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How Did We Get Here? The Tangled History of the Second Law of Thermodynamics

Stephen Wolfram

But he had a second hypothesis too—based, he said, on the ideas of “that most ingenious gentleman, Monsieur Descartes”: that instead air consists of “flexible particles” that are “so whirled around” that “each corpuscle endeavors to beat off all others”.

Energy 88
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Computational Foundations for the Second Law of Thermodynamics

Stephen Wolfram

Once one has the idea of “equilibrium”, one can then start to think of its properties as purely being functions of certain parameters—and this opens up all sorts of calculus-based mathematical opportunities. That anything like this makes sense depends, however, yet again on “perfect randomness as far as the observer is concerned”.

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Launching Version 13.0 of Wolfram Language + Mathematica

Stephen Wolfram

When you do operations on Around numbers the “errors” are combined using a certain calculus of errors that’s effectively based on Gaussian distributions—and the results you get are always in some sense statistical. Also in the area of calculus we’ve added various conveniences to the handling of differential equations.