A random‐walk interpretation of the incompressible navier‐stokes equations

We introduce a stochastic process that roughly corresponds to a random walk of a single molecule in an incompressible fluid, and we consider the force (per unit volume) exerted by such a “molecule” on the rest of the fluid. Averaging this force over an ensemble of such molecules and taking an appropriate limit, we obtain the Navier‐Stokes equations. The origin of time‐irreversibility in these equations is discussed in terms of the model.