  In this work, we study a bipartite system composed by a pair of entangled
qudits coupled to an environment. Initially, we derive a master equation and
show how the dynamics can be restricted to a "diagonal" sector that includes a
maximally entangled state (MES). Next, we solve this equation for mixed qutrit
pairs and analyze the $I$-concurrence $C(t)$ for the effective state, which is
needed to compute the geometric phase when the initial state is pure. Unlike
(locally operated) isolated systems, the coupled system leads to a nontrivial
time-dependence, with $C(t)$ generally decaying to zero at asymptotic times.
However, when the initial condition gets closer to a MES state, the effective
concurrence is more protected against the effects of decoherence, signaling a
transition to an effective two-qubit MES state at asymptotic times. This
transition is also observed in the geometric phase evolution, computed in the
kinematic approach. Finally, we explore the system-environment coupling
parameter space and show the existence of a Weyl symmetry among the various
physical quantities.
