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Most of the cases when I see applications of statistical mechanics is when Fermi-Dirac or Bose-Einstein statistic are used in condensed matter or the equilibrium equation of neutron stars.

Besides the Poisson-Boltzmann equation for colloids and plasma screening, I would like to know what are the modern developments/applications of classical statistical mechanics.

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closed as too broad by Qmechanic Jun 7 at 5:46

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  • $\begingroup$ What is classical about Bose-Einstein and Fermi-Dirac statistics? $\endgroup$ – G. Smith Jun 7 at 2:08
  • $\begingroup$ I never said those were classical. $\endgroup$ – AndresB Jun 7 at 2:12
  • $\begingroup$ Sorry, I misunderstood your question. $\endgroup$ – G. Smith Jun 7 at 2:14
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If by "classical statistical mechanics" one means the equilibrium statistical mechanics, i.e. excluding applications of statistical mechanics to systems out of equilibrium, the last half century or so has witnessed many new developments/applications. It is difficult to make an exhaustive list, but certainly it should contain the following items:

  • interacting systems: development of exact methods
  • interacting systems: development of numerical simulation algorithms
  • interacting systems: development of perturbation methods
  • interacting systems: recasting of the theory as a Density Functional Theory
  • applications to disordered systems (liquids, structural glasses, spin glasses,...)
  • determination of phase diagrams
  • applications to phase transitions
  • theory and applications to critical phenomena, in particular the Renormalization Group approach.

It depends on the exact definition of classical statistical mechanics to include or not in such a list the study of equilibrium dynamical properties (time correlation functions, transport coefficients, kinetic theory and alike). Personally, I would include them, since they all hinge on the basic principles of equilibrium statistical mechanics.

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