The steady state of a Hall device is the state of minimum Joule heating, with zero transverse current and edge currents proportional to the edge charge accumulation.
These two terms are constant so that the electochemical potential of the stationary state is harmonic: ∇2µst = 0
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Surface currents in Hall devices
The steady state of a Hall device is the state of minimum Joule heating, with zero transverse current and edge currents proportional to the edge charge accumulation.