Fluctuations, response, and the thermodynamics in small nonequilibrium systems

小型非平衡系统中的波动、响应和热力学

基本信息

批准号：
16540337
负责人：
SASA Shin-ichi
金额：
$ 1.73万
依托单位：
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：
2004
资助国家：
日本
起止时间：
2004 至 2006
项目状态：
已结题

项目摘要

I present a brief summary of important results obtained through this research project as follows.1. In small non-equilibrium systems, the states are easily set to be far from equilibrium. It has been known that fluctuation-response relations are violated substantially. Mathematically, it is not surprising because the detailed balance property is lack in such states. The natural question arising in these days when the violation has been just observed in experiments is whether or not there is no rule for the states far from equilibrium. In this situation, we have found that the violation of a fluctuation-response relation is connected with energy dissipation as a simple and beautiful equality.2. The second law of thermodynamics is valid even in small systems if a transition between equilibrium states is concerning. Furthermore, in our previous study, an extension of the thermodynamic law was proposed so that it can be applied to a transition between steady states. Based on this formula, … More we have proposed an idea of effective force under non-equilibrium conditions. Furthermore, we have summarized our present understanding of phenomenological description based on extended thermodynamics.3. A nano-fluid system is the simplest example in which non-trivial rheological behavior is observed. We have presented an elegant theoretical framework for rheological properties. As one example, we have calculated a shear thinning exponent as 2/3. This result will be a starting point for understanding of rheological properties in more complicated systems.4. Glassy systems exhibit a singular non-linear response. Related to this singularity, the fluctuation properties are also rather strange. In order to elucidate a mechanism of the transition, we have proposed a new theory in which the ergodicity breaking transition corresponds to the saddle connection bifurcation. Developing a fluctuation theory around the bifurcation point, we have calculated the critical exponents that characterize critical fluctuations of dynamical events. Less

我简要概述了通过此研究项目获得的重要结果。1。在小型的非平衡系统中，各州很容易设置为远离平衡。众所周知，波动 - 响应关系被大大违反。从数学上讲，这并不奇怪，因为此类状态缺乏详细的平衡属性。在实验中刚刚观察到的违规时，出现的自然问题是，各州是否没有均衡的规则。在这种情况下，我们发现违反波动 - 响应关系的行为与能量消散是一种简单而美丽的平等。2。如果涉及平衡状态之间的过渡，热力学的第二定律即使在小型系统中也有效。此外，在我们先前的研究中，提出了热力学定律的扩展，以便将其应用于稳态之间的过渡。基于此公式，…更多，我们提出了一个在非平衡条件下有效力的想法。此外，我们总结了我们目前对基于扩展热力学现象学描述的理解。3。纳米流体系统是观察到非平凡的流变行为的最简单例子。我们为流变学特性提出了一个优雅的理论框架。作为一个例子，我们计算出剪切变薄的指数为2/3。该结果将是理解更复杂系统中流变特性的起点4。玻璃系统表现出奇异的非线性响应。与这种奇异性有关，波动属性也很奇怪。为了阐明过渡的机制，我们提出了一种新理论，其中超生性断裂过渡与鞍形连接分叉相对应。我们围绕分叉点开发了波动的理论，我们计算了表征动态事件关键波动的关键指数。较少的