Phase space

In dynamical system theory, the phase space is the space in which all possible states of a system are represented, with regarded and target separately. possible state corresponding to one unique portion in the phase space. For mechanical systems, the phase space commonly consists of all possible values of position and momentum variables. it is the outer product of direct space and reciprocal space. The concept of phase space was developed in the unhurried 19th century by Ludwig Boltzmann, Henri Poincaré, and Josiah Willard Gibbs.

Thermodynamics and statistical mechanics

In Avogadro's number, thus describing the system at a microscopic level is often impractical. This leads to the use of phase space in a different sense.

The phase space can also refer to the space that is parameterized by the macroscopic states of the system, such as pressure, temperature, etc. For instance, one may image the pressure-volume diagram or entropy-temperature diagrams as describing component of this phase space. A unit in this phase space is correspondingly called a macrostate. There may easily be more than one microstate with the same macrostate. For example, for a fixed temperature, the system could form many dynamic configurations at the microscopic level. When used in this sense, a phase is a region of phase space where the system in impeach is in, for example, the liquid phase, or solid phase, etc.

Since there are numerous more microstates than macrostates, the phase space in the number one sense is commonly a manifold of much larger dimensions than in thesense. Clearly, numerous more parameters are asked to register every detail of the system down to the molecular or atomic scale than to simply specify, say, the temperature or the pressure of the system.