Parable Of The Gas Explained

A while back I wrote The Parable Of The Gas without explanation:

Consider a spherical, sealed glass container of gas. Further suppose that the gas inside is all the same -like helium in a balloon. Room temperature and stable. Everything equal inside...but it's not. The individual gas atoms in the container have unequal energies because there's a range--a statistical distribution--of energies present: Some atoms move more slowly than others, some more quickly, some much more quickly.

How can we make things fair? How can we make it such that each individual (atom) has the same energy as its next nearest neighbor? We cannot. The only way to approach that state is to remove energy from the entire system. Cool the economy. Everything slows. Eventually, approaching zero Kelvin, all motion stops. Of course catastrophic things like condensation (downsizing from gas to liquid) and solidification (loss of liquidity) occur along the way. But the goal is achieved: every atom is finally the same (or nearly the same) energy wise.

Here is what I was picturing:

Original

The figure shows how at higher temperatures the average speed increases but so does the spread (inequality). The range narrows at lower temperatures which is what some policymakers seem to want. But what they want is also unnatural and contrived. An Austrian physicist named Ludwig Boltzmann first came up with the mathematical model behind all this in 1877. He based his derivation on entropy--arguing that a situation where all members of a group have identically the same velocity is highly improbable--as improbable as all the gas molecules being located on just one side of the vessel. It's much more probable (favorable) to allow each member of the group to experience a range of velocities and not to constrain them into one single energy or spatial configuration.

Another physicist named Max Planck extended Boltzmann's ideas and also changed the world by extending statistical mechanics to heat and light thus introducing quantum mechanics.  Einstein ran even further with Planck's ideas.  Both men would have their doubts--"God doesn't roll dice" and all that--but neither man denied reality.

Added:  When I liken the economics of wealth and poverty to a gas, it's important to remember that "rich" and "poor" may interconvert: link