The phase space of a physical system is the set of all possible physical states of the system under a given parameterization, with each possible state corresponding to exactly one point in the phase space. For mechanical systems the phase space typically consists of all possible values of the position and momentum parameters, forming the direct product of ordinary space and reciprocal space. The concept of phase space was developed in the late nineteenth century by Ludwig Boltzmann, Henri Poincare and Josiah Willard Gibbs.
Facts
Origin YearMarks Gibbs own Elementary Principles in Statistical Mechanics (1902), the first formalization of the modern phase-space concept per this source; the term phase space itself was coined later, by Paul and Tatyana Ehrenfest in 1911. Connections
Associated With
Source Phase Space (Wikipedia)
Source Phase Space (Wikipedia)
In Branch
Sources
1. The Tangled Tale of Phase Space (Physics Today)
Physics Today (American Institute of Physics)Gibbs and Ehrenfest passageQuote, Gibbs and Ehrenfest passage
If we regard a phase as represented by a point in space of 2n dimensions, the changes which take place in the course of time in our ensemble of systems will be represented by a current in such space.
Phase Space (Wikipedia)
Wikimedia FoundationLead section
The phase space of a physical system is the set of all possible physical states of the system when described by a given parameterization.
Associated With: Dynamical System, Principles section, third sentence
The system's evolving state over time traces a path (a phase-space trajectory for the system) through the high-dimensional space.
Associated With: Henri Poincare, Lead section, last sentence
The concept of phase space was developed in the late 19th century by Ludwig Boltzmann, Henri Poincaré, and Josiah Willard Gibbs.
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