When I studied thermodynamics for the first time I didn't really get much the conceptual understanding on reversibility, but nonetheless I've got a rough understanding and a mathematical criterion for it.

The rough understanding I got was the following: If we consider a process connecting two equilibrium states we might ask whether the inverse process could occur naturally or not. If it can the process would be reversible and otherwise it would be irreversible.

The criterion for a reversible process would be $\Delta S =0$. The whole point is that the entropy maximum postulate states that the entropy must be maximized. If when a constrant is removed a system goes from $A$ to $B$ with $\Delta S > 0$, then certainly $S_B>S_A$, hence naturally the system could never return from $B$ to $A$, because it wouldn't maximize the entropy.

On the other hand if $\Delta S = 0$, we would have $S_A = S_B$ and nothing would prevent the return.

This is a mathematical criteria and more than that, requires the idea of entropy.

My question here is: suppose we are simply given the description of a process (for example: "a piece of hot metal is thrown into cold water" or "a pendulum with a frictionless support swings back and forth"), in that case we don't know the fundamental relation, and there's no mathematics whatsoever here.

In that case, just from a conceptual description of a process how can one judge whether the process is reversible or irreversible? What is a criterion that can be used when we are discussing the process just conceptually without math involved and without any knowledge about entropy?

  • $\begingroup$ The main criteria of reversibility is you can return to your initial state by reversing the operation; no information is lost. Irreversibility means there is a form of dissipative work- information is lost during the operation and hence you can't return back to your initial state even by reversing the operation. $\endgroup$
    – user36790
    Mar 16, 2016 at 12:36
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    $\begingroup$ As Feynman said: make a movie of the process, then show the film backwards. If the audience laughs, the process was irreversible. $\endgroup$
    – rob
    Mar 16, 2016 at 16:46
  • $\begingroup$ My answer on this topic over on Worldbuilding.SE may be useful. $\endgroup$ Mar 16, 2016 at 16:53
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    $\begingroup$ I think you may have a misconception. A reversible process implies there is no entropy generated as the system moves between two states ($S_{\mathrm{gen}}=0$). This does not mean that the entropy is constant. When the entropy remains constant ($\Delta S=0$), and the process is called isentropic. A general open or closed system can have interactions with the surroundings, and a reversible process does not in general mean the process is also isentropic. When the system is isolated, however, there is no interaction with the surroundings, and a reversible process must also be isentropic. $\endgroup$ Mar 16, 2016 at 17:53

2 Answers 2


There are two techniques that I use for simple situations.

First, can I actually imagine how the reverse process would work? Intuitively, it makes sense that I can just push a pendulum back to the original state. But obviously, if I were to put a piece of room temp. metal in room temp. water, they wouldn't suddenly diverge in temperature. This is essentially just playing the system backwards in time, and seeing if it follows your intuition. Knowledge about entropy helps though.

The other technique stems from the mathematicians definition of invertible functions. If multiple initial conditions can result in the same outcome, then the situation isn't invertible. For example, slightly hotter metal and slightly colder water result in the same outcome: so there would be no way to know which original situation to pick if you tried the inverse. A caveat though: it is very hard to tell when situations are exactly identical, as opposed to nearly identical. If they are just nearly identical, then the system could just be chaotic (large dependence on initial conditions) but reversible.

However, these can become difficult to apply in complex scenarios; that's why the entropy definition is so powerful, and why we use it.

  • $\begingroup$ That's a really interesting thought: "If multiple initial conditions can result in the same outcome, then the situation isn't invertible." Can you expand your answer and/or provide a reference which explores that idea more rigorously? $\endgroup$ Mar 16, 2016 at 16:47

For a closed system, if there is no viscous dissipation of mechanical energy during the process, no finite rate of heat conduction, no finite rate of species diffusion, the process is reversible. Under such circumstances, the process path between the initial and final equilibrium states of the system consists of a continuous sequence of thermodynamic equilibrium states. The system is never more than slightly removed from being at thermodynamic equilibrium.


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