# Does reduced density matrix in a bipartite system evolve unitarily such that $\rho(t) = U(t)\rho_0U^{*}(t)$?

It is known that for density matrix, the von Neumann equation holds. $$\dot{\rho} = -i[H,\rho]$$ and thus $$\rho(t) = U(t)\rho_0 U^{*}(t)$$ where $$U$$ refers to a unitary matrix. But what happens for reduced density matrix of $$A$$ in a bipartite system $$AB$$? Would above be satisfied? That is, for $$\rho_A = Tr_B\{\rho_{AB}\}$$, would $$\rho_A(t) = U_A(t)\rho_0 U_A^{*}(t)$$ be satisfied, where $$U_A$$ is some unitary matrix?

• Are the subsystems A and B interacting, and if not are they also initially decorrelated? – Ian Sep 12 at 5:55
• @Ian $A$ and $B$ are interacting and are entangled/correlated. – Neijal Kanderbalt Sep 12 at 6:01