Abstract
As usually stated, the second law of thermodynamics is asymmetric under time reversal, and is thus not compatible with a microscopic mechanics symmetric under time reversal. In its most popular form, the second law states that the entropy of a closed system tends to increase. Attempts to derive this from time-symmetric physical laws are self-defeating because any argument which leads to increasing entropy may be time reversed to produce an equally valid argument leading to decreasing entropy. Yet irreversibility is a fact of life. This is Loschmidt's paradox1.
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References
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HILLEL, A. Alternative Statement of the Second Law of Thermodynamics. Nature 242, 456–457 (1973). https://doi.org/10.1038/242456a0
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DOI: https://doi.org/10.1038/242456a0
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