标题： 非平衡双温度$(T_x, T_y)$诺斯-霍弗细胞模型中的混沌 显示英文标题

标题： Chaos in Nonequilibrium Two-Temperature $(T_x, T_y)$ Nosé-Hoover Cell Models

摘要： 我们重新研究了一个嵌入在二维周期性2x2单元中的双温度Nosé-Hoover游动粒子，该单元在$(x,y) = (\pm 1, \pm 1)$处有四个光滑的排斥角落，以探索各向异性恒温器引起的混沌。 该模型在x和y方向上使用独立的恒温器，从而实现对平衡的受控偏离。 通过积分完整的六维运动方程并计算完整的李雅普诺夫谱，我们确认了混沌，并以高数值精度量化了相空间收缩。 总收缩率被解释为熵产生，随着恒温器各向异性非线性增长，并遵循超二次幂律$\Lambda\propto -\delta^{2.44}$，偏离了线性响应理论。 近似的Kaplan-Yorke维数揭示了一个分形吸引子，随着$|T_x - T_y|$的增加而集中。 动量统计显示在强驱动下表现出显著的非高斯行为。 尽管该模型具有耗散性，但仍保持严格的时间可逆性，为微观可逆性与宏观熵产生共存提供了一个教学丰富的例子。 显示英文摘要

摘要： We revisit a two-temperature Nos\'e-Hoover wanderer particle embedded in a two-dimensional periodic 2x2 cell with four smooth repulsive corners at $(x,y) = (\pm 1, \pm 1)$ to explore chaos with anisotropic thermostatting. The model employs separate thermostats in the x and y directions, enabling controlled deviations from equilibrium. By integrating the full six-dimensional equations of motion and computing the complete Lyapunov spectrum, we confirm chaos and quantify phase-space contraction with high numerical precision. The total contraction rate, interpreted as entropy production, grows nonlinearly with the thermostat anisotropy and follows a superquadratic power law, $\Lambda\propto -\delta^{2.44}$, deviating from linear-response theory. The approximate Kaplan-Yorke dimension reveals a fractal attractor that concentrates as $|T_x - T_y|$ increases. Momentum statistics show significant non-Gaussian behavior under strong driving. Despite its dissipative nature, the model remains strictly time-reversible, offering a pedagogically rich example of microscopic reversibility coexisting with macroscopic entropy production.