Second law of thermodynamics

The second law of thermodynamics states that the entropy of an isolated system cannot decrease with time.

Systems generally relax to a state of maximum entropy (“equilibrium”).

After an isolated system undergoes any process, the number of compatible microstates is at least equal, often greater. Each possible micrsostate in the initial macrostate $S_0$ evolves into a microstate in $S_1$, but there are also microstates that are compatible with $S_1$ that don’t correspond to any in $S_0$. The critical observation is that it’s impossible to distinguish between the two. Once we’re in $S_1$, we can’t tell which possible microstates could have bene in $S_0$ and which couldn’t have.

The diagram above shows how microstates in the initial ensemble correspond to a subset of the microstates in the final ensemble.