Thermodynamic entropy and excess information loss in dynamical systems   with time-dependent Hamiltonian
  We study a dynamical system with time dependent Hamiltonian by numerical experiments so as to find a relation between thermodynamics and chaotic nature of the system. Excess information loss, defined newly based on Lyapunov analysis, is related to the increment of thermodynamic entropy. Our numerical results suggest that the positivity of entropy increment is expressed by the principle of the minimum excess information loss. 
S. Sasa and T. S. Komatsu