Thermodynamic entropy and excess information loss in dynamical systems with time-dependent Hamiltonians

The Fermi-Pasta-Ulam model with the time-dependent nonlinear term is used to explore the relation between the thermodynamic entropy change due to irreversible processes and the change of information loss as a chaotic dynamical system. We define a novel quantity called the "excess information loss" and conjecture a quantitative relation between the thermodynamic entropy increase and this new quantity, purely defined by dynamical system theory.