Maximum entropy is when thermal equilibrium is reached and no further vaporisation is possible.

Benford's law is obtained as maximum entropy distribution of balls in boxes under the assumption that the number of balls in a box can be 1,2,3....9.

For derivation see Oded Kafri "entropy principle in direct derivation of Benford's law" at arxive (2009) .

Maximum entropy.

Heat death is a hypothetical situation in which there is no more usable energy in the Universe. In relation to entropy, it means that entropy is at its maximum - it can't increase any more.

when jesus christ wants it to be. watch for him!

When entropy increases to maximum.