Rigorous definition of Hysteresis
I have been studying thermodynamics and have come across this concept of hysteresis but am struggling to find a rigorous way to define it. Here are the types of definitions I have come across
1. Say a process takes a system from one point in a state space to another and then back. Upon return, if some physical quantities have changed, there was hysteresis.
This doesn't make sense to me because why not extend the state space to include the changed factor? If energy changed, add that as a dimension to the state space and in fact you did not return. It's not hysteresis then. In other words, how does one define the state space rigorously then?
1. The same as before but instead of saying physical quantities of the system changed, the surroundings have changed.
I feel like this is just wrong because, often, hysteresis does refer to changes in the system itself like the energy change due to friction or something.
1. Take some process p and conduct it on the system. 749
Now conduct "p^-1" which is basically do it backwards i.e. pull the piston up and then down. If the system's state does not return to the same point, then there is hysteresis.
My problem with this is that I'm not sure how well-defined "p^-1" actually is or if, in general, it makes sense to think about it. What if there existed a process where there was no obvious way to do it backwards but there still existed friction and other hysteresis-creating entities. Does it have hysteresis or no? I find it hard to believe that the existence of hysteresis is dependent on the process's ability to be done in reverse but this definition I think is closest.
1. Hysteresis is the dependence of the state of the system on its history.
To be honest, not even sure what this means. This could mean that either a) now there are two entities that uniquely describe the system's current condition: its position in state space AND its history (which I don't think it's saying) or b) the state it is in is determined by it history but this means the history doesn't actually add information about the system i.e. if the magnetic moment is different based on how it got there, simply adding the magnetic moment as another dimension to the state space should make the history irrelevant.
If someone could please help me see what I am missing or let me know if hysteresis is simply ill-define in a general sense, that would be greatly appreciated! 28