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Can the value of the potential energy, which is responsible for driving the system, diminish in time, while the system itself is stationary during that time? Can there be dissipation in a system, while no physical degrees of freedom (at all levels) are changing?

Maybe this should be formulated as "Can I write down a time dependend energy, whos total value reduces in time, while this change has no impact on the equations of motion."

Maybe this is just equivalent to a time dependend exteriour force in every case - then I guess the answer is no, in the sense that the exteriour force is also a physical degree of freedom.

(The question is probably motivated by me wondering if one can replace all (spatial?) boundary condition in a system by other forces: A chemical potential equilibration holds particles back from moving in one direction and so replaces a wall, which would be a coordinate restriction in a more mechanical pov. Can one similarly get rid of all spatial aspects of a classical theory? Maybe d'Alamberts principle goes in this direction. Mathematical phase space reduction kind of obscures physical system, I don't know what's real anymore.)

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I might have misinterpreted your question. Where's the dissipation here? – Ron Maimon Aug 28 '12 at 10:57
@RonMaimon: My formulations are a little over the place here. The first point is essentially asking if you can write down a system such that the following is the case: If the system would be released (all physical degrees of freedom are left to their unbounded dynamics) at one time, the force (F = -gradU) would be such and such, while if the system would be released at a later point, where (in some way) the potential energy would be lower (disspipation) the equation of motions would still be the same, but there is force. Time-depended energy U(t), while still a system with conservative forces. – NikolajK Aug 28 '12 at 11:47
@RonMaimon: The question is in the vain of‌​ime-dependent-classical-system-be-conservative, but don't bother answering untill I've come up with a more logical presentation of the question. – NikolajK Aug 28 '12 at 11:53

Since the energy is only defined up to a constant classically, you can do this by letting a system constrained to a horizontal surface free-fall in a gravitational well. Adding a time-dependent constant to the potential never changes the equations of motion, it is a phase transformation of the wavefunction in QM.

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In an ideal case no - the mechanical energy is a result of a mechanical state, without changing the state you can't release the energy.

In a real world case some of the energy will go into physical/chemical changes in the material, stress creep, different crystal states etc, so a spring left wound for a long time won't give quite the same energy as a freshly unloaded one.

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