Statistical properties of nonstationary weak Gibbs states and analysis of dissipative phenomena for those invertible extensions

非平稳弱吉布斯态的统计特性和可逆外延的耗散现象分析

• 批准号: 21340018
• 负责人: YURI Michiko
• 金额: $ 10.4万
• 依托单位: Hokkaido University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21340018/
• 关键词: Dissipative phenomena; Intermittency; Entropy production; Weak Gibbs measure; Non-hyperbolicity; Equilibrium state; Sofic system; Invertible extension

For nonhyperbolic, noninvertible piecewise invertible systems , we constructed natural extensions of both (bi)nonsingular measures and absolutely continuous invariant weak Gibbs measures under the finite range structure condition. Furthermore, we obtained a criterion for deciding the processes arising from those invertible extensions exhibit dissipation and new phenomena arising from intermittent sofic systems preserving weak Gibbs measures, which are not observed near equilibrium, that is dissipation of the phase volume with zero asymptotic averaged entropy production and bottomless source of the Gibbs entropy with zero asymptotic averaged entropy production. For families of partially defined maps on compact metric spaces, we clarified when self-homeomorphic sets can be determined. In particular, under sofic condition we gave a sufficient condition for potential functions admitting conformal measures.

对于非双曲、不可逆分段可逆系统，我们在有限域结构条件下构造了（双）非奇异测度和绝对连续不变弱吉布斯测度的自然扩张。此外，我们获得了一个标准，用于决定由可逆扩展引起的过程表现出耗散，以及由保留弱吉布斯测量的间歇性索菲克系统引起的新现象，这在平衡附近没有观察到，即渐近平均熵产生为零的相体积耗散以及渐近平均熵产生为零的吉布斯熵的无底源。对于紧度量空间上的部分定义映射族，我们澄清了何时可以确定自同胚集。特别是，在 sofic 条件下，我们给出了允许保形测量的潜在函数的充分条件。

项目成果

Nonequilibrium steady states far from equilibrium for intermittent sofic systems

间歇性沙发系统的非平衡稳态远离平衡

• 发表时间: 2011
• 作者: K.Saji;M.Umehara;K.Yamada;Seiichi Kamada;近藤 剛史;Masato Wakayama;塩谷 隆;Michiko Yuri
• 通讯作者: Michiko Yuri

Nonequilibrium steady state with internal noise : decidability of the infinite past and reversibility

具有内部噪声的非平衡稳态：无限过去的可判定性和可逆性

• 发表时间: 2012
• 作者: Shioya;Takashi;Michiko Yuri
• 通讯作者: Michiko Yuri

Nonequilibrium steady states with infinite memory arising from intermittent systems

间歇性系统产生的具有无限记忆的非平衡稳态

• 发表时间: 2009
• 作者: K.Nishi;Y.Nishiura;T.Teramoto;Michiko Yuri
• 通讯作者: Michiko Yuri

Nonequilibrium steady states with internal noise : decidability of the infinite past and time reversibility

具有内部噪声的非平衡稳态：无限过去的可判定性和时间可逆性

• 发表时间: 2012
• 作者: Isozaki;Hiroshi;T.Sakajo;納谷信;鎌田 聖一;若山正人;坂上貴之;Michiko Yuri
• 通讯作者: Michiko Yuri

Nonequilibrium steady states with infinite memory arising intermittent systems

具有无限记忆的非平衡稳态产生间歇系统

• 发表时间: 2009
• 作者: Isozaki;Hiroshi;Masato Wakayama;Michiko Yuri
• 通讯作者: Michiko Yuri