As I understand it, a perpetual motion machine does continuous work without additional energy input. If a perpetual motion machine of the second kind exists, it violates the second law of thermodynamics and decreases the entropy of the universe. But how does this violation make it a “perpetual” motion machine?

I’ve seen examples like Gamgee’s Zeromotor, which claims to absorb heat from a colder ammonia gas to restore the system and surroundings to initial conditions. But I suspect this is too concrete to apply to all such PMMs. Can every such PMM be assumed to get back to the initial conditions of the universe? Wouldn’t this imply $ΔS = 0$ not $ΔS ≤ 0$ as expected for a second law violation?

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    $\begingroup$ A machine of the second kind should be able to extract work from inside a gas in thermal equilibrium $\endgroup$ Commented Jan 25 at 6:32
  • $\begingroup$ But is a gas required ? Can it be any liquid? $\endgroup$ Commented Jan 25 at 6:36
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    $\begingroup$ Yes sure, but it has to be at a constant temperature, so your device cannot move heat from a large temperature reservoir into a colder one, but just extract work from a thermal bath. Such thing is impossible though, other than happening by random chance as an unlikely fluctuation $\endgroup$ Commented Jan 25 at 6:38
  • $\begingroup$ Thanks, but what actually makes any such machine “perpetual“? I understand that they cannot exist. $\endgroup$ Commented Jan 25 at 13:31
  • $\begingroup$ that you can run a motor without an energy source other than that coming from a thermal bath. $\endgroup$ Commented Jan 25 at 17:01

2 Answers 2


The “perpetual motion machine of the second kind”—meaning an impossible machine that destroys entropy—is named after the classic perpetual motion machine (of the first kind), another type of impossible machine that independently provides mechanical work forever. In modern understanding, moving parts are not essential to this concept, so the reference to motion is somewhat of a misnomer.

Consider thinking of the term as an idiom—a phrase whose understood meaning differs from the literal interpretation of its words. If you must take it literally, you could associate it with a machine that also provides work forever, but not independently—it cools down everything around it toward absolute zero. This satisfies conservation of energy but remains impossible because of the entropy destruction when converting so-called “heat”—thermal energy—to work.

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    $\begingroup$ And you could always couple it to a heat pump to get something perpetual $\endgroup$
    – Dale
    Commented Jan 25 at 17:31

It is perpetual in the sense that it would perpetually do work while being in contact with a single reservoir. Therefore you could in principle extract the heat from some object (hotter than the system that you are trying to put in motion) and then convert all that heat into work. You could then convert that work back into heat, and so on. In reality you cannot convert all the heat received from the reservoir completely into work, there must be some fraction of it that goes (to a colder reservoir) and never comes back. So you cannot have a perpetual motion if this kind.

  • $\begingroup$ That makes sense. You can feed the output into a heat pump that converts work into heat. But I think it would have to be 100% efficient in order to achieve perpetual energy flow. Please correct me if I’m wrong. $\endgroup$ Commented Jan 27 at 7:19
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    $\begingroup$ Yes, you are correct. The idea is that 100% conversion of work to heat is possible, but the reverse is not. You cannot have 100% conversion efficiency of heat to work. This is what Carnot (which conceived the most efficienct cycle on paper) showed. Even a reversible (ideal) engine would have an efficiency less than 100%, because there is a law that forbids the complete transformation of heat to work. $\endgroup$ Commented Jan 27 at 7:57
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    $\begingroup$ In the end the motion stops, because even though you can restore all the heat using the work produced, you cannot do the same amount of work back again. Each time you have to convert heat into work, there is less and less available energy to do so. In the end all the available energy to do work goes to zero, and the motion stops. $\endgroup$ Commented Jan 27 at 8:01

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