Phase space

In mathematics and physics, a phase space of a dynamical system is a space in which all possible states of a system are represented, with each possible state corresponding to one unique point in the phase space. For mechanical systems, the phase space usually consists of all possible values of position and momentum variables. The concept of phase space was developed in the late 19th century by Ludwig Boltzmann, Henri Poincaré, and Willard Gibbs.

Introduction

In a phase space, every degree of freedom or parameter of the system is represented as an axis of a multidimensional space; a one-dimensional system is called a phase line, while a two-dimensional system is called a phase plane. For every possible state of the system, or allowed combination of values of the system's parameters, a point is included in the multidimensional space. The system's evolving state over time traces a path (a phase space trajectory for the system) through the high-dimensional space. The phase space trajectory represents the set of states compatible with starting from one particular initial condition, located in the full phase space that represents the set of states compatible with starting from any initial condition. As a whole, the phase diagram represents all that the system can be, and its shape can easily elucidate qualities of the system that might not be obvious otherwise. A phase space may contain a great number of dimensions. For instance, a gas containing many molecules may require a separate dimension for each particle's x, y and z positions and momenta as well as any number of other properties.

Phase space (disambiguation)

Phase space can refer to:

Phase Space (story collection)

Phase Space (subtitled Stories from the Manifold and Elsewhere) is a 2003 science fiction collection by Stephen Baxter containing twenty-three thematically linked stories, in which the human relationship with the universe is explored: whether humanity is truly alone in the universe, if there are other intelligent species, if these have turned their backs on us, or if expansion itself is destined to fail.

Written in the same style as most of Stephen Baxter's work, Phase Space is a collection of more or less scientifically based stories in the tradition of Arthur C. Clarke. The stories are mostly set in the same Multiverse as the books in his Manifold series, with a few stories related to his separate NASA Trilogy.

The book contains the following short stories: