Arithmetic-geometric means for electrical energies

The paper indicates an important arithmetic-geometric relation for the behavior of linear passive reciprocal n-ports. The active energies dissipated in the unit time interval in any linear passive time invariant reciprocal resistive system satisfy the inequalities P1+ P2≥ 2P0√P1P2≥ P0where P1= (V1, I1), P2= (V2, I2), P0= (V1, I2) = (V2, I1). A generalization of the above leads to Re(ZI1,I1) ċ Re(ZI2,I2) > |((Re Z) I2, I1)|². On account of the reciprocity, one can assess the resulting fluctuations of the active energy dissipated by a linear system when the input vector is perturbed.