That's basically the gist of it. The entropy of a system is proportional (via Boltzmann's constant) to the natural log of the number of available microstates, w

That's basically the gist of it. The entropy of a system is proportional (via Boltzmann's constant) to the natural log of the number of available microstates, where microstates are configurations the system could be in, and available denotes that they have the same total value for all conserved quantities as the aggregate system. Consequentially the system is free to spontaneously transition between any of its available microstates.