Subsystem isolated spin

The density matrix of a mixed state can be constructed even for a system which has no quantum mechanical states since it is not isolated and constitutes only a subsystem of a larger system. For example, the spin system of a molecule in a liquid is not isolated owing to the presence of interactions between the degrees of freedom of the spins and other, mostly rotational, degrees of freedom which are usually called the lattice. The state of the entire system may be represented by the basis set which is formed from the direct product of the basis sets of its subsystems ... 

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