To analyze the system, Deutsch divided it into two parts: a subsystem outside the CTC and the CTC itself. To describe the combined evolution of both parts over time, he used a unitary operator (U). This approach relies on a specific mathematical framework to describe quantum systems. The overall state is represented by combining the density matrices (ρ) for both the subsystem and the CTC using a tensor product (⊗). Notably, Deutsch assumed no initial correlation between these two parts. While this assumption breaks time symmetry (meaning the laws of physics wouldn't behave the same forwards and backwards in time), Deutsch justifies it using arguments from measurement theory and the second law of thermodynamics.