利用Bochkov-Kuzovlev非线性涨落耗散定理导出了Narayanaswamy的物理老化唯象理论，其中高度非线性的物理老化现象用线性物质-时间卷积积分来描述。Narayanaswamy老化描述的一个特性是物质-时间平移不变性，这是在这里作为推导的基本假设。它表明，只有一种可能的定义的材料时间服从这种不变性，即平方的距离从配置的系统远远回的时间。论文最后提出了测试物质时间平移不变性后果的计算机模拟建议。其中之一是“唯一三角形性质”，根据该性质，系统路径上的任何三个点形成三角形，使得两个边长确定第三个;这相当于老化自旋玻璃的时间自相关函数的众所周知的三角关系[L. F. Cugliandolo和J. Kurchan，J.Phys.A：Math.Gen.27，5749（1994）]。独特的三角形属性意味着一个简单的几何解释的平衡时间自相关函数，这延伸到老化以前提出的框架，这样的功能在平衡[J. C. Dyre，cond-mat/9712222]。
英文摘要：
The Bochkov-Kuzovlev nonlinear fluctuation-dissipation theorem is used to derive Narayanaswamy's phenomenological theory of physical aging, in which this highly nonlinear phenomenon is described by a linear material-time convolution integral. A characteristic property of the Narayanaswamy aging description is material-time translational invariance, which is here taken as the basic assumption of the derivation. It is shown that only one possible definition of the material time obeys this invariance, namely the square of the distance travelled from a configuration of the system far back in time. The paper concludes with suggestions for computer simulations that test for consequences of material-time translational invariance. One of these is the "unique-triangles property" according to which any three points on the system's path form a triangle such that two side lengths determine the third; this is equivalent to the well-known triangular relation for time-autocorrelation functions of aging spin glasses [L. F. Cugliandolo and J. Kurchan, J. Phys. A: Math. Gen. 27, 5749 (1994)]. The unique-triangles property implies a simple geometric interpretation of out-of-equilibrium time-autocorrelation functions, which extends to aging a previously proposed framework for such functions in equilibrium [J. C. Dyre, cond-mat/9712222].
Logarithmic Aging Diffusion from a Multiplicative Event Clock: Rare Event Statistics, Ultraslow Transport, and Ensemble-Time Inequivalence
Center for Advanced Quantum Studies, School of Physics and Astronomy, Beijing Normal University（北京师范大学物理与天文学部先进量子研究中心）；Key Laboratory of Multiscale Spin Physics, Ministry of Education（教育部多尺度自旋物理重点实验室）；School of Science, Tianjin University of Technology and Education（天津职业技术师范大学理学院）；Interdisciplinary Center for Theoretical Physics and Information Sciences, Fudan University（复旦大学理论物理与信息科学交叉中心）；International Center for Quantum Materials, School of Physics, Peking University（北京大学物理学院量子材料国际中心）；Hefei National Laboratory（合肥国家实验室）
