Figure 2
From: Collective excitations of germinating pollen grains at critical points
Dynamic Shannon entropy as a function of temperature for living tobacco pollen tubes. The data points (solid squares), calculated separately in the R programming language from the original time series, were interpolated using the sinc function and showed a zero-bias peak and splitting (bound state) at criticality. The red ball with the arrow, representing thermally activated proton over-the-barrier hopping dynamics, points to the attractor basin, which can be interpreted as a 2H+ ion(s) energy gap (\(\Delta\)) that was approximately 2.25 K (0.00019(1) eV) wide, which indicated the readiness of the pollen tubes for an extreme (fast) and stable elongation at a critical range. Note the clear local maxima that can be interpreted as potential barriers (the system can tunnel through them to achieve a stable minimum), which also represent points of instability. Fit parameters: coefficient of determination R2 = 0.62587 (χ2 = 0.057), y0 = 1.95(8), a = − 0.19(5), b = 3.57(6); \(y = y_{0} + \frac{{a {\text{sin}}\left( {bx} \right)}}{x}\). Photomicrograph of the elongating pollen tubes of Nicotiana tabacum L.
