Yes, it is possible to measure the entropy of a system before and after it becomes entangled. Entropy is a measure of the uncertainty or randomness in a system. In the context of quantum mechanics, the entropy of a quantum system is typically quantified using the concept of von Neumann entropy.
Before Entanglement: If the system consists of separate, non-interacting subsystems, each with its own well-defined state, the entropy of the overall system