Irreversibility in high-dimensional dynamical systems

高维动力系统中的不可逆性

• 批准号: 12834005
• 负责人: SASA Shin-ichi
• 金额: $ 1.66万
• 依托单位: The University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2001
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12834005/
• 关键词: entropy; chaos; non-equilibrium; 不可逆性

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)

1.我们发现，扩展的第二定律适用于不同稳态之间的过渡，香农熵差等于多余的热量除以无限慢过程中获得的温度，（论文出版）2。我们数值研究了具有时间相关力的台球系统，我们的结果表明，正如我们的理论之前所建议的那样，汉密尔顿混沌中稳态之间可能的转变存在限制，（提交的论文）3。我们发展了热传导系统中稳态非平衡态的唯象理论。我们发现本质上存在唯一的相容热力学，并作出具体的预言，即：新的渗透压的存在和共存温度的变化。这些预测允许人们通过与实验进行比较来测试SST的定量有效性，（提交的论文）4。通过数值模拟的仓本方程，它显示了高维耗散混沌，我们发现了一个数量代表的成本为维护一个空间不均匀的结构。出现在化学振荡波的相湍流中，（论文提交）

项目成果

T.Hatano, S.Sasa: "Steady state thermodynamics of Langerin systems"Physical Review Letters. 86. 3463-3466 (2001)

T.Hatano, S.Sasa：“Langerin 系统的稳态热力学”物理评论快报。

T.Hatano, S.Sasa: "Steady state thermodynamics of Lungerin systems"Physical Review Letters. 86. 3463-3466 (2001)

T.Hatano, S.Sasa：“Lungerin 系统的稳态热力学”物理评论快报。