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Stochastic Thermodynamics in Mesoscopic Chemical Oscillation Systems

Stochastic Thermodynamics in Mesoscopic Chemical Oscillation Systems. Zhonghuai Hou ( 侯中怀 ) 2009.12 XiaMen Email: hzhlj@ustc.edu.cn Department of Chemical Physics Hefei National Lab for Physical Science at Microscale University of Science & Technology of China (USTC).

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Stochastic Thermodynamics in Mesoscopic Chemical Oscillation Systems

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  1. Stochastic Thermodynamics in Mesoscopic Chemical Oscillation Systems Zhonghuai Hou (侯中怀) 2009.12 XiaMen Email: hzhlj@ustc.edu.cn Department of Chemical Physics Hefei National Lab for Physical Science at Microscale University of Science & Technology of China (USTC)

  2. Our Research Interests • Nonlinear Dynamics in Mesoscopic Chemical Systems • Dynamics of/on Complex Networks • Nonequilibrium Thermodynamics of Small Systems (Fluctuation Theorem) • Mesoscopic Modeling of Complex Systems Nonequilibrium + Nonlinearity + Complexity

  3. Irreversibility Paradox ? Microscopic Reversibility Macroscopic Time Arrow t-t, p-p the 2nd law How the second law emerges as the system size grows? Key: Thermodynamics of Small Systems ! Molecular Motors 2~100nm Solid Clusters 1~10nm Quantum Dots 2~100nm Subcellular reactions…

  4. Small Systems? • Fluctuations begin to dominate • Heat, Work: Stochastic Variables • Distribution is more important Polymer Stretching Protocol：X(t) Heat Work Physics Today, 58, 43, July 2005

  5. Fluctuation Theorem Nonequilibrium Steady States • Second Law: • Must have P(-)>0  Second law violation ‘events’ • P(+)/P(-) grows exponentially with size and time • For large system and long time, the 2nd Law holds overwhelmingly • For small system and short time, 2nd Law violating fluctuations is possible (Molecular motor) Adv. In Phys. 51, 1529(2002); Annu. Rev. Phys. Chem. 59, 603(2008); ……

  6. Stochastic Thermodynamics (ST) Stochastic process(Single path based) A Random Trajectory Trajectory Entropy Total Entropy Change Exchange heat Fluctuation Theorems Second Law Prof. Udo Seifert

  7. Many Applications…… • 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 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)

  8. Our Work Stochastic Thermodynamics Chemical Oscillation Systems

  9. Chemical Oscillation • Self-Organization far from Equilibrium • Important: signaling, catalysis • Nanosystems: Fluctuation matters Synthetic Gene Oscillator CO+O2 Rate Oscillation

  10. Modeling of Chemical Oscillations • Macro- Kinetics: Deterministic, Cont. N Species, M reaction channels, well-stirred in V Reaction j: Rate: Hopf bifurcation Nonequilibrium Phase Transition (NPT)

  11. Modeling of Chemical Oscillations Exactly Kinetic Monte Carlo Simulation (KMC) Gillespie’s algorithm Approximately Internal Noise Deterministic kinetic equation • Mesoscopic Level: Stochastic, Discrete Master Equation

  12. Our concern… N, V (Small) How ST applies ? Fluctuation Theorem ? Second law? Role of Bifurcation? • Small • Far From • Equilibrium • Stochastic • Process ……

  13. The Brusselator Concentration： Stochastic Oscillation Molecular number： State Space Random Walk

  14. Path and Entropy Master Equation： Random Path：Gillespie Algorithm Entropy： Dynamic Irreversibility

  15. Entropy Change Along Limit Cycle Stochastic Oscillation: Closed Orbit (Limit Cycle) • Distribution not sensitive to Hopf Bifurcation (HB) • 2nd-Law Violation Events happens( ) • Second Law:

  16. Fluctuation Theorem Holds

  17. NPT: Scaling Change Abruptly Role of HB？ Entropy Production Above HB Below HB  Universal for Oscillation Systems? Entropy production and fluctuation theorem along a stochastic limit cycle T Xiao, Z. Hou, H. Xin. J. Chem. Phys. 129, 114508(Sep 2008)

  18. General Meso-Oscillation Systems Chemical Langevin Euqations(CLE): Fokker-PlanckEquations(FPE):

  19. Path Integral … Trajectory Entropy Entropy Change Along Path: Total System Medium Entropy Production

  20. Stochastic Normal Form Theory Centre Manifold: Oscillatory Motion Stable Manifold: Decay Much faster T Xiao, Z. Hou, H. Xin. ChemPhysChem 7, 1520(2006); New J. Phys. 9, 407(2007)

  21. Analytical Result Slow Oscillatory Mode Dominants

  22. Scaling Relations: Universal Normal form theory tells: Scaling relation

  23. General Picture Universal FT Holds Stochastic Thermodynamics in mesoscopic chemical oscillation systems T Xiao, Z. Hou, H. Xin. J. Phys. Chem. B 113, 9316(2009)

  24. Concluding Remarks • ST applies to mesoscopic oscillation systems with trajectory reversibility • Oscillatory motion(circular flux) leads to the dynamic irreversibility • FT holds for the total entropy change along a stochastic limit cycle • The scaling of E.P. with V changes abruptly at the HB (NPT), which can be explained by the stochastic normal form theory

  25. Acknowledgements Support: National science foundation of China Thank you Detail work: Dr. Tiejun Xiao (肖铁军)

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