Duality and reciprocity of fluctuation-dissipation relations in conductors

TL;DR

This paper develops a unified theoretical framework linking microscopic carrier fluctuations to macroscopic noise and dissipation in conductors, revealing duality and reciprocity relations in fluctuation-dissipation phenomena across classical and quantum regimes.

Contribution

It introduces a duality and reciprocity framework for fluctuation-dissipation relations in conductors, incorporating microscopic noise sources and extending to degenerate and fractional statistics.

Findings

Spectral densities relate mutually exclusively to noise sources.

Macroscopic fluctuations exhibit dual properties via plasma conductance and resistance.

Zero-temperature velocity fluctuations in Fermions cause diffusion but not current noise.

Abstract

By analogy with linear-response we formulate the duality and reciprocity properties of current and voltage fluctuations expressed by Nyquist relations including the intrinsic bandwidths of the respective fluctuations. For this purpose we individuate total-number and drift-velocity fluctuations of carriers inside a conductor as the microscopic sources of noise. The spectral densities at low frequency of the current and voltage fluctuations and the respective conductance and resistance are related in a mutual exclusive way to the corresponding noise-source. The macroscopic variance of current and voltage fluctuations are found to display a dual property via a plasma conductance that admits a reciprocal plasma resistance. Analogously, the microscopic noise-sources are found to obey a dual property and a reciprocity relation. The formulation is carried out in the frame of the grand canonical (for current noise) and canonical (for voltage noise) ensembles and results are derived which are valid for classical as well as for degenerate statistics including fractional exclusion statistics. The unifying theory so developed sheds new light on the microscopic interpretation of dissipation and fluctuation phenomena in conductors. In particular it is proven that, as a consequence of the Pauli principle, for Fermions non-vanishing single-carrier velocity fluctuations at zero temperature are responsible for diffusion but not for current noise, which vanishes in this limit.