Schema della sezione

  • Introduzione

    Minimizza tutto Espandi tutto

    Bibliografia

    PP Luca Peliti, Simone Pigolotti, Stochastic Thermodynamics: An Introduction, Princeton University Press (PP)

    HT1 H. Touchette,
    A basic introduction to large deviations: theory, applications,

    https://arxiv.org/pdf/1106.4146

    HT2 H. Touchette,

    Introduction to dynamical large deviations of Markov processes
    https://arxiv.org/pdf/1705.06492

    HT3 H. Touchette

    The large deviation approach to statistical mechanics

    https://www.sciencedirect.com/science/article/pii/S0370157309001410?via%3Dihub

  • Lezione 1

    Introduzione al corso

    Binomial vs gaussian distribution, cumulant generating function PB 6.1

    Richiami sulla trasformata di Legendre, PB appendix A2

  • Lezione 2

    Trasformata  di Legendre-Fenchel PB appendix A.2

    Funzione generatrice dei cumulanti, Lage deviation principle and Gärtner-Ellis theorem,

    PB 6.1

    HT1, 2.1, 2.2, 2.3

    Calculating rate functions, Gaussian and exponential PDFs

    HT3, 3.3

    Richiami sul metodo del punto di sella per integrali di funzione complessa in variabile complessa: un qualunque libro di testo di Metodi Matematici per la Fisica

  • Lezione 3

    Legendre "duality". Linear tails of the rate function HT3 3.5.3

    Varadan's theorem, HT3 3.5.4

    Static and Dynamic observables, systems close to equilibrium PP 6.2

    Large deviations in equilibrium statistical mechanics HT3 5.

  • Lezione 4

    Large deviations in equilibrium statistical mechanics (cont.)

    the case of the Ising model in mean field, and calculation of the entropy

    Large deviation principle for the single particle diffusing on a lattice

  • Lezione5

    Tilting,  PP 6.5, HT1 4.3

    Application of the tilted generator to the single particle on a 3 state loop.

  • Lezione6

    Symmetries of the tilted generator and fluctuation relations, Gallavotti Cohen symmetry

    PP 6.3, 6.4

    Qubit in contact with 2 baths (intro.)

  • Lezione7

    Single qubit in contact with two baths, statistics of the heat current

    note del docente in Lezione8

  • Lezione8

    Single Brownian particle in contact with two baths, statistics of the heat current

    note del docente

  • Lezione 9

    Lattice models with kinetic constraints: 

    Fredrickson-Andersen (FA) model and Bosonic FA model.

    Master operators

    https://iopscience.iop.org/article/10.1088/1742-5468/2006/03/P03006Fredrickson-Andersen (FA) model

  • Lezione 10

    Dynamical Phase Transitions in Kinetically Constrained Models,  large-deviation  approach

    https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.98.195702

  • Lezione11

    Numerical algorithms for the large deviations

    Slides del docente

    PP 6.8

    Cristian Giardina · Jorge Kurchan · Vivien Lecomte ·
    Julien Tailleur, Simulating Rare Events in Dynamical Processes

    https://link.springer.com/article/10.1007/s10955-011-0350-4

    Vivien Lecomte and Julien Tailleur,  A numerical approach to large deviations in continuous time

    https://iopscience.iop.org/article/10.1088/1742-5468/2007/03/P03004/meta

    Per prepararsi alla lezione 11, leggere l'articolo

    Computation of extreme heat waves in climate models using a large deviation algorithm

    https://www.pnas.org/doi/10.1073/pnas.1712645115

    An interesting article, not related to the lecture's main subject

    Large deviations and portfolio optimization

    https://arxiv.org/abs/cond-mat/9802059

  • Lezione 12

    Algoritmi con bias per sistemi Browniani, note del docente