Understanding The Meaning and Use of Phase Space

[farowitz]

Hi, I am trying to fully understand the meaning and usage of phase space in the various contexts it's used. For example particle physics, classical mechanics, statistical mechanics, thermodynamics, relativity. Also, there is configuration space, parameter space, and state space. How are all of these things formally defined in all of the contexts they are used? How can I find some reliable, complete and detailed information about these topics? Which and how much maths and physics do I need to study to fully understand these topics, and be capable of performing meaningful data analysis on simulation data (particle physics, plasma physics, etc)?

 

[Andy Resnick]

Hi, I am trying to fully understand the meaning and usage of phase space in the various contexts it's used. <snip>

Phase space is a fairly general mathematical framework for different formulations of mechanics, which is one reason for all those different names (configuration space, parameter space, etc.). The motivating problem is how to represent systems with more than 1 degree of freedom. I suppose a related problem is identifying the degrees of freedom as well.

For example: Lagrangian and Newtonian mechanics use 'configuration spaces' to describe motion. The configuration space is a differentiable manifold on which a group of diffeomorphisms acts. Hamiltonian mechanics is geometry in (even-dimensional) phase space having the structure of a symplectic manifold. Thermodynamics phase space is odd-dimensional: a contact manifold.

I'm not sure where to point you, perhaps others have better suggestions. I suggest Arnold's "Mathematical Methods of Classical Mechanics" and Frankel's "The Geometry of Physics".