The arrow of time is globally derived from the global increase of entropy. In an information theory sense as a system evolves in time it becomes more random, the system can be in more possible configurations otherwise known as states. Likewise from the second law of thermodynamics a closed system cannot be reversed. It cannot evolve backwards in time to its initial conditions. However irreversibly of a system is ambiguous in the sense that if enough information is known and enough computational power is available then an observer can reverse the system close to its initial conditions but not precisely. The increase of randomness in a system over time is deterministic but tends towards chaos in the sense that the error associated with calculating the initial conditions increases exponentially. So as the arrow of time marches forward it becomes exponentially difficult to calculate the initial conditions of any closed system to the point where it is fundamentally impossible due to a physical computational limit. Therefore, if this fundamental computational limit lies on a closed timelike curve there wouldn't be sufficient enough information to determine causality and thus can said to be preserved. In an analogy consider an observer with an infinite amount of memory and records its entire journey. The CTC is so large that eventually its memory starts to decay and break down, conserving information but scrambling it. When it returns to its initial position it would have retained nothing from its journey. Is this possible?