Diezemann Gregor
Institut für Physikalische Chemie, Universität Mainz, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Jul;72(1 Pt 1):011104. doi: 10.1103/PhysRevE.72.011104. Epub 2005 Jul 12.
The fluctuation-dissipation relation is calculated for stochastic models obeying a master equation with continuous time. In the general case of a nonstationary process, there appears to be no simple relation between the response and the correlation. Also, if one considers stationary processes, the linear response cannot be expressed via time-derivatives of the correlation function alone. In this case, an additional function, which has rarely been discussed previously, is required. This so-called asymmetry depends on the two times also relevant for the response and the correlation and it vanishes under equilibrium conditions. The asymmetry can be expressed in terms of the propagators and the transition rates of the master equation but it is not related to any physical observable in an obvious way. It is found that the behavior of the asymmetry strongly depends on the nature of the dynamical variable considered in the calculation of the correlation and the response. If one is concerned with a variable which randomizes with any transition among the states of the system, the asymmetry vanishes in most cases. This is in contrast to the situation for other classes of variables. In particular, for trap models of glassy relaxation, the fluctuation-dissipation ratio strongly depends on the observable and the asymmetry plays a dominant role in the determination of this ratio also if only neutral variables are considered. Some implications of a nonvanishing asymmetry with regard to the definition of an effective temperature are discussed.
针对服从具有连续时间的主方程的随机模型计算涨落耗散关系。在非平稳过程的一般情况下，响应与关联之间似乎不存在简单关系。此外，如果考虑平稳过程，线性响应不能仅通过关联函数的时间导数来表示。在这种情况下，需要一个此前很少被讨论的附加函数。这个所谓的不对称性也取决于与响应和关联相关的两个时间，并且在平衡条件下它会消失。不对称性可以用主方程的传播子和跃迁速率来表示，但它与任何物理可观测量没有明显的关联。结果发现，不对称性的行为强烈依赖于在计算关联和响应时所考虑的动力学变量的性质。如果关注的是一个在系统状态之间的任何跃迁中都会随机化的变量，那么在大多数情况下不对称性会消失。这与其他类型变量的情况形成对比。特别是对于玻璃态弛豫的陷阱模型，涨落耗散比强烈依赖于可观测量，并且即使仅考虑中性变量，不对称性在确定该比值时也起着主导作用。讨论了非零不对称性对于有效温度定义的一些影响。
