Studies Of Nonequilibrium Statistic Problems In Mesoscopic Chemical Systems

In the recent years,mesoscopic chemical systems had gained growing attention with the rapid progresses in nanotechnology and life science.Chemical reactions in mesocopic scale are discrete stochastic processes described by master equation,so internal noise or the molecular fluctuation is intrinsic property of chemical systems. A mesoscopic chemical system contains only a small amout of molecular,so the internal noise will be significant,and will affect the dynamics and thermodynamics. In this thesis,we have studied the following two kinds of nonequilibrium statistic problems which are relavent to the internal noise in mesoscopic chemical systems:●Optimal System Size Effect of Internal Noise on DynamicsWhen driven away from equilibrium,chemical systems exhibit aboundant dynamic behaviors,such as the oscillation in gene networks,Calcium spiral wave in the myocardial,reaction rate oscillations,spiral wave and spatio-temporal chaos in nano particle surfaces.Since internal noise is significant in mesoscopic systems,how will it affect such dynamic behaviors? In 2004,our group found a novel phenomenon in the mesoscopic chemical systems that are near Hopf bifurcation,which is called 'Optimal systems size effect',i.e.,internal noise could induce oscillation,and the signal-to-noise-ratio of these noise induced oscillations undergoes a clear maximum under a suitable systems size.After that,we apply ourselves to find its underly mechanism.Herein,we contribute to this issue by theoretic analysis.Starting from chemical Langevin equations,using the normal form theorem and stochastic average method,a unified 'stochastic averaged normal form' is obtained.We had succedully explained the internal noise induced oscillation and optimal system size effect.We had also checked the validity of our method in the Brussel model and a Circadian clock model.We had also used our method to study the effect of noise correlation in controlling the noise induced oscillations.●Stochastic ThermodynamicsIn recent years,nonequilibrium thermodynamics of small systems has gained extensive attention.Of particular interests are the fluctuation theorem and stochastic thermodynamics.Herein,fluctuation theorem and stochastic thermodynamics in mesoscopic oscillate chemical systems are discussed.By direct simulation in the irreversible Brusselator,we had checked the validity of the detailed fluctuation theorem for the entropy producton along a stochastic trajectory,and found that the entropy producton on system size have different scaling on system size when the control parameter is befor or afer Hopf bifurcation.Further more,basing on the chemical Langevin equation,we had studied the stochastic thermodynamics of mesoscopic chemical reaction networks.Using the path intergral and stochastic normal form theory,we had derive explicit theoretical expressions for the mean entropy production in the stationary state,and demonstrated that the scaling law of entropy production on system size and the scaling exponent change abruptly at Hopf bifurcation point is universal in mesoscopic chemical systems,suggesting a relation between dynamic bifurcation and stochastic thermodynamics behaviors.We had also studied the fluctuation theorem of entropy production of single reaction channel.