What does this equation mean?

Einstein’s equation described one physical system: particles buffeted by a fluid held at a fixed temperature, governed by a single constant D . Within a decade, physicists working on an unrelated problem — how the energy of a rotating electric dipole settles under both random radiative kicks and a systematic damping force in a radiation field — found they needed the same mathematical object with one addition: a drift term standing alongside the diffusion term. Adriaan Fokker wrote down that generalization in 1914, and Max Planck rederived and extended it in 1917; the combined equation has carried both names since [ 3 ] . In one dimension it reads $\frac{\partial p(x,t)}{\partial t} = -\frac{\partial}{\partial x}\big[\mu(x,t)\,p(x,t)\big] + \frac{\partial^{2}}{\partial x^{2}}\big[D(x,t)\,p(x,t)\big]$. where the first right-hand term carries the probability density along a deterministic drift $\mu(x,t)$ and the second spreads it by diffusion at rate D(x,t) [ 3 ] . Andrei Kolmogorov arrived at the identical equation independently in 1931, from pure probability theory, as the forward equation governing how the probability distribution of any continuous-time Markov process evolves [ 3 ] . Kolmogorov’s work also produced a companion equation, run backward in time from a fixed outcome rather than forward from a fixed start, that turns out to be the more convenient tool for asking what a process is heading toward rather than where it began — a distinction that mattered when the same mathematics was pointed at a population instead of a particle. That third, unrelated derivation is what turned Einstein’s equation from a fact about pollen grains into a piece of mathematics indifferent to what its variable represents — a state of affairs population genetics was about to test.