Everyday entropy: the collapsing boundary

 

c8.7x7.fluid_.mosaic1321498942047.jpg
The modular wall

The term

$\displaystyle \dot{S}_\textrm{heat transfer} \left(= \frac{1}{T}\frac{dQ}{dt},\textrm{ or }
\frac{\dot{Q}}{T}\right)$

which is associated with heat transfer to the system, can be interpreted as a flux of entropy. The boundary is crossed by heat and the ratio of this heat flux to temperature can be defined as a flux of entropy. There are no restrictions on the sign of this quantity, and we can say that this flux either contributes towards, or drains away, the system’s entropy. During a reversible process, only this flux can affect the entropy of the system. This terminology suggests that we interpret entropy as a kind of weightless fluid, whose quantity is conserved (like that of matter) during a reversible process. During an irreversible process, however, this fluid is not conserved; it cannot disappear, but rather is created by sources throughout the system. While this interpretation should not be taken too literally, it provides an easy mode of expression and is in the same category of concepts such as those associated with the phrases “flux of energy” or “sources of heat.” In fluid mechanics, for example, this graphic language is very effective and there should be no objections to copying it in thermodynamics.”

MIT thermodynamics online

The entropy of an isolated system increases, but what about the entropy of an open system?  If entropy only existed for isolated systems, then it wouldn’t exist at all, because a truly isolated system is only possible as a thought experiment. Clearly, a non-isolated system is subject to the same entropic processes as an identical system in isolation.  When we talk about a system, what we mean is a thing that is isolated in some way from its surroundings.  Whether it be a bottle of gas, a working engine, or a planet, a “system” is isolated in such a way that the systems around it either don’t affect it thermodynamically or affect it in a way that is totally predictable.  The point is that entropy is meaningful for anything that is allowed to evolve spontaneously within its boundary.  For an open system, this entropic boundary will collapse inward as the effects of outside influences spread.  This is where entropy goes at night, and why it can always increase without the universe ceasing to exist.  The entropy within the boundary increases while the boundary collapses to nothing.  After that, you have to start over with a new boundary.  If you want to have a meaningful understanding of the change in entropy in any system, the important thing is to start your consideration with an entropic boundary that is far enough out from your focus area that the boundary won’t collapse on you.  Another way of thinking of the entropic boundary is an inverse explosion.  The boundary of energy expands; the boundary of entropy collapses.

 

People usually build walls to keep energy in and to keep out what they see as entropy – strangers, foreigners, immigrants and vagrants.  This is backwards.  Isolation only accelerates entropy.   City walls can, however, do something else.  They can stop the city from spoiling its surrounding countryside.  What is important isn’t keeping people out; it’s keeping construction in.  Ironically, an opening for the free flow of people and goods through the wall allows the entropy to dissipate between productive cycles.  This is how cells survive, but achieving this at a macroscopic scale is very difficult.  If you think of the cell membrane, it is a constant state of disintegration and reconstruction and its fluid state allows waste to exit while nutrients enter.

As regards walls, fences and collapsing entropy, the automobile goes a long way to solving a common problem: how can rich people avoid contact with poor people.  Originally, they built castles and employed knights to bring in food and keep serfs out, but the isolation was depressing and the knights had no loyalty.  In the Forbidden City, the Chinese emperor found another solution: a fully functioning social economy dedicated to himself and uncontaminated by poverty in any way.  The automobile seemed to make these makeshift solutions obsolete.  It was suddenly possible for wealthy people to put real distance between themselves and those less fortunate, and unlike a horse, an automobile was very hard to spook.  Which was great until the aspirational classes, in particular those aspiring to be something other than poor, started using automobiles as well. Then the streets became cluttered and the need for traffic signals made wealthy people vulnerable to carjacking.  The truly rich moved on to helicopters and private islands.  But there is a limit to the defence of mobility.  Mobility requires force, and the application of force results in an increase in entropy.

If people could share space, the automobile would be a wonderful toy, not a middle-class entrance fee.  The curious thing about Donald Trump’s war against Mexican immigrants is that, like Hitler attacking  Jews and Gypsies, he is attacking the people most adept at sharing space.  This seems ironic, but these attacks make sense if you have a reverse understanding of entropy.  Because they share space, Mexican immigrants are visibly using space, whereas upper-class Americans hide behind walls and invisibly waste one another’s space.

It may not be fair to compare Trump to Hitler, but then again, it may be. More importantly, the feeling of betrayal that pervaded the Nazi era has returned throughout Europe and America. There is also a pervasive notion that someone has taken the value out of work, whether immigrants or the Chinese or the liberals, someone has taken the energy out of America’s heartland. If you didn’t understand that entropy grows from within, you would demand a reckoning for the hobgoblin undermining the wealth of the nation. Liberals on either coast are just as  clueless about the cause of the ill will in the middle as the middle is clueless about the source of their frustration. Trump may be the talisman of racist nationalists, but that doesn’t explain the phenomenon, which didn’t originate with Trump and always seems to arise under the same social and economic conditions.  It’s wrong, but even racist nationalists know it’s wrong.  They just can’t think of another answer (and maybe they don’t want to.)  The frustration itself isn’t irrational. Middle America has an immense infrastructure that has filled its space with junk businesses and tried to isolate itself from the vagaries of commerce (interpersonal, interstate, international, all commerce).  This is a recipe for the catastrophic increase in entropy for a heat engine, so it isn’t at all surprising that middle America’s engine is breaking down.

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