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We consider a nonequilibrium transition that leads to the formation ofnonlinear steady-state structures due to the gas flow scattering on a partiallypenetrable obstacle. The resulting nonequilibrium steady state (NESS)corresponds to a two-domain gas structure attained at certain criticalparameters. We use a simple mean-field model of the driven lattice gas withring topology to demonstrate that this transition is accompanied by theemergence of local invariants related to a complex composed of the obstacle andits nearest gas surrounding, which we refer to as obstacle edges. Theseinvariants are independent of the main system parameters and behave as localfirst integrals, at least qualitatively. As a result, the complex becomesinsensitive to the noise of external driving field within the overcriticaldomain. The emerged invariants describe the conservation of the number ofparticles inside the obstacle and strong temporal synchronization orcorrelation of gas states at obstacle edges. Such synchronization guaranteesthe equality to zero of the total edge current at any time. The robustnessagainst external drive fluctuations is shown to be accompanied by strongspatial localization of induced gas fluctuations near the domain wallseparating the depleted and dense gas phases. Such a behavior can be associatedwith nonequilibrium protection effect and synchronization of edges. Thetransition rates between different NESSs are shown to be different. Therelaxation rates from one NESS to another take complex and real values in thesub- and overcritical regimes, respectively. The mechanism of these transitionsis governed by the generation of shock waves at the back side of the obstacle.In the subcritical regime, these solitary waves are generated sequentially manytimes, while only a single excitation is sufficient to rearrange the systemstate in the overcritical regime.

Nonequilibrium protection effect and spatial localization of noise-induced fluctuations under gas flow scattering on partially penetrable obstacle