The stick-slip phenomenon, at the basis of friction, is crucial for several applications ranging from nanotechnology and biophysics to mechanics and geology. Deep understanding of friction mechanisms and, in particular, the methodologies for its reduction must be sought in its nanoscopic nature, where atomic interactions and stick-slip processes play a crucial role. At this scale, thermal fluctuations clearly have a major effect on the physics of the problem. Hence, we develop here a theory for rate-independent stick-slip, based on equilibrium statistical mechanics. In particular, we introduce suitably modified Prandtl–Tomlinson and Frenkel–Kontorova models in order to study the system with one particle and the chain with N particles, respectively. The adopted corrugated substrate is composed of a sequence of quadratic wells. Interestingly, the calculation of corresponding partition functions shows a conceptual link with the theory of Jacobi and Riemann theta functions, allowing an efficient determination of the average static frictional force and other relevant quantities. We show some applications including the study of structural lubricity and thermolubricity.

以摩擦为基础的粘滑现象对于从纳米技术和生物物理学到力学和地质学的多种应用至关重要。必须在其纳米级性质中寻求对摩擦机制的深入理解，特别是其减少的方法，其中原子相互作用和粘滑过程起着至关重要的作用。在这个尺度上，热波动显然对问题的物理学产生了重大影响。因此，我们在这里开发了一种基于平衡统计力学的与速率无关的粘滑理论。特别是，我们引入了适当修改的 Prandtl-Tomlinson 和 Frenkel-Kontorova 模型，以研究具有一个粒子的系统和具有N的链粒子，分别。所采用的波纹基板由一系列二次井组成。有趣的是，相应配分函数的计算显示了与 Jacobi 和 Riemann theta 函数理论的概念联系，从而可以有效地确定平均静摩擦力和其他相关量。我们展示了一些应用，包括结构润滑性和热润滑性的研究。