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 multiscale dynamics and evidence of phase transitions, and externally driven networks evolve to efficiently connect external positive and negative potentials. The model implements techniques for rapid, global , reversible, conservative equilibration of node states followed by slow, local , irreversible, dissipative adaptation of the edge states as a means to create multiscale order. All interactions in the network are local and the network structures can be generic and recurrent. The model integrates concepts of  fluctuation, dissipation, adaptation and equilibration and offers an illustration of the thermodynamic evolution URLanization in open systems. The key conclusion of the work is that the  dissipation of conserved physical quantities can drive the URLanization of open thermodynamic systems.
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. The model integrates techniques for rapid, large-scale , reversible, conservative equilibration of node states and slow, small-scale , irreversible, dissipative adaptation of the edge states as a means to create multi-scale order. All interactions in the network are local and the network structures can be generic and recurrent. The model integrates concepts of conservation, potentiation, fluctuation, dissipation, adaptation , equilibration to illustrate the thermodynamic evolution URLanization in open systems. A key conclusion of the work is that the transport and dissipation of conserved physical quantities drives the URLanization of open thermodynamic systems.
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