Definition of "phase space"

phase space

noun
countable and uncountable, plural phase spaces
1. (mathematics, physics, dynamical system theory) Given a (dynamical) system, any topological space such that every point in the space's underlying set uniquely represents a state of the system and every possible state is represented by some point;(less formally) the underlying set of such a topological space.
  Quotations
  The phase space of a single material point is a manifold M×V*, and the Newton state-space is identifical[sic] with M×V.
  1991, Jan J. Slawianowski, Geometry of Phase Spaces, Wiley, page 485
  Their energies are those of the level sets p 2 / 2 + V ( x ) = E {\displaystyle p^{2}/2+V(x)=E} that enclose an area of 2 π ℏ ( n + 1 / 2 ) {\displaystyle 2\pi \hbar (n+1/2)} in the classical phase space. Despite embracing a configuration space point of view, these methods have produced a phase space result.
  2006, Matthew Charles Cargo, Phase Space Approaches to Higher Order WKB Approximations, University of California, Berkeley, page 8
  The distribution of particles in phase space is given either by the injector characteristics and injection process or in the case of electron beams by the equilibrium of quantum excitation due to synchrotron radiation and damping.
  2007, Helmut Wiedemann, Particle Accelerator Physics, Springer, page 377