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We demonstrate a new type of non-Hermitian phase transition in open systemsfar from thermal equilibrium, which takes place in coupled systems interactingwith reservoirs at different temperatures. The frequency of the maximum in thespectrum of energy flow through the system plays the role of the orderparameter, and is determined by an analog of the -potential. The phasetransition is exhibited in the frequency splitting of the spectrum at acritical point, the value of which is determined by the relaxation rates andthe coupling strengths. Near the critical point, fluctuations of the orderparameter diverge according to a power law. We show that the critical exponentdepends only on the ratio of reservoir temperatures. This dependence indicatesthe non-equilibrium nature of the phase transition at the critical point. Thisnew non-Hermitian phase transition can take place in systems withoutexceptional points.

A new type of non-Hermitian phase transition in open systems far from thermal equilibrium