A rock is not life because its maintained crystalline structure (eg an NaCl crystal) is a lowest-energy, most-probable configuration, given the thermodynamic regime and material availability in the environment. There is no need for particular information embedded in that structure to influence the surrounding physics and chemistry to achieve greater than thermodynamically expected longevity of the structure.
If you equate the information in the crystal structure (all several bits of it) with the form (and bonding-energy configuration) of the structure, then I SUPPOSE you could say that that information embedded in/ implicit in that structure is related to the structure's thermodynamic stability. In more life-y persistent structures, there is a more complex causal relationship between the information's form and the persistence of the structure. Also, there is typically much more information, and therefore much lower probability of the information pattern's spontaneous formation or maintenance in the thermodynamic regime, so much more NEED for self-causation by the information. If something was inevitably going to happen anyway to some matter and energy, due to its statistical distribution and the surrounding thermodynamic regime and fundamental forces, do we say that that future state (or equivalence class of states) required a particular cause (beyond the operation of the simple physical laws on the situation?) No. So particular local information is not required to cause anything, in thermodynamically and physically stochastically EXPECTED states. Information is only required to be able to be self-causal when the persistence of the information (and the material forms and processes it persists in) are NOT OTHERWISE thermodynamically and physically probable/expected.
Rocks are expected (from operation of simple physics laws), so are not life-y self-causal by particular information.