Telomeres might be the key, so why doesn't society as a whole focus on immortality? The tendency for (closed systems in) our universe to evolve toward states of greater entropy isn't an effect of any of our specific physical laws, though. In a purely mathematical model of all of the possible instantaneous states of the universe, completely agnostic to the physical laws governing transitions from one state to another, states where energy is spread out more evenly are more common, and states where it is more concentrated are less common. Think of, for example, ways that air molecules could be arranged in a box: there's only relatively few arrangements that have them all clumped in the same corner, but a whole lot of arrangements that have them spread out pretty evenly across the whole volume of the box.
It's not that there are more high-entropy states than low-entropy ones because the physical laws make high-entropy ones more likely; the high-entropy ones are more likely because there's just more of them that are possible (and that is actually what defines them as high-entropy), so even if there was no law-like behavior at all, and the whole system just evolved randomly, you would just expect it to evolve into a higher-entropy state at random.
It's actually thought that the second law of thermodynamics is really the fundamental law of the universe, and that all of the other laws are really just that combined with restrictions on what kinds of states are even possible. Other laws define possible ways that the universe could be, and then the universe just randomly changes, one tiny bit at a time, everywhere, constantly, from one of those possible ways to one of the most similar other possible ways that it could be, and the overall tendency for it to change predictably in certain ways, from X to Y, is just because there are more possible ways that are like Y than there are like X, so randomly stepping through possible states just tends to leave things more Y-like than X-like over time.
I actually like to think of time in exactly that way: picture an abstract space of all the possible states of the universe (we can only really picture a two- or three-dimensional space, which could only visualize two or three variables, but just imagine that for simplicity). Each point in that space represents one way the universe could be, and points that are close to each other represent similar ways the universe could be. Some regions of that space are filled with points representing less-entropic states than others, but those are necessarily just little corners of the space, and the bulk of the volume is filled with points representing more-entropic states. The dimension of time is just any line through that abstract space, where the direction toward more-entropic states is "the future" and the direction toward less-entropic states is "the past".
There are therefore multiple possible timelines, multiple paths through all the possible configurations of the universe, but because more-entropic configurations are more common and less-entropic ones are less common, lines toward "the past" quickly converge, while lines toward "the future" diverge, which is why the past seems determined (few similar possible states are less-entropic than the present one, so the ways the past could have been to lead to this present are limited) but the future does not (many similar possible states are more-entropic than the present one, so the future could turn out in many different ways from this present).
And we perceive the arrow of time that way because the process of forming our memories, and the processes that form all other records of the past, occur in accordance with laws that are driven by the increase of entropy, so the states that are recorded in our brains or in rock strata or any other records will necessarily be of less-entropic states in the past, and our projections of trends in those recorded past states will therefore be toward the more-entropic states of the future.