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Phase Space

In physics, mathematics and statistical mechanics, the term phase space is a space in which all possible states of a system are represented. Each possible state of the system is a unique point in the phase space, representing all degrees of freedom of the system as an axis in a multidimensional space. Plotting states in this way can represent the system's evolution over time as well. States may include any variable within the system, such as position, momentum, pressure, temperature, etc.

A plot of position and momentum variables of a quantum particle or system, or the various regions of stability of thermodynamic phases in a chemical system is also called a phase diagram. The motions of ensemble systems in phase space coordinates can then be studied by classical statistical mechanics.

An interesting use of phase space is an application to the fine-tuning of the universe of Steven Hawking and Jacob Beckenstein's calculations for black hole entropy. Oxford mathematician Roger Penrose calculated the likelihood of our particular universe (with all its fine-tuned constants) to be 1 in a phase space of 10 to the 10th to the 123rd [1:1010123].

Web Resources On Phase Space

Phase Space (Wikipedia)
Phase Space (hyperphysics)

Book Resources On Phase Space

The Symmetry Perspective: From Equilibrium to Chaos in Phase Space and Physical Science by Martin Golubitsky and Ian Stewart
Geometric Optics on Phase Space (Texts and Monographs in Physics) by Kurt B. Wolf
Phase Space Picture of Quantum Mechanics: Group Theoretical Approach (Lecture Notes in Physics Series) by Y.S. Kim and Marilyn E. Noz

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