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We investigate macroscopic behaviors of fluctuating domain walls innonequilibrium open systems with the help of the effective field theory basedon symmetry. Since the domain wall in open systems breaks the translationalsymmetry, there appears a gapless excitation identified as the Nambu-Goldstone(NG) mode, which shows the non-propagating diffusive behavior in contrast tothose in closed systems. After demonstrating the presence of the diffusive NGmode in the $(2+1)$-dimensional dissipative Josephson junction, we provide asymmetry-based general analysis for open systems breaking the one-dimensionaltranslational symmetry. A general effective Lagrangian is constructed based onthe Schwinger-Keldysh formalism, which supports the presence of the gaplessdiffusion mode in the fluctuation spectrum in the thin wall regime. Besides, wealso identify a term peculiar to the open system, which possibly leads to theinstability in the thick-wall regime or the nonlinear Kardar-Parisi-Zhangcoupling in the thin-wall regime although it is absent in the Josephsonjunction.

Effective field theory of fluctuating wall in open systems: from a kink in Josephson junction to general domain wall