Entropy in physics has little to do with ageing.
Physical entropy deals with how many microstates are compatible with a given macrostate. Commonly we say that disordered states have high entropy since many microstates are compatible with the macrostate we observe, while in a highly ordered state the number of microstates is relatively low.
Ageing is a gradual loss of homeostasis and adaptability of an organism, in the end caused by the lack of evolutionary selection for long-term maintenance far beyond reproductive age. Various systems lose their efficiency because of build-up of substances that cannot be broken down, mitochondria and immune cells that do not work effectively, there is DNA damage and so on.
But note that the bad things about ageing are not due to high entropy. The entropy of an old and a young body of the same mass are more or less equal, and mostly due to the degrees of freedom of water molecules. Entropy in physics does not well describe the macroscopic disorder of bodies or messy rooms.
Most importantly, bodies are open systems that persist through time by having a flow of energy and material pass through them. This allows them to reduce their entropy in principle arbitrarily. The fact that this ability fails is a separate issue. There are non-ageing species: had entropy applied strictly, then they would have been impossible.
One can argue that we can describe the gradual disorganisation of the functions of the body due to ageing as entropy but within the abstract system of bodily states. I am sceptical that this approach is likely to produce any fruitful results: the functional physiological states are also an open system. There is no shortage of papers playing around with analogies of entropy and ageing, but few, if any of them have produced anything of lasting value in biogerontology as far as I know.