Spectral gap for the BGNST piston model

Let $N\in\mathbb Z^+$ be the number of ball-piston pairs aligned along a one-dimensional chain, and consider the associated piston model. Spectral-gap conjecture. The spectral gap of the piston model is bounded below by $\mathrm{const.}\,N^{-2}$, where the constant is strictly positive. This transposes Sasada's spectral-gap estimate for the Gaspard–Gilbert model to the BGNST model; the supplied context presents it as an unresolved problem for the hydrodynamic-limit analysis.