Toward an extension of the Constructal Law to sub-macroscopic scales

Bejan's Constructal Law establishes that finite-size macroscopic systems spontaneously morph their architectures to maximize transport access, yet this thermodynamic imperative remains formally unproven at the quantum scale. Here, we generalize the Constructal Law to open, non-equilibrium quantum systems via a field-theoretic formulation. We demonstrate that coherent state transport is governed by a variational quantum dissipation potential. At critical excitation, modulational instabilities arise within homogeneous quantum fluids. The competition between coherent drive and non-unitary decay forces spontaneous symmetry breaking. This reconfigures the continuous field into an asymptotic topological attractor that balances energy input with environmental dissipation. The framework is validated via a 3D constructal phase diagram unifying vortex lattices, supersolids, and ferromagnetic states, while predicting the conditions for an interstitial vortex-supersolid. Macroscopic quantum phase transitions are thus revealed as emergent geometric adaptations toward thermodynamic attractors that optimize entropy transfer at the sub-macroscopic limit. Within this variational framework, maximizing flow access manifests not as the altering of external constraints, but as the morphing of internal topological interfaces. Driven by microscopic fluctuations and pulled by non-linear gradients, the quantum fluid spontaneously breaks continuous symmetries to maximize irreversible entropy export. This self-organization embodies the Constructal extremization of the system-environment interface, exemplifying what we term the Principle of Extremized Dissipative Topologies: complex phase transitions across quantum and macroscopic scales arise from extremizing a global dissipation potential.