Quantum Energy-Flow Vorticity (QEFV): A Topological Paradigm for Collective Nonequilibrium Quantum Transport
Abstract
Traditional formulations of quantum transport and non-equilibrium thermodynamics have predominantly focused on the magnitude and divergence of energy current densities, treating energy flow primarily as a directional vector field driven by thermal or chemical potential gradients. In this paper, we introduce the concept of Quantum Energy-Flow Vorticity (QEFV), proposing that microscopic and macroscopic energy flows can possess non-removable topological curls. By defining the energy-flow vorticity operator as the curl of the energy current density, Omega_E = nabla x J_E, and evaluating its non-zero circulation along closed loops, given by the contour integral of J_E dot dl != 0, we reveal the existence of stable, quantized energy vortices. These structures represent a novel class of collective energy excitations that transcend conventional diffusive and convective paradigms. We establish the theoretical foundation of QEFV, explore its implications for macroscopic quantum phenomena, and discuss its profound potential to reshape our understanding of non-equilibrium collective states of matter.
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