physical meaning of: on - equilibrium and off - equilibrium

Hi there

I´ve been reading docs about LBM and is not quite clear to me the physical meaning of: on-equilibrium and off-equilibrium
any tips are welcomed



basically, the Boltzmann is shown to be equivalent to the Navier-Stokes equations by doing a Chapman-Enskog expansion. This expansion is done by assuming that the distribution functions are a small perturbation around an equilibrium distribution (which looks like a Maxwell distribution) :

f = feq + fneq (fneq << feq)

The equilibrium distribution is given in terms of the macroscopic quantities of our system (density and velocity in the weakly compressible case) whereas the non-equilibrium contribution depends on the gradients of these macroscopic quantities.

I think that’s what people mean by equilibrium and non-equilibrium.