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Abstract: The most recent results in the dynamics of infinite systems of particles have shown there is no necessary connection between the performance of a deterministic supertask and the non-conservation of energy. Much more difficult to prove is the non-existence of any necessary connection between the performance of an indeterministic supertask and the non-conservation of energy; however, this paper does just that. So the requirement that energy be conserved does not mean we can exclude as “non-physical” either of the two major types of supertask considered to date. The paper also proposes, in this context, a “hidden variables method” to prove general results of compatibility in dynamics. [Copyright &y& Elsevier]