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In Physics, there is a chapter about "Statistical Mechanics" where I do not really understand a notation: Let there be four coins, each of which can be either heads or tails. Set them in a given configuration and then arrange a game such that on every time step we choose one of the four coins at random and flip it. Let us denote the probability of being in the macrostate with $n$ tails by $P(n)$.

For $P(4)$, we have that the probability of a transition from $n=3$ is $P(4|3) = 1/8$ since it requires the only head in the $n=3$ macrostate to flip. Going the other way, we find that $P(3|4) = 1/2$ because whichever of the coins we choose to flip to head will result in our ending up in one of the states of $n=3$. Then, the equation for the evolution of $P(4)$ for a single time step is

$$\Delta P_{t+1}(4) = P(4|3) P_t(3) - P(3|4) P_t(4).$$

I have read this last sentence many times and tried to understand what $\Delta P_{t+1}(4)$ is supposed to be using context, but I did not succeed. Could anyone help me out?

Thanks in advance.

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