Methods for Non-Equilibrium Statistical Mechanics (12h) 

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Lecture #1

Lecture #2

Lecture #3

Lecture #4

Lecture #5

Lecture #6

Lecture #7

Lecture #8

1. Master Equation and stochastic processes: 

The physics behind a master equation

Fokker-Planck equation

Stochastic calculus

A breather with a few useful examples

One final tool in the toolbox: path integrals

2. In, or out of, equilibrium

Characterizing equilibrium

 A brief overview of fluctuation theorems

 How about a single active particle

 An active particle in a potential

 Actually measuring the distance to equilibrium

3. Rare events

Kramers as usual

How about an active Kramers formula

For a particle subjected to a white but non-Gaussian noise

A trapping problem

4. Collective phenomena in active systems

Introduction, and the two-particle problem

From 2 to N particles

A detour via equilibrium

Mesoscopic description of scalar active matter

5. A chemical reaction 

Mean-field and the importance of fluctuations

Langevin description, and beyond

Towards a quantum formulation

Exploiting the Doi-Peliti formalism

Back to the chemical reaction

The particular one-dimensional case

6.  Epidemics

 The SIR model and its connection to percolation

 The SIS model, sandpiles, and the depinning transition

 The SIS model and directed percolation

 Connection to directed percolation

 Dynamical scaling

 Critical discussion of diffusive models. Epidemics on networks

 Front propagation into an unstable state

 Branching and annihilating random walks

7. Preys and Predators

Around Lotka and Volterra

Incorporating fluctuations, the two-species problem 

 Three-species population 

A set of extended lecture notes