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Equilibrium is the condition of a system in which all competing influences are balanced. These can range from forces (static/dynamic equilibrium), to chemical processes (chemical equilibrium) and temperature gradients (thermal equilibrium).

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Necessary and Sufficient Conditions for an Equilibrium to be Stable

By Lyapunov's theorem, if the potential function $U(z) \in C^1$ has a strict minimum at an equilibrium $z_0$, then $z_0$ is stable. … (For example, see What is the state of the equilibrium for a second derivative equal to zero?) …
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