Phase_space - Wikiparency

# Phase space Phase space is the multidimensional manifold whose coordinates are the complete set of position and momentum (or generalized) variables of a system; each point is a possible state and trajectories trace temporal evolution. Liouville's theorem, [[Attractor|attractors]], Poincaré sections, and Wigner distributions connect classical, statistical, and quantum dynamics.  ## Microsims (promoted from legacy — three.js first) ### MicroSim spec - **Recommended sim type:** phase space / [[Attractor|attractor]] - **Microsimmability score:** 86/100 - **Layout:** drawing region (canvas) on top; control region (sliders/buttons) below. ### Parameters (tunable controls) - `Parameter a` - `Parameter b` - `Initial condition` ### What animates A point traces the system's path through phase space, revealing cycles or fixed points. ### Learning objective Read a system's behavior from its trajectory in phase space. ### MicroSim spec - **Recommended sim type:** [[Dynamical_system|dynamical system]] / phase space - **Microsimmability score:** 84/100 - **Layout:** drawing region (canvas) on top; control region (sliders/buttons) below. ### Parameters (tunable controls) - `Initial position` - `Initial velocity` - `Damping` ### What animates A trajectory traces the system's state through position-[[Velocity|velocity]] phase space as it evolves. ### Learning objective Read a system's behavior from the shape of its trajectory in phase space.   ## Microsims — three.js ### Phase space (three.js) <div class="microsim-player"> <iframe src="https://wikitube-3d-microsims.netlify.app/Phase_space.html" width="100%" height="620" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Phase space — three.js microsim"></iframe> </div> **Open it full-screen:** [Phase_space.html](https://wikitube-3d-microsims.netlify.app/Phase_space.html) · library `threejs` · route `microsim/threejs/` ### Related microsims Live sims on neighbouring articles — 6 of them inside this article's own Wikipedia link tree: - [[Agent-based_model]] *(in tree)* - [[Complex_system]] *(in tree)* - [[Emergence]] *(in tree)* - [[Feedback]] *(in tree)* - [[Network_theory]] *(in tree)* - [[Self-organization]] *(in tree)* *Sim hosted off-article; the article owns the reference, not the runtime (WIKI_RULES §10.4). Placed by `g08_place_microsims.py`.*  ## Reveal %%REVEAL:p5%% %%REVEAL:three%% --- *Concept aligned with [Wikipedia](https://en.wikipedia.org/wiki/Phase_space); adapted text, where present, is licensed [CC BY-SA 4.0](https://creativecommons.org/licenses/by-sa/4.0/).* ## Overview The construction descends from [[Joseph-Louis_Lagrange|Lagrange]]-era mechanics through [[Hamiltonian_mechanics|Hamiltonian mechanics]] and [[Lagrangian_mechanics|Lagrangian mechanics]] to [[Henri_Poincaré|Henri Poincaré]]'s qualitative geometry and [[Ludwig_Boltzmann|Ludwig Boltzmann]] and [[Josiah_Willard_Gibbs|Josiah Willard Gibbs]]'s ensembles in [[Statistical_mechanics|statistical mechanics]] — the room where [[Thermodynamics|thermodynamics]] counts its states, and where [[Quantum_mechanics|quantum mechanics]] later drew its distributions. For the [[Dynamical_system|dynamical system]] it is the native canvas: solutions of a [[Differential_equation|differential equation]] or [[Ordinary_differential_equation|ODE]] flow as trajectories, the [[Lorenz_system|Lorenz system]] paints [[Chaos_theory|chaos]], [[Lyapunov_stability|Lyapunov stability]] and [[Perturbation_theory|perturbation theory]] read the geometry, each [[State_variable|state variable]] spans an axis of the [[State-space_representation|state-space representation]], and [[Molecular_dynamics|molecular dynamics]] and [[Physics|physics]] at large integrate through it numerically via [[Numerical_integration|numerical integration]]. ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Phase_space) : [Wikitube](https://en.wikitube.io/wiki/Phase_space) ## Previous hub tags Hubs: `Systems`. Portals: [[PORTAL_Systems]], [[PORTAL_Phase_space]].