Reassessing thermodynamic advantage from indefinite causal order

Indefinite causal order is a key feature involved in the study of quantum higher transformations. Recently, intense research has been focused on possible advantages related to lack definite processes. Quite often switch claimed provide information-theoretic and thermodynamic tasks. We address here question whether indefinite resource for thermodynamics. Inspired by previous results literature, we show that not necessary reported increase free energy ergotropy. More specifically, simple causally ordered process, which replaces system's state with new one before final measurement, outperforms all tasks considered so far. further similar advantage can be also achieved without completely discarding system, if allow non-Markovian interactions between system an environment. extend analysis more extreme examples order, showing they do either. Finally, discuss way may arise from general scenario.