Equilibrium-fluctuation expression for the resistance of a Norton circuit

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Abstract
In the familiar Green-Kubo expressions, transport coefficients are related to equilibrium fluctuations. The equilibrium ensemble which generates these fluctuations is obtained by setting the thermodynamic force to zero. For the special case of electrical conductivity, we show how the transport coefficient is related to fluctuations in the conjugate equilibrium ensemble where the thermodynamic flux, rather than the force, is set to zero. We show that the conjugate equilibrium correlation function so obtained is the memory function of the flux autocorrelation function.