There are irreversible processes in organic chemistry. You can't uncook an egg. But the question has to be asked -- at what point exactly does a person (or a cell) die? What would it mean in your system of thought to take the DNA from a dead cell and transplant it to a healthy cell?
I'm sure you are aware that the definition of clinical death has shifted considerably in the last hundred years. Why?
Indeed, I am aware that the definition of clinical death has changed over the years. And DNA serves a useful purpose in forensics long after the organism is dead.
The rigorous support, the curiosity, the epistemological zeal to ask and answer these questions comes from the mathematicians and physicists who have entered the field. And they are not closeted theorists. With regard to information theory and molecular biology, I have been using Tom Schneider as the primary authority he works in cancer research for the National Institute of Health.
The information theory brought to the table is rigorous, quantifying attributes which remain fuzzy to biologists. Based on Shannon-Weavers model, there is no confusion about what is alive and what is not alive. Also, it is the Shannon theory which explains the transaction of state changes in molecular machines, the DNA, the coding and opens the door for abiogenesis theory. The proof of the Shannon model lies in the physics, the transfer between Shannon entropy to thermodynamic entropy.
Likewise, it is cellular automata (von Neumann, Wolfram) and Kolmogorov complexity which tackles the rise of complexity in biological systems - a subject which usually garners a dismissive hand-wave from biologists. Failure to address complexity, makes the fuzziness an issue in itself and a soft underbelly to the theory of evolution.
Without these mathematics, the biologists will continue to stand at the door, fumbling with the keys convinced that one of them must surely fit the lock.
I cannot make the biologists curious but, by golly, I can destroy any claim they make to having answers when they refuse to look and decry those who do.