  We discuss fluctuations near the second order phase transition where the free
energy has an additional non-Hermitian term. The spectrum of the fluctuations
changes when the odd-parity potential amplitude exceeds the critical value
corresponding to the PT-symmetry breakdown in the topological structure of the
Hilbert space of the effective non-Hermitian Hamiltonian. We calculate the
fluctuation contribution to the differential resistance of a superconducting
weak link and find the manifestation of the PT-symmetry breaking in its
temperature evolution. We successfully validate our theory by carrying out
measurements of far from equilibrium transport in mesoscale-patterned
superconducting wires.
