Suppose that Hamiltonian of a global system is time-independent. Two subsystems encompass this global system. Adopt Heisenberg picture, and density matrix and state vector are constant. von Neumann entropy is defined on (reduced) density matrix, so in Heisenberg picture, entropy of a subsystem is constant. But this cannot be the right way of thinking.
So should one not use usual von Neumann entropy equation when in Heisenberg picture? Or is entropy of a subsystem indeed constant when Hamiltonian of a global system is time-independent? Is entangelment entropy different from von Neumann entropy?