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

2. Cluster Polymer Single molecule Pump

3. Biological cells

4. Protein AtomicMesoscopic

5. Is thermodynamics applicable to nanosystems? Peculiar features: 1.Thermodynamic limit not fulfilled. Free energy contains more contributions Surface contribution

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

7. Diffusion Fick i)Large scales ii)Long times Description in terms of average values

8. Thermodynamics of diffusion Gibbs; local equilibrium

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

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

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

12. Currents Kramers

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

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

15.  (Q) Q 1 2 Q1Q1 Q0Q0 Q2Q2 NET: two-state system 1 2 quasi-equilibrium at each well Examples: chemical reactions, nucleation, adsorption, active transport, thermoionic emission, etc.

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

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

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 crystal Metastable phase Order parameter embryo

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