# What does "A reversible process can be reversed by inducing infinitesimal changes of external condition" mean?

The Wikipedia said "A reversible process is a process whose direction can be "reversed" by inducing infinitesimal changes to some property of the system via its surroundings, while not increasing entropy. What does "inducing ..." means? I know that the reversible process is the process which can always be reversed in a way that the system follows an exactly same path of a direct process with an opposite direction. The Wikipedia statement looks to show how to initiate reversing the process. Could you provide me a physical meaning of "inducing ..." or some intuitive examples of it?

• It just means by making an infinitesimal change to the surrondings Apr 17, 2017 at 1:10

Inducing means persuading or bringing about, rather than changing something directly. Examples : you induce someone to move by persuading them, or pricking them with a pin; you induce a change in volume by applying external pressure; you induce charge to come from the Earth onto a grounded conductor by bringing another charge close to it.

The way the statement is framed (...a process whose direction can be reversed by inducing...), it seems to imply that some external agency (may be even a conscious observer who makes the decision to reverse it) is required to make the system go backward on a reversible process that it has executed. But a reversible process, which by definition does not cause an entropy change of the universe, does not have a unique direction associated with it. This means that it can go backwards and forwards all by itself with no preference for either direction. This seems to contradict our ability to plot a reversible path on a thermodynamic diagram showing how a system undergoes a (reversible) change from one state to another. This contradiction vanishes when we see a reversible path as the limit of a quasi-static process (see Thermodynamics by Callen).

Suppose a thermodynamic system changes state from $1$ to $2$, plotted as two distinct points on a thermodynamic diagram. Now you must be aware that only equilibrium states can be plotted on a thermodynamic diagram. Suppose in going from state $1$ to $2$, the system goes through a chain of intermediate equilibrium states, $p_1,p_2,...,p_n$, as follows: $1\to p_1\to p_2\to ...\to p_n\to 2$. Between any two consecutive equilibrium states the process is irreversible. However as you increase the number of points on the path indefinitely, i.e. in the limit $n\to\infty$, you get a continuous path which is nothing but a reversible path connecting the states $1$ and $2$.*

Now to take a system from state $1$ to $p_1$ say, both of which are equilibrium states, it is necessary that some constraint on the system be relaxed. To take up a concrete example, consider reversible expansion of a gas in a piston-cylinder arrangement. The ambient pressure has to be only slightly below the gas pressure so that the gas expands only by a tiny amount, thus generating only a tiny amount of entropy. In the initial equilibrium state, ambient pressure was equal to gas pressure, and this constraint was relaxed a little bit (otherwise the system wouldn't change its state, disregarding fluctuations). However if this constraint is reinstated, i.e. if the ambient pressure were to be increased by a tiny amount so that it goes back to its initial pressure, then the gas will also go back to its initial state. Of course this process will also generate (a tiny amount of) entropy, but in the limit that the state $p_1$ approaches state $1$ arbitrarily close, the generated entropy can be made arbitrarily small (which statement is true of the forward process as well). This is exactly what the statement in the Wikipedia article is referring to. However so far as state $1$ is not identical to state $p_1$, but only very close, then it is an irreversible process and therefore requires inducing (which word is only a convenient substitute for "manipulation of constraints on the thermodynamic system under consideration").

* There is the question of how a continuum of points is obtained by a limit which actually gives you a countable infinity; I don't know the answer

In this context, the word "inducing" seems to mean "being brought about from the outside rather than the inside." That is, there is something in the environment which causes the system to undergo a (reversible) change.

In a way, this may be adopted as an alternative definition or at least a criterion for irreversibility. If the changes are induced, there is a chance that they are reversible. If they are spontaneously occurring within the system itself, they are irreversible. It should be noted that this idea hinges on one's definition of a system, its scope and so on.