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Lecturers :

Annie Colin
Anthony Maggs

Hélène Montes

Research center

Level : 1st year

Course Language : French

Term : core curriculum

Number of hours : 90

ECTS Credits : 7,5
PSA Statistical mechanics: methods and applications
Teaching site :
Lectures: 30 h - Tutorials: 15 h - Laboratory sessions: 45 h


This course is an introduction to the general ideas of statistical physics. Particular attention is paid to basic concepts (entropy, temperature) and to pertinent methods used in other disciplines. We will discuss classical examples (e.g perfect gas, paramagnetism, elasticity of polymers) along with the physics of phase transitions and collective phenomena and quantum statistics. We will attempt to maintain a (difficult) balance between an intuitive approach to phenomena and more rigorous calculation.


  • Introduction and basic thermodynamics
  • Probability and random walks
  • Statistical physics of isolated systems: microcanonical ensemble
  • Statistical physics at constant temperature: canonical ensemble
  • Statistical physics of classical systems with no interactions
  • Ideal quantum gases
  • Phase transitions, mean field approximations
  • Langevin equation and fluctuation-dissipation theorem

Laboratory sessions

  1. Emulsion
    4 main experiments are proposed to the students :

    • Solide-gaz phase diagram, sorting based on depletion mechanism
    • Metastable systems, drainage, coalescence, Oswald ripening
    • Absorption of a surfactant at a liquid-air interface
    • Measurement of the chemical activity of salted water

    These four experimental cases are good examples of the importance of the interfaces in divided matter.

  2. Simulation and analysis of the thermodynamical properties of hard spheres and hard disks
    In this lab, we explore some of the consequences of the atomist hypothesis, by studying, for a hard spheres system, the equation of state of the gaz and its phase transitions, the Brownian motion of a macromolecule, and the depletion interaction between two macromolecules. We use numerical simulations whose results are analyzed with programs written in Python.

  3. Phase transitions of simple liquid and polymers observed by differential scanning calorimetry (DSC)

    • Experimental approach of the glass transition of polymers
    • Liquid-crystal phase transition in confined geometry : fusion and crystallization of water

Requirements : A knowledge of Classical thermodynamics and of basic mathematics are required for this course

Evaluation mechanism : Lectures: written exam; lab sessions: mark for the involvement in the session + mark on a written report to be delivered 15 days after the end of the sessions.

Last Modification : Wednesday 6 September 2017

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