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We find a class of spin environment at finite temperature in the thermodynamics limit models where individual quantum trajectories may depend on parameters that are undetermined by the full open system evolution. Our criteria are functions of the given quantum state and detect genuine multipartite entanglement, purity and information entropy that had not been identified so far. They are experimentally accessible without quantum state tomography and are easily computable as no optimization ordoi:10.12785/qir/010203 fatcat:chgxtz6kxbazhiaaebwi4vsk64