Symbolic computation of action functionals for multi-dimensional CRN/ME Hamiltonian systems

Determine whether closed-form (symbolic) computation of the action functional governing expected escape times is possible for multi-dimensional cases beyond the SI process in the Hamiltonian framework associated with chemical reaction networks and epidemic models.

Background

The paper outlines a Hamiltonian approach to estimate escape paths and expected travel times in stochastic CRN/ME systems, where the action functional characterizes asymptotic scaling of escape times.

While an explicit solution is known for the SI process, the authors note that in higher-dimensional settings only numerical integration seems to work; it remains unknown whether symbolic solutions exist in other specific cases.

References

Whether or not symbolic treatment is possible in other particular cases is an open problem.

— Advancing Mathematical Epidemiology and Chemical Reaction Network Theory via Synergies Between Them  (2411.00488 - Avram et al., 2024) in Section “The CRN representation yields a Hamiltonian representation of the expected time spent along escape paths of stochastic CTMC processes”

Several directions remain open. First, the present work focuses primarily on systems with a stable balanced-growth composition. Systems with multiple balanced-growth states would require a global quasipotential constructed from least-action transitions between competing growth modes .

— Large-deviations theory for growing chemical reaction networks  (2609.30970 - Gagrani et al., 25 Sep 2026) in Section Discussion