Szilard's Heat Engine

In 1928, Leo Szilard deviced the first concrete implementationof a Maxwell Demon. With this construction he derived that the thermodynamic equivalent of 1 bit of information is kT ln(2), many years before information theory (or, indeed, bits) existed.

I have completed a rigorous proof that his heat engine obeys the Second Law. While there was ample heuristic understanding that this would be the case, there was, rather surprisingly, no proof of this fact. Furthermore, my proof uncovered a most curious fact about the engine that had passed unnoticed: its phase space contains a strange topological object, called in jargon a ``branched manifold''. This particular branched manifold is called ``the Williams template for the Bernoulli Shift''; the Bernoulli shift is a chaotic, ergodic and mixing map whose topological entropy is log(2). These objects have been used extensively in deterministic dynamical systems, but their use in the context of stochastic dynamics requires some care as to how the dynamics is defined at the branches.

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