Fluctuation theorem

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The fluctuation theorem addresses the probability under statistical mechanics that the entropy of a system not at thermodynamic equilibrium (maximum entropy) will increase or decrease over a period of time.

The second law of thermodynamics predicts that such entropy should increase until equilibrium. But under the theory of statistical mechanics there would always be a nonzero probability that the entropy of an isolated system will spontaneously decrease. The fluctuation theorem precisely quantifies such probability under the theory of statistical mechanics.