Outline 1

1
Outline 1

• Work and heat fluctuations in out of equilibrium
  systems
• 1.1) Fluctuation Theorems
• 1.1a) Introduction et motivation
• 1.1.b) Stochastic systems
• - Electric circuit
• - Harmonic oscillator
• 1.1.c) Dynamical Systems
• - Power dissipation in a granular
  medium
• - Turbulence (Rayleigh-Benard
  Convection
• Wind
  pressure)
• 1.2) Jarzinsky equality
• - Experiments in biophysics
• - Harmonic oscillator

2
Outline 2

• Properties of aging of glasses and other
  amorphous materials
• - Definition of a glass
• - Definition of aging
• - Connections with out of equilibrium
  systems
• - Memory effects
• - Definition of an effective temperature
• - Thermal noise properties of amorphous
  materials
• - Connections with the points 1 of these
  lectures

3
Fluctuations in out of equilibrium systems
What is the probabilty that the heat flows from
the cold to the hot reservoir ?
Fluctuation Theorem ?
What is the probability that the object moves
against the wind ?
4
Outline of the first lectures

• Fluctuation Theorems, Jarzynski and Crooks
  relations
• Motivation for experiments.
• Test of the theorem predictions in stochastic
  systems
• a) The electric noise out of equilibrium
• b) The mechanical oscillator
• Conclusions
• Test in hydrodynamic flows

5
Predictions of the Gallavotti-Cohen Fluctuation
Theorem (FT)
The original proof of FT was based on the
deterministic dynamics of many particle systems
6
Sinai scaling function
Why is interesting to study these two relations
in experiments ?
7
Short comment on FT
FT imposes that
8
Hypothesis to prove the FT for dynamical systems

• Chaotic Hypothesis (Anosov system)
• Time reversal symmetry

9
Motivations for studying FT in dynamical
systems

• Check in experiments the analytical and
  numerical studies on FT

• Check on real hydrodynamic flows the
  hypothesis of the theorem

• What is the good variable to look at ?
• Does it exist a local version of the theorem ?
• Is the chosen variable representative of the
  total dynamics?

• Extreme fluctuations of averaged quantities.
• The FT allows us to know the probability of the
  negative fluctuations just using the probability
  of the positive ones.

10
Outline 1

• Work and heat fluctuations in out of equilibrium
  systems
• 1.1) Fluctuations Theorems
• 1.1a) Introduction et motivations
• 1.1.b) Stochastic systems
• - Electric circuit
• - Harmonic oscillator
• 1.1.c) Dynamical Systems
• - Power dissipation in a granular
  medium
• - Turbulence (Rayleigh-Benard
  Convection
• Wind
  pressure)
• 1.2) Jarzinsky equality
• - Experiments in biophysics
• - Harmonic oscillator