Algebraic Statistics of Poincaré Recurrences in a DNA Molecule

The statistics of Poincaré recurrences is studied for the base-pair breathing dynamics of an all-atom DNA molecule in a realistic aqueous environment with thousands of degrees of freedom. It is found that at least over five decades in time the decay of recurrences is described by an algebraic law with the Poincaré exponent close to β=1.2. This value is directly related to the correlation decay exponent ν=β-1, which is close to ν≈0.15 observed in the time resolved Stokes shift experiments. By applying the virial theorem we analyze the chaotic dynamics in polynomial potentials and demonstrate analytically that an exponent β=1.2 is obtained assuming the dominance of dipole-dipole interactions in the relevant DNA dynamics. Molecular dynamics simulations also reveal the presence of strong low frequency noise with the exponent η=1.6. We trace parallels with the chaotic dynamics of symplectic maps with a few degrees of freedom characterized by the Poincaré exponent β~1.5.