Non-Equilibrium 11/15/21

Science with Richard Bleil

At my gun club, I rather surprised a young woman when I mentioned that everything that happens, including falling in love (no, we didn’t) must happen according to the laws of thermodynamics.  To be fair, though, not everything follows these laws (although love does).  And believe it or not, I’m not talking about quantum theory, where subatomic particles follow Schroedinger.  Rather, I’m talking about non-equilibrium thermodynamics.

See, the laws of thermodynamics with which you are familiar (more so than most people realize) are more correctly referred to as “equilibrium thermodynamics”.  The interesting thing is that even chemical processes that are not in equilibrium still follow equilibrium thermodynamics.  See, in thermodynamics, “equilibrium” has a rather strange definition that goes something like this.  If you consider any process, chemical or physical, it will follow equilibrium thermodynamics if, on taking an infinitesimally small time slice (dt for my calculus friends), that system is just as likely to return to its previous state as it is to proceed to the next. 

I know, it’s complicated.  Let’s take a more humanistic example.  Suppose you take a photograph, essentially freezing time, just as a customer is handing a twenty-dollar bill to a cashier.  At this point in time, both the cashier and the client have ahold of the bill.  In the next instant, you would expect the bill to move “forward” into the hands of the cashier, but you don’t really know.  It might turn out that the customer is a joker, or just decided to change in another way, and will yank the bill back.  Either is technically equally likely.  This can be thought of as an equilibrium for that very thin instant slice of time.  It could move forward, or backwards.

Almost every action in a physical or chemical process follows a series of very small time slice steps at equilibrium.  A water molecule breaks its bond with bulk water in the evaporation process, but before going off to become vapor, it might just re-adsorb back into the water.  It’s an equilibrium step, even though the bulk of water in an evaporation process go on into the vapor phase, but sitting there, right there, at the water surface, it could go either way. 

Some processes, although rare, do not follow equilibrium thermodynamics, and might even appear to violate them.  These “non-equilibrium” reactions or processes are usually so fast, and so violent, that they need their own thermodynamic laws.  You’ve seen them; we’re talking about things like explosions, for example.  One of my favorite hobbies is target shooting.  Inside the bullet is a small amount of explosive (gunpowder) and the equivalent of a blasting cap.  When the hammer hits that blasting cap, it causes an explosion inside of the bullet, with fire, rapidly expanding gases (that push the projectile forward), heat and so forth.  This is an example of a non-equilibrium process.

To explain these violent and extreme process, statistical thermodynamicists often use the Ornstein-Zernike equation.  It’s a very difficult and complex (but simple looking) equation that few thermodynamicists even know how to utilize.  In a strange kind of way, it throws an extra term into classical thermodynamics that acts as an extra entropy generation term.  This can be thought of as the entropy of lack of understanding of the processes in this very violent and rapid process or equation.  Classical thermodynamics includes entropy, but it’s a well-behaved entropy term related to change in heat, but these non-equilibrium processes do not have entropy that behaves as its supposed to. 

Interestingly, I’ve recently heard “Ornstein-Zernike Equation” used in a science fiction movie, or television program (I’m not sure which), and it was almost used correctly which is the impetus of this post. 

So, there are really four types of thermodynamics.  There’s classical (equilibrium) thermodynamics that I enjoy discussing from time to time along with its applicability to processes that you might not have considered.  There’s quantum theory that applies to particles and their behavior if they are sufficiently small and fast that their wave component of behavior becomes significant, or, to put it more succinctly, sub-atomic particles.  There is Statistical Thermodynamics which is the bridge between the quantum world and the macroscopic since, after all, if you get enough oddly behaving sub-atomic particles together, their behavior has to add up to the classical thermodynamics limit.  And, as it turns out, there is a special type of thermodynamics, non-equilibrium thermodynamics, for misbehaving processes and reactions that is too fast and violent for the old-fashioned classical laws of thermodynamics.  And what does this mean to you?  Just that it’s a far more complicated world than most people realize. 

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