【作者】 肖铁军；

【导师】 侯中怀；

【作者基本信息】 中国科学技术大学 ， 物理化学， 2009， 博士

【摘要】 随着生命科学与纳米技术的发展,介观化学体系获得了越来越多的关注。介观尺度上的化学反应可以用离散随机过程来描述,内涨落(分子涨落)是其内禀属性。一般说来,内涨落的强度和体系的尺度或者体系内反应分子总数成反比。在介观化学体系中,内涨落可以达到显著的程度,它可能使得体系的动力学以及热力学性质与宏观相比有着显著差异。研究内涨落如何影响介观体系的动力学以及热力学性质,是当前非平衡统计物理研究中的前沿课题,也是本论文的重要研究内容。本论文着重研究了介观化学体系中的如下两类非平衡统计问题:●介观化学体系内涨落的动力学尺度效应人们已经知道,在远离平衡条件下,化学体系可以出现丰富的动力学现象,比如合成基因网络中的蛋白质浓度振荡,心肌细胞中的钙螺旋波,纳米粒子表面催化体系的反应速率振荡、螺旋波以及时空混沌等.既然在介观体系中内涨落不可忽略,那么它对于这些动力学现象会有何影响呢?2004年我们组曾在表面和细胞体系中模拟发现内涨落导致的‘最佳尺度效应’,结果表明,内涨落在那些靠近霍普夫分岔点的体系中可以诱导出有效振荡,并且振荡的信噪比在合适的体系尺度下可以达到极大。后来我们在许多体系中都发现了这种现象,但是一直不清楚它的形成条件以及机理。在本论文中,作者利用随机过程理论以及非线性动力学的理论方法,建立了霍普夫分岔点附近的普适的随机范式方程,成功解释了內涨落诱导振荡和最佳尺度效应的机理。在两变量布鲁塞尔体系和三变量生理时钟体系中,我们验证了随机范式方程的有效性(这方面的工作发表在ChemPhyschem以及New J.Phys.上);我们还使用随机范式方程研究了色噪声关联性质对噪声诱导振荡的调控应用(此工作发表在Chaos上)。●介观化学体系的随机热力学近年来,小体系的非平衡热力学特别是涨落定理和随机热力学的研究引起了人们的广泛关注。我们将小体系热力学的最新研究进展应用到了介观化学体系中,特别是考察了涨落定理在介观振荡体系中的具体形式,以及霍普夫分岔对熵产生等热力学量的影响.在不可逆布鲁塞尔体系中,基于对主方程的动力学蒙特卡洛模拟,我们检验了沿着轨线的总熵变满足的细致涨落定理,且发现平均熵产生对体系尺度的依赖在霍普夫分岔点前后显示出不同的标度率(此工作发表在J.Chem.Phys.上)。进一步,从描述物种浓度演化的朗之万方程出发,我们研究了任意介观化学振荡体系的随机热力学。根据随机过程的路径积分方法以及随机范式理论,得到了霍普夫分岔点附近熵产生的理论表达式,从理论上证实,熵产生对体系尺度的标度关系以及在霍普夫分岔点前后标度指数发生突变是介观化学振荡体系的普适特性。我们的工作表明有可能在体系的动力学分岔与随机热力学性质之间可以建立起某种关联(这方面的工作即将发表在J.Phvs.Chem.B)。我们还对介观化学反应体系单个反应通道的熵变满足的涨落定理进行了初步的研究。更多还原

【Abstract】 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.更多还原