Fluctuations, response, and the thermodynamics in small nonequilibrium systems

我将通过这个研究项目获得的重要成果简要总结如下。在小型非平衡系统中，状态很容易被设定为远离平衡状态。众所周知，波动-响应关系实质上被破坏了。从数学上讲，这并不奇怪，因为在这种状态下缺乏详细的平衡特性。当我们在实验中观察到这种违背时，现在自然会产生这样的问题：对于远离平衡的状态是否没有规则？在这种情况下，我们发现涨落响应关系的破坏与能量耗散是一个简单而美丽的等式。热力学第二定律即使在小系统中也是有效的，如果涉及平衡态之间的过渡。此外，在我们之前的研究中，提出了热力学定律的扩展，使其可以应用于稳态之间的转换。在此基础上，我们提出了非平衡条件下的有效力的概念。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。纳米流体系统是观察到非平凡流变行为的最简单的例子。我们提出了一个优雅的流变性能理论框架。作为一个例子，我们计算出剪切减薄指数为2/3。这一结果将成为理解更复杂系统流变特性的一个起点。玻璃系表现出奇异的非线性响应。与这个奇点有关的涨落性质也相当奇怪。为了阐明这种转变的机理，我们提出了一种新的理论，其中遍历破缺转变对应于鞍连接分岔。建立了围绕分岔点的波动理论，计算了表征动态事件临界波动的临界指数。少

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