Kirchhoff's Loop Law and the maximum entropy production principle
  In contrast to the standard derivation of Kirchhoff's loop law, which invokes electric potential, we show, for the linear planar electric network in a stationary state at the fixed temperature,that loop law can be derived from the maximum entropy production principle. This means that the currents in network branches are distributed in such a way as to achieve the state of maximum entropy production. 
P. Zupanovic, D. Juretic and S. Botric