What is Entropy?

Anyone who thinks they know is going to absolutely hate this answer.

Entropy is a measurement of how much work, with current human knowledge, can be extracted from a system.  It is a measurement of all potential energy that is yet untapped, combined with a theoretical maximum of "useful" work that can be extracted from this energy.  It is a useful fiction, but it is still a fiction.  So is the second law of thermodynamics.

In truth, entropy has the potential to change with every change in human knowledge.

If we discover a new force - say, a subtle attractive force far weaker than gravity, but attenuating far less quickly - the entropic values of all systems change.  You can use this information to extract slightly more energy from the system by building an engine that somehow takes advantage of this new source of potential energy.

In more down-to-earth terms, suppose we just discovered fire today.  Suddenly the potential energy that can be extracted from coal increases enormously - previously, we could just extract whatever energy we could get from its falling, much as we extract enormous energy from the gravitational potential energy in water.  We have to rewrite all of our entropy tables, which previously just concerned themselves with height relative to, say, sea level.

Fortunately for the industrial revolution, we already discovered fire, so we already had enormous amounts of potential energy to extract - although never as much as we would have liked, which produced our obsession with calculating exactly how much energy we -could- extract.  Entropy is an engineer's concept which arose from that obsession.

Entropy is really just an elaborately-dressed up way of saying that time flows in one direction - that the physical processes flow in one direction.  Coal burns; carbon dioxide doesn't draw heat in and convert itself into coal, raining down upon us.  If the reverse were true - carbon dioxide drew heat in and converted itself into coal, it would be an endothermic, instead of exothermic, reaction - these kinds of processes do in fact exist in real life.  If it did -both-, we couldn't extract any useful energy from the process, because as we "burned" coal it would re-consume the energy and re-precipitate carbon - these kinds of processes -also- exist in real life, they're called reversible reactions.

Now, it sounds like a compound like this would be really useful, and you'd be right.  It's exactly what water does - absorbs heat to evaporate, then gives off heat to re-precipitate.  If coal behaved as I described, you'd require a heat source to re-precipitate the carbon dioxide after you've extracted work - and thus heat - from the system, since it would require that energy to re-bond.  (Actually, coal -sort of- works as I described - exposed to the right sort of energy and conditions, it -does- re-precipitate, which is part of what plants do when they convert carbon dioxide into carbon.)  The difficulty is that managing the boundary conditions to make the process cyclic requires something -else- be providing useful work.

Entropy, as a concept, is made much more mysterious than it really is.  In its shortest form, the second law of thermodynamics is just stating that all the laws of physics -continuously- apply.  Time flows in only one direction.

The fiction is in the implication - that a given amount of energy can ever only do some finite amount of work before it is spent for good.  There's nothing we have yet discovered in the laws of physics that says you can't have a perpetual motion machine, or that you can't extract an infinite amount of usable work in a closed system.  There's just nothing in the laws of physics we have yet discovered which -permits- an infinite amount of usable work to be performed in a closed system.

It's an important distinction, because there's a -lot- we haven't yet discovered.