On Thermostats: Isokinetic or Hamiltonian? finite or infinite?

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The relation between finite isokinetic thermostats and infinite Hamiltonian thermostats is studied and their equivalence is heuristically discussed.
6 pages, 1 figure v2: several comments added thanks to the referees' suggestions; v3: collision rules with walls and influence on the form of the equations of motion precised (see acknowledgements). Two columns format

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