Non-Gibbsianness and phase transition in complex systems

复杂系统中的非吉布斯性和相变

基本信息

批准号：
17540132
负责人：
YURI Michiko
金额：
$ 1.98万
依托单位：
HOKKAIDO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2005
资助国家：
日本
起止时间：
2005 至 2006
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-17540132/
关键词：
Nonhyperbolicity Intermittency Phase transition Variational Principle Weak Gibbs measure Equilibrium state Irreversibility Conformal measure variational principle Weak Gribbs measure equilibrium state irreversibility Multifractal f

项目摘要

The main purpose of this project is to clarify typical reasons for phase transition and non-Gibbsianness of equilibrium measures in the context of complex systems. For this purpose, we first established large deviation properties for countable to one Markov systems associated with weak Gibbs measures for non-H"older potentials. We clarified a class of functions in which we can describe free energy function associated to weak Gibbs measures in terms of topological pressure. We established the level-2 upper large deviaition inequality and clarified sufficient conditions for the upper bounds being strictly negative. Furthermore, we studied multifractal large deviation laws for non-hyperbolic systems exhibiting 'intermittency'. In particular, the law is established for countable to one piecewise conformal Markov systems, which are derived systems constructed over hyperbolic regions. We formulated different stages of 'indifferency ' associated with potentials of weak bounded variation, and … More relate new characterization of phase transitions to indifferent periodic points at various stages. We also succeeded to associate non-differentiability of the Hausdorff dimension of level sets with phase transitions for intermittent systems. These results were established in [1]. The second purpose of this project is to describe dissipative phenomena via invertible extensions of non-invertible non-hyperbolic systems. We restrict our attention to countable to one sofic systems and established an explicit topological description of spaces of their invertible extensions under the existence of their dual systems. We also give a topological notion of ' reversibility ' of the invertible extensions. Then we discuss when Rohlin's invertible extension of ergodic absolutely continuous invariant measures are absolutely continuous with respect to a natural physical measure on the spaces that we constructed. We could observe that different nature of observability between original non- invertible systems and their dual systems causes dissipative phenomena in their invertible extensions. Those results are obtained in [4]. The third purpose of this project is to introduce thermodynamic methods to study conformal measures for families of partially defined maps on compact metric spaces which is called a ' dynamical family '. In particular, we could develop some aspects of thermodynamic formalism for countable to one sofic systems. Those results will appear in a joint paper with M.Denker (Gottingen Univ.). Less

该项目的主要目的是阐明复杂系统中相变和平衡测度的非吉布斯性的典型原因。为此，我们首先建立了与弱吉布斯测度相关的可数马尔可夫系统的大偏差属性。我们阐明了一类函数，可以在拓扑压力方面描述与弱吉布斯测度相关的自由能函数。我们建立了二级上大偏差不等式，并阐明了此外，我们研究了表现出“间歇性”的非双曲系统的多重分形大偏差定律，特别是为可数分段共形马尔可夫系统建立了该定律，该系统是在双曲区域上构造的派生系统。制定了与弱有界变化势相关的“无差异”的不同阶段，并将相变的新特征与不同阶段的无差异周期点联系起来。该项目的第二个目的是通过不可逆非双曲系统的可逆扩展来描述耗散现象。并在其对偶系统的存在下建立了其可逆扩张的空间的明确拓扑描述，我们还给出了可逆扩张的“可逆性”的拓扑概念。我们讨论了罗林的遍历绝对连续不变测度的可逆扩展相对于我们构建的空间上的自然物理测度是绝对连续的。我们可以观察到原始不可逆系统及其对偶系统之间可观测性的不同性质会导致耗散现象。这些结果在[4]中获得，该项目的第三个目的是引入热力学方法来研究紧度量空间上的部分定义映射族的共形测度，称为“特别是，我们可以开发可数于一个 sofic 系统的热力学形式主义的某些方面，这些结果将出现在与 M.Denker（哥廷根大学）的联合论文中。

项目成果

期刊论文数量（10）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Phase transition, Non-Gibbsianness and Subexponential Instability

相变、非吉布斯性和次指数不稳定性

DOI：
发表时间：
期刊：
Ergodic Theory and Dynamical Systems (発表予定)
影响因子：
0
作者：
Michiko Yuri;Michiko Yuri;Michiko Yuri;Michiko Yuri
通讯作者：
Michiko Yuri

Large Deviations for Countable to One Markov Systems

DOI：
10.1007/s00220-005-1363-0
发表时间：
2004-11
期刊：
Communications in Mathematical Physics
影响因子：
2.4
作者：
M. Yuri
通讯作者：
M. Yuri

Non-Gibbsianness of SRB measures for the natural extension of Intermittent systems

间歇系统自然扩展的 SRB 测量的非吉布斯性

DOI：
发表时间：
期刊：
Ergodic Theory and Dynamical Systems (発表予定)
影响因子：
0
作者：
Michiko Yuri;Michiko Yuri;Michiko Yuri;Michiko Yuri;Michiko Yuri
通讯作者：
Michiko Yuri

Nonequilibrium steady states arising from number theory

数论产生的非平衡稳态

DOI：
发表时间：
2006
期刊：
Preprint
影响因子：
0
作者：
M. Sakaguchi;Y. Ohtsubo;Yoshio Ohtsubo;Y. Ohtsubo;大坪義夫;大坪義夫;Y. Ohtsubo;Y. Ohtsubo;Y. Ohtsubo;Michiko Yuri
通讯作者：
Michiko Yuri