Before revision: This work describes a thermodynamically motivated neural network model  that URLanizes to transport charge associated with internal and external potentials while in contact with a thermal bath. Isolated networks show multi-scale dynamics and evidence of phase transitions, and externally driven networks evolve to efficiently connect external positive and negative potentials.
After revision: This work describes a thermodynamically motivated neural network model that URLanizes to transport charge associated with internal and external potentials while in contact with a thermal reservoir.