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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

现将本研究项目取得的重要成果简单总结如下： 1．在小型非平衡系统中，状态很容易被设置为远离平衡。众所周知，波动响应关系被严重违反。从数学上讲，这并不奇怪，因为这些状态缺乏详细的平衡属性。如今，当实验中刚刚观察到违规行为时，自然会出现一个问题：远离平衡的状态是否没有规则。在这种情况下，我们发现波动响应关系的违反与能量耗散是一个简单而美丽的等式。2．如果涉及平衡态之间的转变，即使在小系统中，热力学第二定律也是有效的。此外，在我们之前的研究中，提出了热力学定律的扩展，以便它可以应用于稳态之间的转变。基于这个公式，我们提出了非平衡条件下有效力的想法。此外，我们还总结了目前对基于扩展热力学的现象学描述的理解。 3．纳米流体系统是观察到重要流变行为的最简单的例子。我们提出了一个优雅的流变特性理论框架。作为一个例子，我们计算出剪切稀化指数为 2/3。这一结果将成为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。与这个奇点相关的，波动特性也相当奇怪。为了阐明转变的机制，我们提出了一种新的理论，其中遍历性破坏转变对应于鞍连接分岔。我们围绕分岔点发展了波动理论，计算了表征动态事件临界波动的临界指数。较少的