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 P 1 + P 2 ≥ 2P 0 √P 1 P 2 ≥ P 0 where P 1 = (V 1 , I 1 ), P 2 = (V 2 , I 2 ), P 0 = (V 1 , I 2 ) = (V 2 , I 1 ). A generalization of the above leads to Re(ZI 1 ,I 1 ) ċ Re(ZI 2 ,I 2 ) > |((Re Z) I 2 , I 1 )|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.