Suppose we have an $n$ by $n$ chessboard and each square can be in two states: "on" or "off". At time $t=0$ all bits are off. Every second one square is selected at random uniformly out of the $n^2$ squares and the corresponding bit is flipped. How to define entropy of "on" bits in this process and show that it increases? This came out of a model of a gas in a container, where we divide the container using a grid. Each grid point is "on" or "off" iff there is a gas molecule in the corresponding square. It should increase on average right? Seems to me it could be related to the variance of the "on" squares but I am no expert in the field, any hints?
Thanks in advance!