Physics · Primitives
Equilibrium
A dynamical system's stationary state — where the dynamics leave it unchanged
Definition
Mechanism
A State of a dynamical system in which the system's time evolution under its own dynamics is stationary — once the system occupies the state it remains there absent external perturbation. Every dynamical system has equilibria (possibly empty), and they are classified by their response to perturbation: *stable* (small deviations decay back to the state), *unstable* (small deviations amplify away), *neutral* (deviations neither decay nor grow). Substrate property: equilibria are implied by a system's dynamics, not designed. Higher patterns test for equilibrium as a signal that a process has settled; some coordination protocols explicitly drive toward or away from a chosen equilibrium.
Invariants
- Stationary: under its own dynamics the system does not leave the State.
- Classifiable as stable, unstable or neutral by its response to perturbation.
- Not unique: occupying this equilibrium is a fact about history, not necessity.
Risks
Failure modes
Transient mistaken for equilibrium
a slow-moving state is read as settled.
Stability inferred from occupancy
the system sits here, so it is assumed to return here.
Relationships
Builds on
References
Infrastructure
System condition at time T
Used by
References
A state-space region dynamics pull toward — fixed points, limit cycles, or chaotic attractors
Infrastructure
Controlled randomization to escape convergence deadlocks
Society
Population grows until output per person falls back to where births and deaths balance, so better techniques raise numbers, not living standards
Reference