Fock-Space Formulation of the Lifetime of a Unicellular Organism

What is life? In this work, we take life to mean a dynamical tendency to
conserve identity for as long as possible. For a single bacterium, identity is
carried by its chromosomal DNA code, so the bacterium is alive precisely
insofar as it actively maintains a well-defined chromosomal configuration over
time and can, in principle, replicate this configuration into progeny. For a
multicellular organism, many cells share essentially the same DNA code and
behave as a single coherent entity; in that case, life corresponds to the
persistence of a common genetic identity across the cellular ensemble, rather
than to the survival of any particular cell. Cell duplication in multicellular
organisms likewise serves to maintain this dynamical tendency to conserve
identity over time.
In previous studies we implemented this idea at the multicellular and colonial
scale using a classical notion of coherence, in which an organism is
represented by a single nonseparable state over the DNA codes of its
constituent cells, while a colony is describable as a separable ensemble. Here
we apply the same principle to the simplest possible case, a single bacterium,
and show that its biological identity can be identified with the coherence of
its chromosomal DNA code within an abstract state space. We then introduce a
Fock-space representation in which bacteria carrying given codes occupy
fermionic modes, and replication, repair, and death are realized as elementary
operators acting on these modes. Within this framework we define the lifetime
of a unicellular organism as the integral coherence time of a code-occupation
autocorrelation function and, in a minimal Markovian model, obtain a compact
expression in which the lifetime coincides with the inverse decay rate of the
corresponding identity mode.