of oscillatory behaviors, damped and sustained oscillation, for the activities of p53 and Mdm2 proteins in response to DNA damage. By exploiting the nonlinear dynamics in the negative feedback loop and through analyzing the dynamical relation between the DNA damage and the activities of p53 and Mdm2 proteins, we propose a nonlinear dynamical model with aiming to describe such the different oscillatory behaviors for the activities of p53 and Mdm2 proteins both in individual and in population of cells in a self-consistent and unified way.2. First we obtain the dynamic response function and the correlation function by deriving the Langevin equation for a system coupled to a heat bath and then we obtain these two functions by another way .These two results are uniform. We explore two forms of the system-heat bath interaction: linear and nonlinear in the heat bath coordinates. Through the analysis of the results we find that different α represents different physical process , and there are no big differences between the nonlinear and linear response theory.