Servizi per la didattica
PORTALE DELLA DIDATTICA

Nomequilibrium statistica mechanics: fundations and applications

01NUNRT

A.A. 2019/20

Course Language

Inglese

Degree programme(s)

Doctorate Research in Matematica Pura E Applicata - Torino

Course structure
Teaching Hours
Lezioni 30
Lecturers
Teacher Status SSD h.Les h.Ex h.Lab h.Tut Years teaching
Rondoni Lamberto Professore Ordinario MAT/07 30 0 0 0 14
Co-lectuers
Espandi

Context
SSD CFU Activities Area context
*** N/A ***    
2019/20
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.
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.
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
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
ModalitÓ di esame:
Exam:
...
Gli studenti e le studentesse con disabilitÓ o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'UnitÓ Special Needs, al fine di permettere al/la docente la declinazione pi¨ idonea in riferimento alla specifica tipologia di esame.
Exam:
In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.
Esporta Word


© Politecnico di Torino
Corso Duca degli Abruzzi, 24 - 10129 Torino, ITALY
Contatti