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A longstanding challenge in nonequilibrium thermodynamics is to predict theemergence of self-organized behaviours and functionalities typical of livingmatter. Despite the progress with classical complex systems, it remains farfrom obvious how to extrapolate these results down to the quantum scale. Here,we employ the paradigmatic master equation framework to establish that somelifelike behaviours and functionalities can indeed emerge in elementarydissipative quantum systems driven out of equilibrium. Specifically, we findboth energy-avoiding (low steady dissipation) and energy-seeking behaviours(high steady dissipation), as well as self-adaptive shifts between these modes,in generic few-level systems. We also find emergent functionalities, namely, aself-organized thermal gradient in the system's environment (in theenergy-seeking mode) and an active equilibration against thermal gradients (inthe energy-avoiding mode). Finally, we discuss the possibility that our resultscould be related to the concept of dissipative adaptation.

Emergence of energy-avoiding and energy-seeking behaviours in nonequilibrium dissipative quantum systems