“phase space”的概念、定义、翻译、参考文献-科学参考

phase space

Physics

For a system with n degrees of freedom, the 2n-dimensional space with coordinates (q₁, q₂, …, q_n, p₁, p₂, …, p_n), where the qs describe the degrees of freedom of the system and the ps are the corresponding momenta. Each point represents a state of the system. In a gas of N point particles, each particle has three positional coordinates and three corresponding momentum coordinates, so that the phase space has 6N-dimensions. If the particles have internal degrees of freedom, such as the vibrations and rotations of molecules, then these must be included in the phase space, which is consequently of higher dimension than that for point particles. As the system changes with time the representative points trace out a curve in phase space known as a trajectory. See also attractor; configuration space; statistical mechanics.

Chemistry

For a system with n degrees of freedom, the 2n-dimensional space with coordinates (q₁, q₂, …, q_n, p₁, p₂, …, p_n), where the qs describe the degrees of freedom of the system and the ps are the corresponding momenta. Each point represents a state of the system. In a gas of N point particles, each particle has three positional coordinates and three corresponding momentum coordinates, so that the phase space has 6N-dimensions. If the particles have internal degrees of freedom, such as the vibrations and rotations of molecules, then these must be included in the phase space, which is consequently of higher dimension than that for point particles. As the system changes with time the representative points trace out a curve in phase space known as a trajectory. See also attractor; configuration space; statistical mechanics.

Geography

1 Very simply, a continuum representing two variables: A and B. The continuum ranges from 100% A, 0% B, to 0% A, 100% B. See, for example, Hooke (2003) TIBG 28, 2 on the phase space of meander movement and bend curvature. Melton (1958) J. Geol. 66 describes a mature drainage basin phase space with four variables.
2 Very much less simply, an abstract concept that captures all the possible spaces in which a spatio-temporal system might exist in theoretical terms; not just what happens but what might happen; ‘the space of the possible’ (J. Cohen and I. Stewart 1994). ‘The geography of phase space is flexible, but not totally arbitrary: the main possibilities are “already there”, constrained by contextual realities’ (I. Stewart and J. Cohen 1997). This use of the concept is not totally distinct from 1; there are just many more factors involved. Martin (in Harrison et al. (2006) Area 38, 4) draws on Richards in J. Matthews and D. Herbert (2004) to see phase space as ‘a middle road between relational space and more fixed notions of spatiality’.
Hooke (2007) Geomorph. 91, 3–4 uses phase space plots to help uncover emergent behaviour in meandering rivers.

单词	phase space
释义	phase space Physics For a system with n degrees of freedom, the 2n-dimensional space with coordinates (q₁, q₂, …, q_n, p₁, p₂, …, p_n), where the qs describe the degrees of freedom of the system and the ps are the corresponding momenta. Each point represents a state of the system. In a gas of N point particles, each particle has three positional coordinates and three corresponding momentum coordinates, so that the phase space has 6N-dimensions. If the particles have internal degrees of freedom, such as the vibrations and rotations of molecules, then these must be included in the phase space, which is consequently of higher dimension than that for point particles. As the system changes with time the representative points trace out a curve in phase space known as a trajectory. See also attractor; configuration space; statistical mechanics. Chemistry For a system with n degrees of freedom, the 2n-dimensional space with coordinates (q₁, q₂, …, q_n, p₁, p₂, …, p_n), where the qs describe the degrees of freedom of the system and the ps are the corresponding momenta. Each point represents a state of the system. In a gas of N point particles, each particle has three positional coordinates and three corresponding momentum coordinates, so that the phase space has 6N-dimensions. If the particles have internal degrees of freedom, such as the vibrations and rotations of molecules, then these must be included in the phase space, which is consequently of higher dimension than that for point particles. As the system changes with time the representative points trace out a curve in phase space known as a trajectory. See also attractor; configuration space; statistical mechanics. Geography 1 Very simply, a continuum representing two variables: A and B. The continuum ranges from 100% A, 0% B, to 0% A, 100% B. See, for example, Hooke (2003) TIBG 28, 2 on the phase space of meander movement and bend curvature. Melton (1958) J. Geol. 66 describes a mature drainage basin phase space with four variables. 2 Very much less simply, an abstract concept that captures all the possible spaces in which a spatio-temporal system might exist in theoretical terms; not just what happens but what might happen; ‘the space of the possible’ (J. Cohen and I. Stewart 1994). ‘The geography of phase space is flexible, but not totally arbitrary: the main possibilities are “already there”, constrained by contextual realities’ (I. Stewart and J. Cohen 1997). This use of the concept is not totally distinct from 1; there are just many more factors involved. Martin (in Harrison et al. (2006) Area 38, 4) draws on Richards in J. Matthews and D. Herbert (2004) to see phase space as ‘a middle road between relational space and more fixed notions of spatiality’. Hooke (2007) Geomorph. 91, 3–4 uses phase space plots to help uncover emergent behaviour in meandering rivers.
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