Abstract
We discuss how the state in quantum dynamics evolves toward thermal equilibrium in the entropic perspective. For comparing the evolution in semi-classical dynamics which can be expected directly by thermal equilibrium and in quantum dynamics, we set up a simple model to calculate the entropies. In the quantum dynamical region, the reduced density matrix is adopted to derive the entropy of subsystems. We find that the entropy of the whole system would be kept to zero in quantum dynamics due to the unitary time evolution operator, if the system starts with a pure state. The finite entropy would be gained from the reduced density matrix associated with local measurement . The main cause is that the partial tracing operator would break the unitary property of the entropy for subsystems. We apply the method of the tracing out the heat bath and propose a model for generating W state in multi-qubits with fermion particles. The method is the conditional measurement for the common quantum well. From the non-unitary property of the conditional measurement and the translational symmetry of this model, the W state can be made in these qubits with high fidelity.