Living cells exhibit well-organized dynamics in bio-soft matter assemblies, such as membrane deformation, cell division, and cell differentiation 1 , which are essential features that distinguish living systems from non-living matter. Recently, liquid-liquid phase separation (LLPS) droplets of bio-soft matter have been found in living cells, and their dynamic behaviors have attracted attention , such as nucleolar assembly through non-equilibrium processes of rRNA transcription , sol-gel transition , and activation/inhibition of molecular reactions . These examples show that precise temporal control of biological LLPS droplets via non-equilibrium chemical reactions realizes such dynamic behaviors. Synthetic LLPS droplets have recently been explored in bottom-up synthetic biology for constructing artificial cells , molecular robots , molecular computers , and biomedical nanodevices . Various dynamic behaviors of synthetic LLPS droplets have been reported, such as sequestration of molecules , motion , and division . More recently, non-equilibrium dynamics such as cyclic assembly/disassembly and transient shell-formation of synthetic coacervate droplets were achieved by coupling LLPS droplets with non-equilibrium chemical reactions such as phosphorylation/dephosphorylation and enzymatic synthesis of polynucleotide . However, temporal control of LLPS droplet dynamics remains difficult. Programmable temporal control methods must be developed to mimic cell dynamics.