  Charge fluctuations in nano-circuits with capacitor components are shown to
give rise to a novel type of long-ranged interaction, which co-exist with the
regular Casimir/van der Waals force. The developed theory distinguishes between
thermal and quantum mechanical effects, and it is applied to capacitors
involving graphene nanostructures. The charge fluctuations mechanism is
captured via the capacitance of the system with geometrical and quantum
mechanical components. The dependence on the distance separation, temperature,
size, and response properties of the system shows that this type of force can
have a comparable and even dominant effect to the Casimir interaction. Our
results strongly indicate that fluctuations induced interactions due to various
thermodynamic quantities can have important thermal and quantum mechanical
contributions at the micro- and nanoscale.
