The concept of time and its relationship to entropy and the ultimate fate of the universe is a topic of ongoing scientific research and speculation. While I can provide you with a general understanding of the current understanding, please note that our knowledge in this area is still evolving, and future discoveries may refine or change our understanding.
Entropy is a measure of the disorder or randomness in a system. In the context of the universe, the idea of maximum entropy is often associated with the concept of the "heat death" or "big freeze" scenario, where the universe reaches a state of maximum entropy and thermal equilibrium. In this scenario, all usable energy is evenly distributed throughout the universe, and the temperature becomes uniform. Essentially, it is a state of maximum disorder and low energy.
According to current scientific understanding, if the universe continues to expand indefinitely and entropy keeps increasing, it is hypothesized that the universe will eventually reach a state of maximum entropy. However, it's important to note that this doesn't necessarily mean that time itself will come to an end.
The relationship between entropy, time, and the finiteness or infiniteness of the universe is still an open question. There are different theoretical perspectives on this matter, and it largely depends on the nature of the universe and the fundamental laws of physics that govern it.
Some theories suggest that time could continue even in a state of maximum entropy, but it might lack the distinguishable order and structure we perceive in our current experience. Other theories propose that the universe could undergo a cyclic process, where a new universe emerges from the remnants of the previous one, suggesting an infinite sequence of universes.
It's important to emphasize that these ideas are still highly speculative, and our understanding of the ultimate fate of the universe, the nature of time, and the relationship between entropy and finiteness is an active area of research in cosmology and theoretical physics.