On van der Waals friction between two atoms at nonzero temperature

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We find the non-retarded van der Waals force between two identical oscillators, in initially uncorrelated mixed states appropriate for a common temperature T and mean energy , constrained to move at constant relative velocity on parallel trajectories a fixed finite distance apart. It is shown that the probability distributions of their final states, although correlated, are also thermal; they are appropriate for a slightly higher temperature T+ΔT, with proportional to . Negative friction, i.e. negative , could occur only under conditions where the underlying constraints no longer make physical sense. A crude multi-oscillator multi-collision toy model explores how the temperature might rise with time in a sequence of dynamically similar collisions. An appendix considers conflicting solutions proposed for the same problem.