  Starting from a Langevin formulation of a thermally perturbed nonlinear
elastic model of the ferroelectric smectic-C$^*$ (SmC${*}$) liquid crystals in
the presence of an electric field, this article characterizes the hitherto
unexplored dynamical phase transition from a thermo-electrically forced
ferroelectric SmC${}^{*}$ phase to a chiral nematic liquid crystalline phase
and vice versa. The theoretical analysis is based on a combination of dynamic
renormalization (DRG) and numerical simulation of the emergent model. While the
DRG architecture predicts a generic transition to the Kardar-Parisi-Zhang (KPZ)
universality class at dynamic equilibrium, in agreement with recent
experiments, the numerical simulations of the model show simultaneous existence
of two phases, one a "subdiffusive" (SD) phase characterized by a dynamical
exponent value of 1, and the other a KPZ phase, characterized by a dynamical
exponent value of 1.5. The SD phase flows over to the KPZ phase with increased
external forcing, offering a new universality paradigm, hitherto unexplored in
the context of ferroelectric liquid crystals.
