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Time-reversal and PT symmetry breaking in non-Hermitian field theories. (arXiv:2305.05633v2 [cond-mat.stat-mech] UPDATED)

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We study time-reversal symmetry breaking in non-Hermitian fluctuating field
theories with conserved dynamics, comprising the mesoscopic descriptions of a
wide range of nonequilibrium phenomena. They exhibit continuous parity-time
(PT) symmetry breaking phase transitions to dynamical phases. For two concrete
transition scenarios, exclusive to non-Hermitian dynamics, namely oscillatory
instabilities and critical exceptional points, a low-noise expansion exposes a
pre-transitional surge of the mesoscale (informatic) entropy production rate,
inside the static phases. Its scaling in the susceptibility contrasts
conventional critical points (such as second-order phase transitions), where
the susceptibility also diverges, but the entropy production generally remains
finite. The difference can be attributed to active fluctuations in the
wavelengths that become unstable. For critical exceptional points, we identify
the coupling of eigenmodes as the entropy-generating mechanism, causing a
drastic noise amplification in the Goldstone mode.

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