3.1 Free Energy of an Arbitrary Circuit

  Both the ME and MC methods require as input the tunnel rates of all relevant tunnel events. On the other hand, the rate formulas for first order (2.23) and higher order (2.49) tunneling depend on the change in free energy each tunnel event causes. Thus, the first part of a simulation is the calculation of the free energy before and after all possible tunnel events in an arbitrary circuit. With arbitrary circuit we mean the arbitrary connection of lumped capacitors, tunnel junctions, voltage sources, and current sources.