Editing Statistical Physics (Book) (section)

{{InfoboxBook
|title=Statistical Physics
|image=[[File:Landau statistical physics.jpg]]
|author=[https://en.wikipedia.org/wiki/Lev_Landau Lev Landau]
|language=English
|series=Course of Theoretical Physics
|genre=
|publisher=Butterworth Heinemann
|publicationdate=1982
|pages=564
|isbn13=978-0-08-057046-4
}}

{{NavContainerFlex
|content=
{{NavButton|link=[[Read#Landau|Read]]}}
{{NavButton|link=[[Statistical Mechanics]]}}
}}

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.

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.