  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
($\mathcal{PT}$) 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.
