Physical relevance of time-reversal-symmetric non-reciprocal dissipation

Determine whether time-reversal-symmetric, non-reciprocal dissipative models with real anti-symmetric mixing between fields (i.e., a non-Hermitian but real anti-symmetric Hessian that violates energy conservation and yields complex-conjugate mode frequencies) can provide realistic descriptions of physical systems despite the resulting exponential instability of one mode.

Background

The paper distinguishes two sources of dissipation in free theories: non-reciprocity that preserves time-reversal symmetry and dissipation that breaks time reversal. In the time-reversal-symmetric case, a real anti-symmetric mixing between two scalar fields yields non-conservation of energy and complex-conjugate frequency pairs, implying an instability of one mode.

Despite this instability, the authors raise the question of whether such non-reciprocal dynamics can still model any physical system, leaving this assessment open.