I have an implementation of over-damped Brownian dynamics, with particles that follow the version of the Newtons law where the inertia is absent. This is a common thing to do at micrometer scale.
$m x''(t) = \Sigma F(t) - \gamma x'(t) + \xi (t)$
with no inertia, the equation is reduced to
$ x'(t) = (\Sigma F(t) + \xi (t)) / \gamma$
This equation I solve with a numerical method.
Of course in classical molecular dynamics there is a conserved quantity that allows us to validate the code
But here I lose access to velocity so that I cant calculate the kinetic energy.
Is there any other conserved quantity that can be used in this case instead of energy?
