  An indefinite causal order, where the causes of events are not necessarily in
past events, is predicted by the process matrix framework. A fundamental
question is how these non-separable causal structures can be related to the
thermodynamic phenomena. Here, we approach this problem by considering the
existence of two cooperating local Maxwell's demons which try to exploit the
presence of global correlations and indefinite causal order to optimize the
extraction of work. Thus, we prove that it is possible to have a larger
probability to lower the local energy to zero if causal inequalities are
violated, and that can be extracted more average work with respect to a
definite causal order. However, for non-interacting parties, for the system
considered the work extractable cannot be larger than the definite causal order
bound.
