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the principle of maximum entropy in statistical mechanics

January 3, 2010

Statistical mechanics is an interesting subject.  At least in the (equilibrium) classical case, it is ostensibly concerned with deterministic systems, and yet these systems are modeled by probability distributions with great success.  How and why is this possible?  Can these techniques be extended to other domains?  A particularly interesting approach uses E.T. Jaynes’ maximum entropy (MaxEnt) formalism, which attempts to derive the required probability distributions by searching for the most “ignorant” or “uncertain” distribution subject to the constraints of the problem.   In this way, we see a funny connection between complexity, ignorance, and randomness.  This paper, which was part of a final project for Michael Brown‘s statistical mechanics seminar at Swarthmore College, gives an introduction to the MaxEnt approach in nonequilibrium statistical mechanics, including a derivation of the Evans-Searles Fluctuation Theorem. PDF

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