时间的随机性和非局部性
Stochasticity and Non-locality of Time
摘要：
我们提出了简单的经典动力学模型来说明将非定域性随机性引入时间变量的想法。对于时间上的随机性，这些模型在时间变量中包含噪声，但在“空间”变量中不包含噪声，这与随机动力学的正常描述相反。同样，对于非局部性，我们讨论延迟和预测动力学，其中涉及两个点上的时间轴上分离。随着波动和时间上的非定域性的某些组合，我们观察到“共振”效应。这是一种类似于随机共振的效应，已经在随机动力学的正常背景下进行了讨论，但具有不同的机制。我们将讨论如何开发这些模型，以适应更广泛的背景下，波动和非局部性存在于空间和时间的广义动力系统。
英文摘要：
We present simple classical dynamical models to illustrate the idea of introducing a stochasticity with non-locality into the time variable. For stochasticity in time, these models include noise in the time variable but not in the "space" variable, which is opposite to the normal description of stochastic dynamics. Similarly with respect to non-locality, we discuss delayed and predictive dynamics which involve two points separated on the time axis. With certain combinations of fluctuations and non-locality in time, we observe a ``resonance'' effect. This is an effect similar to stochastic resonance, which has been discussed within the normal context of stochastic dynamics, but with different mechanisms. We discuss how these models may be developed to fit a broader context of generalized dynamical systems where fluctuations and non-locality are present in both space and time.
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