The fluctuation-dissipation theorem (FDT) is a powerful tool in statistical physics for predicting the behavior of non-equilibrium thermodynamical systems. These systems involve the irreversible dissipation of energy into heat from their reversible thermal fluctuations at thermodynamic equilibrium. The fluctuation-dissipation theorem applies both to classical and quantum mechanical systems.
The fluctuation-dissipation theorem relies on the assumption that the response of a system in thermodynamic equilibrium to a small applied force is the same as its response to a spontaneous fluctuation. Therefore, the theorem connects the linear response relaxation of a system from a prepared non-equilibrium state to its statistical fluctuation properties in equilibrium. Often the linear response takes the form of one or more exponential decays.
The fluctuation-dissipation theorem was originally formulated by Harry Nyquist in 1928, and later proven by Herbert Callen and Theodore A. Welton in 1951.
Read more about Fluctuation-dissipation Theorem: General Applicability, General Formulation, Derivation, Violations in Glassy Systems
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