Something I see often in forums discussing future energy sources is perpetual motion of the second kind. Rather than outright denial of the second law, however, they say the fluctuation theorem shows that spontaneous decreases in entropy happen, though less probable than the reverse, and a machine can harvest these statistical anomalies for unlimited useful energy, much like machines powered by fluctuations in ambient temperature and pressure.

Intuitively, this resembles Maxwell's Demon's sorting of fast and slow molecules, which does not violate the 2nd law. However, I'm not nearly familiar enough with physics to understand how exactly these "fluctuation-powered machines" are related or how Maxwell's Demon obeys the second law (like how storing information affects entropy, or what that information even physically is). So while it seems extremely likely these fluctuation-powered machines won't break the 2nd law or enable perpetual motion, I'm at a loss as to why.

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    $\begingroup$ Take a look at the Brownian ratchet: en.m.wikipedia.org/wiki/Brownian_ratchet $\endgroup$ – aghostinthefigures Jul 12 '18 at 21:31
  • $\begingroup$ For an example such machine and an quantitative refutation, see the following (link). $\endgroup$ – DanielSank Jul 12 '18 at 23:17
  • $\begingroup$ Both of those are good examples of simple machines that upon more rigorous inspection do not violate the 2nd law. While that does go a long way, I'm looking for a generic refutation of any possible machine. Since Maxwell's demon is widely considered incapable of violating the 2nd law, I mentioned it in hopes that any possible machine can be somehow equated to it and thus refuted. $\endgroup$ – BatWannaBe Jul 13 '18 at 4:53

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