Ends and Odds

If you wait long enough, everything goes to equilibrium – a strange state of balance where it looks like nothing is changing. But look more closely and you see a frenzy of activity that seems to go… well, nowhere. Why?

 

A macroscopic process seems irreversible. A drop of ink in water spreads out and smears until it uniformly colors the liquid. You’ll never see the colored liquid turn back into colorless water and an ink droplet. But at the microscopic level (actually nanoscopic), the motion of jittery molecules does not distinguish between forward and reverse. Molecules just keep moving back and forth, and forth and back. Our experience is that macroscopic processes are unidirectional along the flow of time, while microscopic processes are time-reversible – you can’t tell if it’s going forwards or backwards and it makes no difference.

 

I’ve been reading Knowing by Michael Munowitz and enjoying his lucid explanations into the nature of… well, nature. Today’s post is about Chapter 10, aptly and cleverly titled “Ends and Odds”. It’s about thermodynamics. It’s about the fate of all macroscopic processes (to reach equilibrium!). It’s about the elusive nature of time, flowing unidirectionally toward greater and greater entropy. It’s about statistics. What makes the time-agnostic microscopic world into the one-way flow of the macroscopic world is a matter of odds. Munowitz declares this is about freedom. While the frenzy of the jittery microscopic motion never stops, this “freedom [of motion] leads to equality: freedom of position, equality of distribution.” This is what it means to be at equilibrium.

 

Munowitz walks the reader through three examples: pressure, temperature, and distribution. Molecules freely move until all pressures equalize, all temperatures equalize, and all concentrations equalize. It all comes from statistics. Considering pressure, Munowitz writes that it “arises from the impacts of individual molecules against the walls of a container. Each single impact is small, yet there is strength in numbers. The collisions come rapidly and in tremendous quantity, averaging together to produce a steady macroscopic pressure at equilibrium: a statistical average, emerging clear and sharp from the microscopic confusion. Microscopic randomness gives way to macroscopic reliability.” The same thing happens for temperature and distribution (concentration). Macroscopically there is a reliable one-way gradient. Heat flows from hot to cold. Solute molecules flow from a more concentrated area to a less concentrated one.

 

Here are a few more quotes from Munowitz that I liked:

·      “Always in motion, microscopic particles exchange energy and influence as they slip into a state of equilibrium… We need to understand particles as crowds, and we need to understand them as individuals and small groups. For the many, we need statistics.”

·      “To be in equilibrium is to lose track of time, to disappear the into the gray sameness of an unchanging macroscopic state… Without change, time disappears. The clock ceases to tick.”

·      “Once a system attains equilibrium, all memory of the past is gone. Looking at the present, nobody can say when the system got, how it got there, why it got there… The scant macroscopic information to be gleaned (… constant this, constant that) provides no clue to what came before. It Is, at least for the present, the end of history.”

 

An equilibrium can be stable; it can be unstable; or it can be metastable, as shown by these three pictures from left to right.

 

Munowitz writes: “a stable equilibrium need not last forever, because stability is always a matter of where one sits in relation to some other possible state… Hit any equilibrated system hard enough, and it will awaken as if from a slumber… there can be a second at after equilibrium, and more than that, too: there must be activity during equilibrium. How else could a quiescent system, lost in the macroscopic timelessness of equilibrium, be able to accept a better offer and embark on a new history? To do so, it must tap a power that comes from within. It must draw upon a microscopic power belied by an overall macroscopic calm.” Munowitz will explain this with the help of two friends, Mack and Mike, and their glaringly different perspectives. I encourage you to read Knowing for the full glory of his prose, here are just snippets:

 

“To Mack, our macroscopic observer, equilibrium is a static affair: a tableau, timeless and unchanging, a still photograph rather than a movie. Except for the occasional fluctuation, which flickers briefly and then disappears, there is nothing to report…”

 

“To Mike, a microscopic observer, equilibrium offers a restless, dynamic picture of infinite variety. Atoms and molecules move this way and that… Some speed up, and some slow down. They smash together an come away with new structures… Microscopic equilibrium is a movie with a cast of zillions, and every frame is different…”

 

“But even as Mike’s fine-grained movie plays on, with one inexhaustibly rich image giving way to another, Mack still sees the same scene frozen in time… with one macroscopic state... Run the tape backward, forward, in random sequence, in whatever way you like – it makes no difference… Meanwhile the microscopic actors work furiously only to have the system stay in place. Atoms and molecules, colliding unceasingly, exchange energy… they vibrate…  interact with fields… reconfigure their electrons… break into bits… react chemically… The give and take of energy never stops, but at equilibrium only the one microstate endures. The microstates partition the total energy in different ways, yet still the equilibrium microstate remains the same.”

 

Mack is amazed by the rich world of interactions that Mike describes. Mack wants to know what is “the special force that guides a system unerringly (almost eerily) to equilibrium and subsequently defends the stable state so stubbornly against small fluctuations.” It’s a mystery to Mack and wants Mike to explain. Mike is confused and says “What mystery? What special force? I see nothing but a lot of little molecules obeying the ordinary laws of mechanics exactly as they should. Believe me, there is nothing unusual going on here.”

 

Maybe not unusual, but something is going on. Munowitz calls it “the law of the land in the Land of the Big, the Many, and the Simple.” It’s statistics. The odds are what leads to the end. But if there’s an end, there’s a beginning. Time moves in one direction, at least that’s our experience as macroscopic organisms. The freedom that leads to equality of distribution drives this process inexorably forward. Entropy reigns supreme over large time scales. Munowitz writes: “Later means a world in which a fixed quantity of global energy has spread to a large number of recipients. Later means a world in which useful energy… has become just a little bit harder to find, a world that has yielded just a little bit more to the relentless pull of statistics.”

 

Today in my statistical thermodynamics class, I waxed poetic about fate and destiny. I derived the equations showing how and why chemists introduce the Gibbs Free Energy. I drew pictures. I grimly talked about the entropy tax that must be paid for any chemical reaction being leveraged to do useful work. I’m not sure if the students shared my rhapsodizing enthusiasm. I’m thinking of assigning them Chapter 10 since Munowitz says it all much better than I do. It’s all about Ends and Odds.