Irreversibility in high-dimensional dynamical systems

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1. We found that the extended Second Law holds for transitions between different steady states and that the Shannon entropy difference is equal to excess heat divided by the temperature obtained in infinitely slow processes, (paper published)2. We numerically studied a billiard system with a time-dependent force, and our results show the existence of a limitation on possible transitions between steady states in Hamiltonian chaos, as previously suggested by our theory, (paper submitted)3. We developed a phenomenological theory for steady nonequilibrium states in systems with heat conduction. We found that there is essentially a unique consistent thermodynamics, and make concrete predictions, I. E, the existence of a new osmotic pressure and a shift in the coexistence temperature. These predictions allow one to test for the quantitative validity of SST by comparing them with experiments, (paper submitted)4. Through numerical simulations of the Kuramoto equation, which displays high-dimensional dissipative chaos, we found a quantity representing the cost for maintenance of a spatially non-uniform structure. That appears in the phase turbulence of chemical oscillatory waves, (paper submitted)