Theory of Brownian motion
Generalized random walk
Langevin and Fokker-Planck equation
Markov chains
Fluctuation-dissipation relation
Linear response theory
Onsager theory of transport
Equilibrium states and nonequilibrium steady states
The driven lattice gas and the TASEP model
Nonequilibrium phase transitions
The BRIDGE model
Isotropic and directed percolation, contact models and SOC
Stochastic dynamics of interfaces
Pattern formation
Roberto Livi and Paolo Politi
Nonequilibrium Statistical Physics - A modern perspective
Cambridge University Press, 2017
Learning Objectives
To provide the main tools for orientation in the large field of nonequilibrium statistical physics.
To give a picture as coherent as possible of the problems and of the methods.
To give a sufficiently detailed overview of relevant research fields.
Prerequisites
A few basic concepts from equilibrium statistical mechanics: statistical weight, statistical ensemble, and phase transitions.
Teaching Methods
Frontal teaching writing at the blackboard. Laptop and slides are used for showing and discussing figures and simulations.
Further information
The first part (from the theory of Brownian motion to the Onsager Theory of transport) is taught by Prof. Roberto Livi. The second part (from equilibrium versus steady states to pattern formation) is taught by Prof. Paolo Politi.
Type of Assessment
Oral examination
Course program
Theory of Brownian motion
Generalized random walk
Langevin and Fokker-Planck equation
Markov chains
Fluctuation-dissipation relation
Linear response theory
Onsager theory of transport
Equilibrium states and nonequilibrium steady states
The driven lattice gas, the TASEP model and its phase diagram
The BRIDGE model: an example of nonequilibrium phase transitions with symmetry breaking
Isotropic and directed percolation: another example of nonequilibrium phase transition
Mean field theory for contact type models
Outline of the self organized criticality
Stochastic dynamics of interfaces: the Edwards-Wilkinson and the Kardar-Parisi-Zhang universality classes
Pattern formation: linear instability scenarios and details about the most important equations representing the three different scenarios (Time Dependent Ginzburg-Landau, Cahn-Hilliard and Swift-Hohenberg)