One of the devices that college lecturers like to employ when illustrating the concept of entropy is the one pictured above. The narrative goes along these lines: When cream is added to coffee, diffusion and convection produces in the course of time a homogeneous-looking mixture. Compared to its components it is very stable, and never reverts back of its own accord to the initial state of pure cream and black coffee. The diffusion of these two miscible liquids is spontaneous, irreversible and entropy-producing, since the mixture has more microstates, and thus more entropy, than the pure components.

I have never found this illustration particularly helpful, for two reasons.

Firstly, it complicates the picture by mixing together (no pun intended) two distinct concepts. Since the coffee is assumed to be hot and the cream cold, the mixing process involves thermal entropy due to heat exchange as well as configurational entropy due to diffusion.

Secondly, it ignores the spoon.

The spoon has an interesting role, because although stirring doesn’t affect the end point at which configurational entropy attains a maximum, it certainly accelerates the process of reaching it.

In the configurational sense – the sole concern of this article from here on – the spoon represents assisted entropy. The phrase floated into my head one day and remained there, with the consequence that I have developed the habit of noting examples of assisted entropy in the world at large.

The interrelation of work and configurational entropy deserves some mention. One formulation of the second law of thermodynamics is that the direction of spontaneous change in an inanimate system is such that work can be obtained in suitable circumstances. In the coffee and cream example, it is difficult to imagine just how the work accompanying such a spontaneous process would be obtained. But it’s real enough when looked at through the equivalent converse statement, that in order to reverse this mixing process and return the system to its initial configurational state, the amount of work that would need to be provided from the surroundings would be at least the same.

If a process resulting in increased configurational entropy is not spontaneous, but is achieved by doing work on a stable system – mixing together separate piles of black and white peppercorns is an example – then the  amount of work required to return the system to its initial configurational state would again be at least the same.

It’s instructive to apply this latter example of assisted entropy to stable deposits of relatively rare minerals that are sourced, processed, manufactured into products, traded and consumed worldwide, and then discarded.

Think of a lithium ion button battery. The valuable lithium inside it originates perhaps from a concentrated brine on some salt flat in Bolivia, then after a lengthy process of extraction, transportation, processing, manufacture, trading, distribution, retailing and purchasing, it ends up in the pocket calculator of someone in New York. The battery comes to the end of its useful life and then, being a tiny worthless object, it gets tossed without much thought into the trash can. From there it is loaded onto a waste truck that drives it about 1,000 kilometres to Ohio where it is dumped along with countless other lithium ion button batteries into a big hole where it gets mixed in with thousands of tons of other NYC waste.

This is a gigantic exercise in assisted entropy, in which the initial configurational entropy of the lithium in the concentrated brine in Bolivia is vastly increased by the time it reaches the hole in Ohio. The work required simply to recover it, let alone recycle it, is astronomical, as would be the cost. It is commercially irrecoverable. The lithium is lost.

The same applies to any consumer electronics product with a limited lifetime, negligible or zero resale value, and a size small enough to be discarded into unsorted waste that will end up as landfill – mobile phones, MP3 players, pocket cameras, gadgets of that sort. Disposable objects that contain increasing amounts of rare earth elements, that will as a result become more than rare, by becoming irrecoverable.

Market forces are the big spoon of assisted entropy, and the world at large has yet to focus on its irreversible effects. But the need already exists for systems that will enable large-scale recovery of small-scale consumer products containing scarce resources, before they hit the trash can and are lost.


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