Statistical Physics (Book)

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Statistical physics is commonly introduced in physics education as the physics of thermodynamics in gases and solids. This is wrong. Firstly, the standard courses neglect what Landau does, deriving the macroscopic concepts from probabilistic (but ultimately deterministic) microscopic motion. There are also numerous other applications of the subject from chemistry to crystals to phase transitions. Souriau takes this further. Statistical mechanics like classical mechanics is based on symplectic geometry, but with the added ingredient of measures. This geometric approach to statistical mechanics leads us eventually to statistical field theory and stochastic quantization with lattice statistical mechanics as a stepping stone to the continuum limit - this makes the connection to quantum field theory manifest. Statistical field theory and stochastic quantization were first coined and motivated by Parisi, who started to make the analogies between e.g. statistical correlation functions and quantum field theory propagators rigorous.

Statistical Physics
Landau statistical physics.jpg
Information
Author Lev Landau
Language English
Series Course of Theoretical Physics
Publisher Butterworth Heinemann
Publication Date 1982
Pages 564
ISBN-13 978-0-08-057046-4

From the physics, other genuinely new types of mathematical objects appear:

  • scale symmetry/renormalization and critical phenomena
  • continuous random processes
  • statistical learning (to be elaborated on in the future)

Understanding the fundamentals of statistical mechanics and its geometric consequences may lead directly to an understanding of complex phenomena at all scales - from weather to neuronal cognition.

Applications

Structure of dynamical systems: a Symplectic View of Physics

Structure of dynamical systems: a Symplectic View of Physics by Jean-Marie Souriau.

Exactly Solved Models In Statistical Mechanics

Exactly Solved Models In Statistical Mechanics by Rodney Baxter.

Quantum Groups: From Coalgebras to Drinfeld Algebras

Quantum Groups: From Coalgebras to Drinfeld Algebras by Shlomo Sternberg and Steven Shnider.

Statistical Field Theory Volume 1

Statistical Field Theory Volume 1: From Brownian Motion to Renormalization and Lattice Gauge Theory by Claude Itzykson and Jean-Michel Drouffe.

Statistical Field Theory Volume 1

Statistical Field Theory Volume 2: Strong Coupling, Monete Carlo Methods, Conformal Field Theory, and Random Systems by Claude Itzykson and Jean-Michel Drouffe.

Stochastic Quantization

Stochastic Quantization by Mikio Namiki