I believe "life" is a fundamental property of the universe. (So is "consciousness", but that's a different and considerably more difficult discussion).
I believe we can eventually quantify life in terms of information.
In the 40's, Shannon and Weaver showed that information and entropy are the same thing.
But to understand the linkage, one has to abstract even further. One can start by considering that both information and Gibbs entropy eventually adhere to Neumann's formulation, in terms of the number of available states. The key word being "number" as in counting. When we count, it's more than just assigning labels to things, we're actually assigning mathematical structure. "Number theory" is an important branch of mathematics. Quantum processes with only two assigned states behave very differently from those that can undergo full Wick rotations.
One of the more interesting results is the Cantor dust. To create it, you take a line segment from 0 to 1, and you chop out the middle third. Then you keep chopping out the middle third of every remaining segment, recursively. Remarkably, Cantor proved that the resulting dust has the same number of points as the original line segment. (We"re "counting points", right?)
en.wikipedia.org