  A simple model of charge transport is provided by a classical particle in a
smooth random potential and a dissipative coupling to the environment in the
form of Markovian noise and friction. The corresponding Non-Equilibrium Steady
State (NESS) can be determined analytically when both the disorder and
dissipation are weak. We use it to illuminate some foundational issues in
non-equilibrium statistical mechanics. We show that Linear Response Theory has
a nonempty regime of validity only in the presence of a dissipative coupling to
the environment, thereby validating van Kampen's objection. We also show that
the Principle of Minimum Entropy Production does not determine the NESS beyond
linear order in the electric field, while entropy maximization fails to produce
the correct NESS already at linear order.
