# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1903.02944