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Do you know a scenario where the second law of thermodynamics breaks down?

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The second law breaks down when some of the assumptions underlying this law (or the thermodynamics itself) are broke.

Among what is typically cited as "violations" of the second law are:

  • Violation of the laws of thermodynamics in small systems. Thermodynamics and statistical physics are applicable in thermodynamic limit that is for systems with a huge number of particles. While in some cases this number may be much smaller than the Avogadro number ($N_A\sim 10^{24}$), violation of the thermodynamics in systems with a finite number of degrees-of-freedom is not surprizing. This is equally true for ratchets and billiards.
  • Entropy decrease in some systems, notably in living systems. This is again not surprizing, since these are open systems, which exchange energy and matter with the environment. Thus, while the entropy of the system might be decreasing, this is accompanied by the increase of entropy in the environment, and the net entropy is growing. See this answer and this answer for more background.
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    $\begingroup$ For the first point cf. en.wikipedia.org/wiki/Stochastic_thermodynamics. $\endgroup$
    – kricheli
    Jul 8, 2022 at 8:34
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    $\begingroup$ A third example is rectification of resistor (i.e., Johnson) noise through an ideal diode to purportedly turn thermal energy into work, in violation of the Second Law; instead, it can thus be shown that no passive ideal diode can actually exist (Sundqvist et al., "Second Law based definition of passivity/activity of devices"). $\endgroup$ Jul 8, 2022 at 18:06
  • $\begingroup$ @Chemomechanics Yes, if you have a way to decrease entropy then the second law doesn't apply. $\endgroup$
    – user253751
    Jul 9, 2022 at 11:55
  • $\begingroup$ That’s not at all what that article says. It’s not possible to turn any amount of thermal energy completely into work in an independent process. (There’s no prohibition, however, on decreasing entropy locally, which happens whenever something cools down. The entropy of the surroundings increases by more than a compensatory amount.) $\endgroup$ Jul 9, 2022 at 15:12
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    $\begingroup$ Certainly; my point was directed to @user253751 that Sundqvist et al. do apply the Second Law and don't claim to reduce global entropy. $\endgroup$ Jul 9, 2022 at 17:30
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There is a really cool example I heard of that was published a few years ago, an instance of it actually being violated in practice, not just in theory.

Very roughly, what they did was construct a thermodynamic analogue to an RLC circuit, where energy oscillates back and forth, instead of entropy uniformly increasing by monotonically increasing uniformity of the system.

The key here is that most of what you learn in statistical mechanics is predicated on slow changes of uniform systems. Kinetics and irreversible processes are much subtler. Bear in mind that most popular science is usually not going to go past the face value statement of a physical law.

https://www.media.uzh.ch/en/Press-Releases/2019/Thermodynamic-Magic.html

DOI: 10.1126/sciadv.aat9953

Edit: To add more clarity, their experiment involved two heat reservoirs connected with a Peltier device that had an inductor connecting the terminals. Heat passing through the Peltier device generates a current, the inductor keeps the current going past the point of equilibrium, causing equilibrium overshoot, so the temperature difference appears like a damped harmonic oscillator instead of monotonically going to zero.

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    $\begingroup$ So it runs a heat engine using a hot object and stores the energy in an inductor and then expends said energy running a heat pump to get the now room-temperature object cold? $\endgroup$ Jul 9, 2022 at 7:46
  • $\begingroup$ @KevinKostlan No, that would be a refrigerator. The second law says that the entropy in a closed system cannot decrease. Their configuration has a damped oscillating temperature difference, which also means that entropy periodically decreases, but after a long time, entropy is maximized. Thing is, systems may take an indirect route to maximizing entropy when they are not quasistatic. But in the end, entropy does tend to maximum in the long time limit. $\endgroup$
    – Liam Clink
    Jul 11, 2022 at 21:53
  • $\begingroup$ The link doesn't work. $\endgroup$
    – Urb
    Jul 26, 2022 at 6:13
  • $\begingroup$ @Urb It works for me. But this is why I included the DOI, you can find it even with link rot $\endgroup$
    – Liam Clink
    Aug 24, 2022 at 15:10

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