# Does hysteresis always cause an increase in entropy?

Question

In thermodynamics does hysteresis always cause an increase in entropy?

This question came about when thinking about two different definitions of a reversible process:

1. A reversible process is one that is quasistatic and has no hysteresis.
2. A reversible process is one that has no change to the surroundings when you do it followed by its reverse.

I am trying to see how these two definitions are equivalent.

• The answer depends strongly on what you mean by "hysteresis", so please, define it. I am not trying to avoid the answer but would you call a Lissajous curve hysteresis? – hyportnex Oct 15 '15 at 21:36
• It is interesting and kind of tricky, if we reverse the cycle in hysteresis, should be entropy decrease? The work would. The only helpful thing that I can think of is that if we apply Jarzynski equality to a cycle, then $\langle\exp(-\beta W)\rangle = 1$, and since the energy does not change, $\langle\exp(\Delta S)\rangle = 1$. Then using $e^x \ge 1 +x$, we get $\langle\Delta S\rangle \ge 0$. – hbp Oct 26 '15 at 17:33