A system at equilibrium is still highly active, dynamic, and constantly making perturbations at the molecular level.
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A spontaneous reaction is a direct consequence of molecular level processes trying to minimize its overall energy (i.e. reaching equilibrium)
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A spontaneous reaction usually leaves a system less orderly. However, a system can become more orderly (e.g. self-assemble) if it can lower its overall energy by forming a regular pattern.
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