Hidden Time-Reversal Symmetry in Dissipative Reciprocal Systems

TL;DR

This paper proves that lossy reciprocal systems possess a hidden time-reversal symmetry, revealing a fundamental link between reciprocity, dissipation, and linearity, and shows how dissipative responses can be approximated by lossless systems.

Contribution

It introduces a novel proof of hidden time-reversal symmetry in dissipative reciprocal systems without microscopic reversibility assumptions.

Findings

Lossy dielectric dissipation channels can be modeled by lossless transmission networks.

Reciprocity in lossy dielectrics is fundamentally linked to hidden time-reversal invariance.

Dissipative material responses can be approximated by lossless material responses.

Abstract

It is proven, without using the microscopic reversibility argument of Onsager, that lossy reciprocal systems have a hidden time-reversal symmetry. The key idea is that the dissipation channels of lossy dielectrics can be mimicked by a distributed network of lossless transmission lines. It is highlighted that the reciprocity of lossy dielectrics is fundamentally rooted on the hidden time-reversal invariance and on linearity of the materials. Furthermore, it is demonstrated that the upper-half plane response of dissipative materials can be approximated as much as desired by the response of some lossless material.