Time Reversal (TR) symmetry is widely regarded as equivalent to reciprocity. However, the two concepts are strictly distinct: a simple lossy system is TR asymmetric while being reciprocal! Given the fact that all the physical systems are inherently lossy, due to causality, this discordance has represented a long-standing fundamental restriction in physics. The paper of Silveirinha resolves this issue in showing that a lossy—and hence TR-asymmetric—system is equivalent to a lossless TR-symmetric system with an extra “hidden” dimension of space that mimics heat dissipation in terms of propagation along a fictitious matched transmission line coupled to the system hyperspace. This extension of TR-symmetry to a lossy reciprocal system is completely macroscopic, and thus provides a convenient alternative to Onsager’s argument of microscopic reversibility. Moreover, the paper insightfully shows that Lorentz-type reciprocity relations are not limited to electromagnetic systems, but generally apply to any linear TR-invariant system.

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