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Quantum mechanics allows the occurrence of events without having any definitecausal order. Here, it is shown that the application of two different thermalchannels in the causally inseparable order can enhance the potential to extractwork, in contrast to any of their definite (separable) order of compositions.This enhancement is also possible even without assigning any thermodynamicresource value to the controlling qubit. Further, we provide the firstnon-trivial example of causal enhancement with non-unital pin maps, for whichit is still not clear how to obtain a superposition of path structure (underdefinite causal order). Hence, it may be a potential candidate to accentuatethe difference between superposition of time and superposition of path.

Thermodynamic advancement in the causally inseparable occurrence of thermal maps