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Nonequilibrium Thermodynamics in Mesoscopic Oscillation Systems ( 介观化学振荡体系的非平衡热力学 )

Nonequilibrium Thermodynamics in Mesoscopic Oscillation Systems ( 介观化学振荡体系的非平衡热力学 ). 侯中怀 2009 年 4 月 成都 中国科技大学化学物理系 合肥微尺度科学国家实验室. Our Research Interest. 非平衡非线性化学动力学 介观化学体系非平衡统计力学 复杂化学体系多尺度理论方法 复杂网络动力学. 非平衡 非线性 复杂性. 不可逆性佯谬. ?. 宏观体系 时间箭头. 微观运动 时间可逆. Solid Clusters 1~10nm.

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Nonequilibrium Thermodynamics in Mesoscopic Oscillation Systems ( 介观化学振荡体系的非平衡热力学 )

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  1. Nonequilibrium Thermodynamics in Mesoscopic Oscillation Systems(介观化学振荡体系的非平衡热力学) 侯中怀 2009年4月 成都 中国科技大学化学物理系 合肥微尺度科学国家实验室

  2. Our Research Interest • 非平衡非线性化学动力学 • 介观化学体系非平衡统计力学 • 复杂化学体系多尺度理论方法 • 复杂网络动力学 非平衡 非线性 复杂性

  3. 不可逆性佯谬 ? 宏观体系 时间箭头 微观运动 时间可逆 Solid Clusters 1~10nm Magnetic Domains < 300nm 小体系热力学性质！ Quantum Dots 2~100nm Ion channels Molecular Motors 2~100nm Subcellular reactions

  4. 小体系非平衡热力学 • 非平衡涨落~均值 , 宏观热力学失效 • 热力学量是随机量, 分布决定性质 实例：拉伸大分子 Protocol：X(t) • 不同次实验，W,Q与U有显著涨落 • 分布P(W)和P(Q)决定体系性质 Physics Today, 58, 43, July 2005;

  5. 涨落定理(Fluctuation Theorem) Nonequilibrium Steady States • Valid beyond linear response • Second Law: • More likely to deliver heat than absorb • P(+)/P(-) grows exponentially with size and time • For small system and short time, capture heat from bath is possible (Molecular motor) Adv. In Phys. 51, 1529(2002); Annu. Rev. Phys. Chem. 59, 603(2008); ……

  6. 随机热力学(Stochastic thermodynamics) Stochastic process(Single path based) A Random Trajectory Trajectory Entropy Total Entropy Change Fluctuation Theorems 第一定律 Second Law

  7. 许多应用…… • Probing molecular free energy landscapes by periodic loading PRL(2004) • Entropy production along a stochastic trajectory and an integral fluctuation theorem , PRL (2005) • Experimental test of the fluctuation theorem for a driven two-level system with time-dependent rates, PRL (2005) • Thermodynamics of a colloidal particle in a time-dependent non-harmonic potential, PRL(2006) • Measurement of stochastic entropy production, PRL(2006) • Optimal Finite-Time Processes （最小功）In Stochastic Thermodynamics, PRL(2007) • Stochastic thermodynamics of chemical reaction networks, JCP(2007) • Role of external flow and frame invariance in stochastic thermodynamics, PRL(2008) • Recent Review: EPJB(2008) Prof. Udo Seifert

  8. 化学振荡：非平衡自组织行为 Oscillation：Temporally Periodic Variations of Concentrations/Numbers Synthetic Gene Oscillator CO+O2 Rate Oscillation Nonequilibrium Statistical Mechanics

  9. 宏观体系：确定性唯象方程 • Macro- Kinetics: Deterministic, Cont. N Species, M reaction channels, well-stirred in V Reaction j: Rate: Hopf bifurcation leads to oscillation

  10. 介观体系：随机过程理论 Exactly Kinetic Monte Carlo Simulation (KMC) Gillespie’s algorithm Approximately Fluctuation ! Deterministic kinetic equation • Mesoscopic Level: Stochastic, Discrete Master Equation

  11. 内涨落效应：噪声诱导振荡 • A model system: The Brusselator Stochastic Deterministic FFT Noisy Oscillation

  12. 最佳尺度效应 Best performance Brusselator: CPC 2004; Circadian clock: JCP 2003; Calcium Oscillation: CPC 2004, CPC 2005, PRE 2005, PCCP 2006; Gene network: CPL ; Surface Catalytic Reaction: JCP 2005; JPCA 2005, JPCA 2007; Neuron Network: CPC 2004, CPC 2006; ……

  13. 问题：介观振荡体系非平衡热力学？ N, V (Small) 小体系非平衡热力学？ 涨落定理？ 振荡特性？ • 小体系 • 远离平衡 • 涨落显著 • 随机过程 分岔行为？ ……

  14. 不可逆Brusselator体系 宏观：Hopf分岔 介观：随机振荡 微观：态空间随机行走

  15. 随机轨线及轨线熵 主方程： 随机轨线： 熵变： 轨线熵： 动力学不可逆性（动力学耗散）

  16. 随机振荡的熵变及分布 熵变的分布： 随机振荡（闭轨）： • Hopf 分岔对总熵变的分布影响不大 • 存在总熵变小于0 的轨线(违反第二定律的事件) • 总熵变的平均值大于0,第二定律满足

  17. 涨落定理

  18. 熵产生的标度律 Hopf 分岔的影响？ 熵产生 分岔前 分岔后 介观动力学分岔的随机热力学特征？ Entropy production and fluctuation theorem along a stochastic limit cycle T Xiao, Z. Hou, H. Xin. J. Chem. Phys. 129, 114508(Sep 2008)

  19. 任意介观振荡体系 化学朗之万方程(CLE)描述 相应Fokker-Planck方程

  20. 轨线熵和熵产生 轨线熵 熵产生动力学耗散 总熵变 系统熵变 路径积分 介质熵变 平均熵产生

  21. Hopf分岔点附近：随机范式理论 Effect of internal noise in mesoscopic chemical systems near Hopf bifurcation T Xiao, Z. Hou, H. Xin. New J. Phys. 9, 407(Nov 2007)

  22. 熵产生：理论结果

  23. 标度律：理论解释

  24. 普适物理图像 FT Holds Stochastic Thermodynamics in mesoscopic chemical oscillation systems T Xiao, Z. Hou, H. Xin. J. Phys. Chem. B (In press)

  25. 小结 • Brusselator体系随机热力学 1. 微观态可逆涨落定理(FT) 2. 分岔点：熵产生分布和FT无定性变化 3. 分岔点前后：熵产生标度律突变 • 任意介观振荡体系 1. CLE水平：熵产生表达式 2. 分岔点：随机范式理论标度律 普适性：介观Hopf分岔的随机热力学特征！

  26. 致谢 Thank you ! Detail work: Dr. Tiejun Xiao (肖铁军), USTC Discussions: Prof. Yijin Yan, HKUST Funding: National Science Foundation of China

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