Causal games of work extraction with indefinite causal order

TL;DR

This paper explores how indefinite causal order, predicted by the process matrix framework, can enhance work extraction in thermodynamic systems with cooperating Maxwell's demons, surpassing bounds of definite causal order.

Contribution

It demonstrates that violating causal inequalities can lead to increased work extraction, linking indefinite causal order to thermodynamic advantages.

Findings

Violating causal inequalities increases the probability of lowering local energy.

More average work can be extracted with indefinite causal order.

Work extractable is bounded by definite causal order for non-interacting parties.

Abstract

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.