Does a statistical mechanics of classical fields exist?

[andresB]

The usual presentation of classical statistical mechanics are based on the Liouville equation and phase space distribution. This, in turn, is based on the Hamiltonian mechanics of a system of point particles.

Real undulatory systems, specially non-linear ones, have to be complex to study without an statistical approach, I guess. I wonder if there exist a general statistical treatment of classical fields, and if so, any good source on the topic?

 

[atyy]

It is possible to study classical fields, including nonlinear ones, without a statistical approach. However, statistical approaches also exist. Kardar addresses fields in the second of his two-part course and book.

https://ocw.mit.edu/courses/physics...statistical-mechanics-of-particles-fall-2013/
https://ocw.mit.edu/courses/physics...ii-statistical-physics-of-fields-spring-2014/

https://www.amazon.com/dp/0521873428/?tag=pfamazon01-20
https://www.amazon.com/dp/052187341X/?tag=pfamazon01-20

 

[andresB]

Thanks for the reference Atty. However, at interesting at it seems, I'm not sure it is what I'm looking for. It seems very quantum focused from the lecture notes, but I have to take a deeper look at it to check.