Dynamical properties of correlated ordered systems

Stabilizing competing orders that are not available in equilibrium has been an integral part of dynamical phase transitions. There have been theoretical and experimental efforts to enhance or give rise to orders that weakly compete or do not coexist at all, such as superconductivity and charge density wave (CDW) states. In the first part, we study the dynamics of two competing order parameters within the time-dependent Ginzburg–Landau framework. Driving the system far from equilibrium reveals an enhancement of the subdominant order and the emergence of a metastable state governed by nonlinear coupling and fluctuation effects. Analytical and numerical results highlight how thermal and nonthermal fluctuations shape the nonequilibrium free-energy landscape and control the lifetime of metastable phases. In the second part, we discuss experimental observations in 1T-TaS₂, where a hidden metallic CDW state—previously thought to exist only transiently—can be stabilized near equilibrium through thermal quenching. The coexistence of commensurate and hidden CDW domains provides a concrete realization of the metastable regime, linking nonequilibrium dynamics to emergent steady states in correlated materials.