We find that a moderate intrinsic twisting rate (ITR) can induce a bistable state for a force-free two-dimensional intrinsically curved filament. There are two different configurations of equal energy in a bistable state so that the filament is clearly different from its three-dimensional counterpart. The smaller the ITR or the larger the intrinsic curvature (IC), the clearer the distinction between two isoenergetic configurations and the longer the filament. In bistable states, the relationship between length and ITR is approximately a hyperbola and relationship between IC and critical ITR is approximately linear. Thermal fluctuation can result in a shift between two isoenergetic configurations, but large bending and twisting rigidities can prevent the shift and maintain the filament in one of these two configurations. Moreover, a filament can have a metastable state and at a finite temperature such a filament has the similar property as that of a filament with bistable state.

中文翻译：

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二维固有弯曲长丝的自发扭曲速率引起的双稳态

我们发现适度的固有扭曲率（ITR）可以为无力的二维固有弯曲长丝诱发双稳态。在双稳态下，存在两种不同的能量相等的配置，因此，灯丝明显不同于其三维对应物。ITR越小或固有曲率（IC）越大，则两个等能量构型之间的区别就越清晰，灯丝越长。在双稳态下，长度与ITR之间的关系近似为双曲线，IC与临界ITR之间的关系近似为线性。热波动会导致两种等能量构型之间的转换，但是较大的弯曲和扭曲刚度可以防止这种位移，并将灯丝保持在这两种构型中的一种。此外，