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In equilibrium this entropy coincides with the conventional von Neumann entropy $S_n=-{\\rm Tr}\\, \\rho\\ln\\rho$. However, in contrast to $S_n$, the d-entropy is not conserved in time in closed Hamiltonian systems. If the system is initially in stationary state then in accord with the second law of thermodynamics the d-entropy can only increase or stay the same. 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