Statistical Physics (S1)

Contact: Pr. Alberto Verga or Pr. Marco Pettini



  • Statistical ensemble: from the microscopic states to thermodynamics
  • Density matrix and the microcanonical distribution of an isolated system
  • Gibbs ensembles
  • Gibbs distribution (classical and quantum); the partition function and the free energy
  • Thermodynamic quantities

Noninteracting systems

  • Energy equipartition
  • Ideal gas
  • Rotation and vibration of molecules
  • Bose distribution, photons and phonons, Debye, Bose condensation
  • Fermi distribution, degenerated electron gas


  • Pauli paramagnetism and mean field ferromagnetism
  • Landau diamagnetism
  • Ising model, low and high energy expansions in 2D
  • Cumulant expansion and virial coefficients
  • Van der Waals equation and liquid-gas transition

Phase transitions and fluctuations

  • Phenomenology and scaling laws
  • Order parameter and Landau free energy
  • Symmetry breaking
  • Linear response and correlations


  • From the binomial distribution to the large number and central limit theorems
  • Chaos, ergodicity and mixing
  • Mixing entropy and the Gibbs paradox
  • Maxwell demon and information theory
  • Two level systems
  • Quantum oscillator
  • Monte Carlo for the ising model
  • 2x2 random matrices, Wigner surmise
  • Lenard-Jones potential and molecular dynamics
  • White dwarf starsBlack hole entropy
  • Yang-Lee theory of phase transitions
  • Quantum spin in a transverse field



  • Chaikin et Lubensky, Principles of Condensed Matter Physics, Cambridge, 1995.
  • Kardar, Statistical Physics, particles (I) and fields (II), Cambridge, 2007.
  • Krapivsky, Redner et Ben-Naim, A Kinetic view of Statistical Physics, Cambridge, 2010.
  • Leach, Molecular Modelling, Prentrice Hall, 2001.
  • Mori et Kuramoto, Dissipative Structures and Chaos, Springer, 1998.
  • Onuki, Phase Transition Dynamics, Cambridge, 2002.
  • Safran, Statistical Thermodynamics of Surfaces, Interfaces and Membranes, Westview, 2003.
  • Sethna, Statisitical Mechanics: entropy, order parameters and complexity, Oxford, 2006.