Servizi per la didattica
PORTALE DELLA DIDATTICA

Nomequilibrium statistica mechanics: fundations and applications

01NUNRT

A.A. 2018/19

2018/19

Meccanica statistica del disequilibrio: fondazioni e applicazioni

PERIOD: APRIL - JULY The course is meant to give the theoretical basis needed to understand nonequilibrium physical phenomena, deriving the standard fluctuation-dissipation relations, linear response theory, and the modern results concerning fluctuations of observables in nonequilibrium systems. These results are of particular interest in the study of systems in conditions far away from equilibrium, and in the modern bio- and nano-technology.

Meccanica statistica del disequilibrio: fondazioni e applicazioni

PERIOD: APRIL - JULY The course is meant to give the theoretical basis needed to understand nonequilibrium physical phenomena, deriving the standard fluctuation-dissipation relations, linear response theory, and the modern results concerning fluctuations of observables in nonequilibrium systems. These results are of particular interest in the study of systems in conditions far away from equilibrium, and in the modern bio- and nano-technology.

Meccanica statistica del disequilibrio: fondazioni e applicazioni

Meccanica statistica del disequilibrio: fondazioni e applicazioni

Meccanica statistica del disequilibrio: fondazioni e applicazioni

Meccanica statistica del disequilibrio: fondazioni e applicazioni

Meccanica statistica del disequilibrio: fondazioni e applicazioni

1. Nonequilibrium thermodynamics: local equilibrium, balance equations and hydrodynamic equations; 2. Brownian motion and fluctuation-dissipation theorem; 3. Onsager reciprocal relations; 4. Green-Kubo relations; 5. Onsager-Machlup theory 6. ensembles and invariant measures: microscopic foundations and the role of chaos; 7. ergodic and chaotic hypotheses; 8. far from equilibrium and nanoscale systems: Equivalence and non-equivalence of ensembles; 9. trasient fluctuation relations (Evans-Searles, Jarzynski, Crooks, Hatano-Sasa); 10. steady state fluctuation relations (Evans-Cohen-Morriss, Gallavotti-Cohen); Bibliografia: D. J. Evans, G. P. Morriss, Statistical mechanics of nonequilibrium liquids, Cambridge Univ. Press (2008) H. B. Callen, Thermodynamics, Wiley (1966) E. Fermi, Thermodynamics, Dover (1956) S. R. de Groot, P. Mazur, Non-equilibrium thermodynamics, Dover (1984) H. Risken, The Fokker-Planck equation, Springer (1989) R. Kubo, M. Toda, N. Hashitsume, Statistical Physics II, Springer-Verlag (1983) D. A. Kirzhnits, Field Theoretical Methods in Many-Body Systems, Pergamon Press (1967) M. I. Friedlin and A. D. Wentzell. Random Perturbations of Dynamical Systems, Berlin, Springer, (1984) G. Gallavotti. Statistical Mechanics: a Short Treatise. Springer Verlag Berlin, 2000 Carlo Cercignani, The Boltzmann Equation and Its Applications, New York, Springer- Verlag, 1988

Meccanica statistica del disequilibrio: fondazioni e applicazioni

1. Nonequilibrium thermodynamics: local equilibrium, balance equations and hydrodynamic equations; 2. Brownian motion and fluctuation-dissipation theorem; 3. Onsager reciprocal relations; 4. Green-Kubo relations; 5. Onsager-Machlup theory 6. ensembles and invariant measures: microscopic foundations and the role of chaos; 7. ergodic and chaotic hypotheses; 8. far from equilibrium and nanoscale systems: Equivalence and non-equivalence of ensembles; 9. trasient fluctuation relations (Evans-Searles, Jarzynski, Crooks, Hatano-Sasa); 10. steady state fluctuation relations (Evans-Cohen-Morriss, Gallavotti-Cohen); Bibliografia: D. J. Evans, G. P. Morriss, Statistical mechanics of nonequilibrium liquids, Cambridge Univ. Press (2008) H. B. Callen, Thermodynamics, Wiley (1966) E. Fermi, Thermodynamics, Dover (1956) S. R. de Groot, P. Mazur, Non-equilibrium thermodynamics, Dover (1984) H. Risken, The Fokker-Planck equation, Springer (1989) R. Kubo, M. Toda, N. Hashitsume, Statistical Physics II, Springer-Verlag (1983) D. A. Kirzhnits, Field Theoretical Methods in Many-Body Systems, Pergamon Press (1967) M. I. Friedlin and A. D. Wentzell. Random Perturbations of Dynamical Systems, Berlin, Springer, (1984) G. Gallavotti. Statistical Mechanics: a Short Treatise. Springer Verlag Berlin, 2000 Carlo Cercignani, The Boltzmann Equation and Its Applications, New York, Springer- Verlag, 1988

Meccanica statistica del disequilibrio: fondazioni e applicazioni

Meccanica statistica del disequilibrio: fondazioni e applicazioni

Meccanica statistica del disequilibrio: fondazioni e applicazioni

Meccanica statistica del disequilibrio: fondazioni e applicazioni

Meccanica statistica del disequilibrio: fondazioni e applicazioni

Meccanica statistica del disequilibrio: fondazioni e applicazioni

Meccanica statistica del disequilibrio: fondazioni e applicazioni

ModalitÓ di esame:

Meccanica statistica del disequilibrio: fondazioni e applicazioni

Meccanica statistica del disequilibrio: fondazioni e applicazioni

Exam:

Meccanica statistica del disequilibrio: fondazioni e applicazioni



© Politecnico di Torino
Corso Duca degli Abruzzi, 24 - 10129 Torino, ITALY
m@il