Nothing Is Ever Used Up

Nothing you do uses energy. The phrase is universal and it is loose, and getting it right explains a surprising amount.

Burn a litre of petrol driving across town. Afterwards, every joule that was in the fuel is still present: in the warmth of the engine block, the heat in the brake discs, the slightly agitated air you pushed through, the friction in the tyres and the road. The total is unchanged. What changed is that the energy began concentrated in chemical bonds and ended spread thinly across a great many things at a temperature barely above their surroundings, where it can no longer be made to do anything.

That is the first law and the second law in one journey. Energy is conserved. Usefulness is not.

The first law is conservation, and it is as firmly established as anything in physics: Noether's theorem ties it directly to the fact that the laws of physics do not change over time, which means overturning it would overturn a great deal else. This is why a claimed perpetual motion machine can be assessed before it is examined. The right posture is not accusation but bookkeeping: draw a boundary around the device and account for everything crossing it. Most such machines are honest errors with an unmeasured input, an ambient temperature gradient, or a battery somebody forgot.

The second law is the interesting one, and the usual gloss (disorder increases) is a serviceable summary that misleads about as often as it helps.

Ludwig Boltzmann gave the definition that makes sense of it. Entropy counts how many microscopic arrangements are consistent with the macroscopic state you can see. A gas confined to one corner of a room corresponds to relatively few arrangements of its molecules; the same gas spread through the room corresponds to an unimaginably larger number. Nothing forbids the molecules from gathering in the corner. It is simply that there are so many more ways to be spread out that a system wandering randomly among its possibilities will be spread out, and will stay that way.

So the second law is a statistical tendency rather than a prohibition, and the enormousness of the numbers is what makes it as good as a law. The probability of the air in your room spontaneously collecting in one half is not zero; it is small in a way that makes the age of the universe irrelevant.

This immediately answers the objection most often raised against evolution, and it is worth doing properly because the answer is not a technicality. Entropy increases in closed systems. The Earth is nothing like closed: it receives a steady stream of high-energy photons from the Sun and radiates a much larger number of low-energy ones to space. That exchange exports entropy on a colossal scale, and everything ordered on the planet (a crystal, a tree, a city) is paid for out of it. A freezer makes ice, decreasing the entropy of the water, while pumping more than enough disorder into the kitchen to cover it. A growing organism is doing the same thing with more finesse.

The second law also sets a hard ceiling on what machines can do. Sadi Carnot worked out in 1824 that the maximum efficiency of a heat engine depends only on the temperatures of its hot and cold reservoirs, and not at all on the working substance or the cleverness of the design. Reaching a hundred per cent would require a cold reservoir at absolute zero. This is not an engineering problem awaiting a breakthrough: heat is energy already distributed across enormous numbers of degrees of freedom, and gathering it back into organised motion has an unavoidable cost. Real engines fall well short of the Carnot limit, which is a separate and genuinely fixable problem, but the limit itself does not move.

And then there is the strangest consequence, which is that the second law appears to be where the direction of time comes from.

Play a film of two billiard balls colliding in reverse and it looks perfectly normal; the underlying mechanics are symmetric in time. Play a film of a cup shattering in reverse and it is obviously wrong. Yet the shattering is nothing but a great many collisions, each individually reversible. The asymmetry is not in the laws; it is in the statistics. The reassembled cup is one of a tiny number of arrangements, the fragments are one of an unfathomable number, and systems move toward the states there are more of.

Which pushes the question back one step, to a place physics has not settled. If entropy has been increasing, it was lower before, and lower still before that. Run it back far enough and the universe began in a state of extraordinarily low entropy, extraordinarily special, in the sense that overwhelmingly few possible initial conditions look like that. Why it did is an open problem, and every arrow you have ever noticed, including the fact that you remember the past and not the future, appears to be downstream of it.