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The mesoscopic dynamics of thermodynamic systems

The mesoscopic dynamics of thermodynamic systems. J.M. Rubi. Single molecule. Cluster. Polymer. Pump. Biological cells. Protein. Atomic. Mesoscopic. Is thermodynamics applicable to nanosystems?. Peculiar features:. Thermodynamic limit not fulfilled.

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The mesoscopic dynamics of thermodynamic systems

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  1. The mesoscopic dynamics of thermodynamic systems J.M. Rubi

  2. Single molecule Cluster Polymer Pump

  3. Biological cells

  4. Protein Atomic Mesoscopic

  5. Is thermodynamics applicable to nanosystems? Peculiar features: • Thermodynamic limit not fulfilled. • Free energy contains more contributions Surface contribution

  6. 2. Fluctuations can be larger than average values fluctuation thermodynamic value Macroscopic: continuum

  7. Diffusion Fick Description in terms of average values • Large scales • Long times

  8. Thermodynamics of diffusion Gibbs; local equilibrium

  9. Single molecule x:center of mass :size, others Force Local equilibrium: Mesoscale local equilibrium:

  10. Mesoscopic thermodynamics Assumption: the system undergoes a diffusion process in (x,v)-space Local equilibrium in (x,v)-space Gibbs equation:

  11. Probability conservation: Entropy production: Currents: Onsager relation:

  12. Currents Kramers

  13. Regimes Equilibrium: Gaussian, T Local equilibrium Fick Far from equilibrium

  14. Nonlinear regime • Two types of nonlinearities: • In the transport coefficients • In the currents MNET can provide nonlinear equations for the currents

  15. 1 2 (Q) 1 2 Q Q2 Q1 Q0 NET: two-state system quasi-equilibrium at each well Examples: chemical reactions, nucleation, adsorption, active transport, thermoionic emission, etc.

  16. NET description Law of mass action linearization Conclusion: NET only accounts for the linear regime

  17. ions …. enzyme intermediate configurations The process is described at short time scales. A local value of the potential corresponds to a configuration at a reaction coordinate

  18. Mesoscopic thermodynamics The activation process is viewed as a diffusion process along a reaction coordinate From local to global:

  19. Nucleation kinetics Basic scenario: melted embryo crystal Order parameter Metastable phase

  20. Transport through protein channels Entropic barrier Scaling law

  21. Polymer crystallization embryopattern Sheared melt

  22. Translocation of a biomolecule

  23. Conclusions • MNET offers a unified and systematic scheme to analyze irreversible processes taking place at the nano-scale. • It can be used in the description of the two basic irreversible processes: transport and activation. • Applications to: transport in materials and in biology, chemical and biochemical kinetics, adsorption, thermoionic emission, spin flip processes, etc.

  24. References • A. Perez-Madrid, J.M. Rubi and P. Mazur, Physica A 212, 231 (1994) • J.M. Vilar and J.M. Rubi, Proc. Natl. Acad. Sci., 98, 11081 (2001) • D. Reguera, J.M. Rubi and J.M. Vilar, J. Phys. Chem. B, 109, 21502 (2005) Feature Article mrubi@ub.edu

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