Irreversibility in high-dimensional dynamical systems

1.我们发现扩展的第二定律对于不同定态之间的跃迁是成立的，并且Shannon熵差等于超额热除以在无限慢过程中获得的温度，(论文发表)2.我们数值研究了一个含时变力的台球系统，我们的结果表明在哈密顿混沌中定态之间可能的跃迁是有限的，正如我们以前的理论所提出的，(论文提交)3.我们发展了一个唯象理论来研究具有热传导的系统的定常非平衡态。我们发现本质上存在唯一一致的热力学，并做出了具体的预测，即存在新的渗透压和共存温度的移动。这些预测使人们可以通过将它们与实验进行比较来检验SST的定量有效性，(提交的论文)4.通过对呈现高维耗散混沌的Kuramoto方程的数值模拟，我们找到了一个代表空间非均匀结构维护成本的量。这出现在化学振荡波的相位湍流中(提交的论文)

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)