关于单向线性时间序列的熵产生
On the entropy production of time series with unidirectional linearity
摘要：
有非高斯时间序列，承认因果线性自回归移动平均（ARMA）模型时，回归过去的未来，但不是当回归过去的未来。原因是，在后一种情况下，回归残差只是不相关，但在统计上与未来无关。在以前的工作中，我们已经通过实验验证了许多经验时间序列确实表现出这样的时间反演不对称性。对于各种物理系统，时间反演不对称性与非平衡态的热力学熵产生有关。在这里，我们表明，这样的链接也存在上述单向线性。我们研究了与无限环境线性耦合的物理玩具系统的动力学演化，并表明动力学的线性性遗传给向前时间条件概率，但不遗传给向后时间条件概率。过去和未来之间这种不对称的原因是，环境永久地提供了在与系统相互作用之前处于产物状态的粒子，但之后显示出统计依赖性。从粗粒度的角度来看，相互作用因此产生熵。我们定量地将后向条件的非线性强度与熵产生的最小量联系起来。
英文摘要：
There are non-Gaussian time series that admit a causal linear autoregressive moving average (ARMA) model when regressing the future on the past, but not when regressing the past on the future. The reason is that, in the latter case, the regression residuals are only uncorrelated but not statistically independent of the future. In previous work, we have experimentally verified that many empirical time series indeed show such a time inversion asymmetry. For various physical systems, it is known that time-inversion asymmetries are linked to the thermodynamic entropy production in non-equilibrium states. Here we show that such a link also exists for the above unidirectional linearity. We study the dynamical evolution of a physical toy system with linear coupling to an infinite environment and show that the linearity of the dynamics is inherited to the forward-time conditional probabilities, but not to the backward-time conditionals. The reason for this asymmetry between past and future is that the environment permanently provides particles that are in a product state before they interact with the system, but show statistical dependencies afterwards. From a coarse-grained perspective, the interaction thus generates entropy. We quantitatively relate the strength of the non-linearity of the backward conditionals to the minimal amount of entropy generation.
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