A system Altered in time by the environment

The symbolism again comes from the language of quantum mechanics.  The Rho (subscript s) and U have their same meaning.  But now a second density operator is present, the environment (env).  The entity is irreversibly altered by the interaction with the environment, generally leading to a loss of coherence and entanglement.  If the two density operators are separable and not entangled, the system will remain essentially unchanged.

A system not Altered in time by the environment

The trademark is in quantum mechanics language.  It describes “an entity moving forward unperturbed by the environment”.  The Greek symbol Rho is the term for a density operator which fully describes a systems, which can be a human.  The flanking U are unitary operators which represent moving forward in time.