We focus on the asymmetry of the interaction in the optimal velocity (OV) model, which is a model of self-driven particles, and analytically investigate the effects of the asymmetry on the fluctuation-response relation, which is one of the remarkable relationships in statistical physics. By linearizing a modified OV model, i.e., the backward-looking optimal velocity model, which can easily control the magnitude of asymmetry in the interaction, we derive $n$ coupled linear oscillators with asymmetric interactions. We analytically solve the equations of the $n$ coupled linear oscillators and calculate the response and correlation functions. We find that the fluctuation response relation does not hold in the $n$ coupled linear oscillators with asymmetric interactions. Moreover, as the magnitude of the asymmetry increases, the difference between the response and correlation functions increases .

中文翻译：

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具有非对称相互作用的n个耦合线性振荡器系统的相关性和响应。

我们关注最优速度（OV）模型中的相互作用的不对称性，该模型是自驱动粒子的模型，并分析研究了不对称性对波动响应关系的影响，该关系是显着关系之一。统计物理。通过线性化修改的OV模型（即后向最佳速度模型），可以轻松地控制相互作用中的不对称幅度，我们得出$ñ$不对称相互作用的线性耦合振荡器。我们以解析方式求解$ñ$耦合线性振荡器并计算响应和相关函数。我们发现波动响应关系在$ñ$不对称相互作用的线性耦合振荡器。此外，随着不对称幅度的增加，响应函数和相关函数之间的差异也会增加。