Open-System Virus Particle Physics: A Path-Integral Viral Lattice Theory Using Non-Self Adjoint Stochastic PDEs and Fock-Space Formalism

We develop a comprehensive theoretical biophysics model grounded in a path integral perspective and an m-sectorial open-system framework, to describe complex, damped viral phonon dynamics in resource limited and noise driven environments. By unifying wave mechanics (via PDEs with multiplicative noise), Markov jumps for occupant or arrangement transitions, and second quantized (Fock-space) expansions, our construction accommodates an unbounded number of viral lattices in a single global wavefunction. In doing so, we capture how an entire population potentially numbering in the millions may be represented by a single operator theoretic state, or orbit, whose evolution is governed by non-unitary semigroups with potential equilibrium or non equilibrium steady states. This approach admits action functionals over the space of system trajectories, enabling large deviation and flux analyses whenever detailed balance is broken by sustained resource inputs, as often happens in real infections. Such a global wavefunction thus synthesizes PDE wavefront modes, occupant transitions, and stochastically induced rearrangements into a single evolution equation, capturing how local capsid vibrations might catalyze large scale replication bursts, and vice versa. Our proofs show that, despite unbounded occupant expansions or morphological continuums, solutions remain finite norm over finite times. The well posedness extends to non-self-adjoint operators with complex damping, irreversibility, and operator-valued-noise, thus mirroring host constraints and immune factors that restrict virus proliferation. Our formalism invites direct experimental cross validation, from single virion tracking to population assays, and offers predictive insights for resource limited replication, capsid reorganizations, and potential intervention strategies in modern virology.