Lecturer: Armando Bazzani (Unibo)

Duration: 12 hours

Dates: March 2024

Learning outcomes: The student will get notions on stochastic differential equations and Markov systems, master equations, and diffusion equations, properties of equilibrium and non-equilibrium stationary states, Gibbs and Information Entropy for Stochastic Systems, existence of Maximal Entropy Principles, Stochastic Thermodynamics and Non-equilibrium Statistical Physics with applications to Complex Systems Physics.

1) introduction to dynamical systems, regular and chaotic dynamics, predictability, Information Entropy, Markov processes and random walks, Wiener process and stochastic dynamical systems

2) Stochastic integrals and properties of the stochastic differential equations, use of the stochastic dynamical systems as models of non-equilibrium Statistical Mechanics, examples

3) Fokker-Planck equation and thermodynamic formalism for stochastic systems, Maximum Entropy Principle and stochastic reversibility, equilibrium states, and non-equilibrium stationary states

4) Smoluchowski equation and applications, and entropy introduction to the stochastic thermodynamics

5) Markov processes and random walks: mathematical properties, master equation, diffusion limit, anomalous diffusions, random walk on graph and their applications

6) Stochastic dynamical system on graph, Dynamical stationary states, and phase transitions, application to complex systems physics.

Dates: Auletta teorici 2nd floor via Irnerio 46, Tuesdays 5-12-19 March, Thursdays 7-14-21 March 2024, all lectures from 14:30 to16:30