| How I understand it: Entropy (according to Boltzmann) is proportional to the number of microstates that can give rise to a particular macrostate of a system. The macrostate with the highest number of possible microstates is the uniform one, where all the accessible microstates are equally likely. So if by the 2nd law entropy must increase, the system will tend towards the uniform configuration. In other words, if a force is pushing water, the configuration with the highest number of states is that where all the particles of water are also moving i.e. indistinguishable microstates, doesn't matter how you rearrange the moleculles, it will look the same as they are all moving uniformly. It would be extremely unlikely that there were a pocket of water that is mysteriously still in the middle of the stream no? Clearly there are not a lot of rearrangements of the mollecules that will keep the macrostate the same, so low entropy, which tends not to be the case. (Edit) How this connects to the "desire to dissipate energy efficiently": Essentially, when we talk about "energy" we really mean "free energy". This is the amount of work that we can extract from a system. This is nothing but a measure of how far a current system is to it's maximum entropy state. So dissipating energy = increasing entropy. The mindblowing part for me is the connection that the process of extracting free energy is the same process that moves a system to its most likely state, uniformity, high entropy. So somehow, the ability to _accelerate_ an already inevitable process lets us reconfigure other systems _away_ from their most likely state!! So if we imagine the arrow of time to progress at the average rate of entropic decay, we are essentially reversing it for some systems by accelerating it for others!!! Man... |
> So somehow, the ability to _accelerate_ an already inevitable process lets us reconfigure other systems _away_ from their most likely state
But this is exactly the part that doesn't make sense to me. Why would it accelerate? There's no principle I'm aware of that would prefer or cause this accelerated version. There's no such "ability".
Rather, the entropy process just happens in this "already inevitable" way you describe, without any self-organizing "resonant" structures or anything or the sort. I don't understand what would cause anything different.
It's kind of like saying boulders eventually roll downhill, so therefore hills spontaneously turn their rocky surfaces into smooth slides so the boulders can roll down faster. But that's not how it works.