Twisted bilayer materials have attracted tremendous attention due to their unique and novel properties. In this work, we derive a thermodynamic model for twisted bilayer graphene (tBLG) within the framework of the classical statistical mechanics. The effect of interlayer twist is introduced by the Moiré-dependent out-of-plane deformation, based on which the twist associated Helmholtz free energy is quantified. Furthermore, the configuration entropy, reflecting the number of micro-states in Moiré unit-cells, is directly derived from both the Helmholtz free energy and the Boltzmann entropy equation with a clear physical interpretation. We show the configuration entropy of a tBLG relative to the AB-stacked bilayer graphene is proportional to the logarithmic function of the ratio of Moiré period ($a_m$) and the lattice constant (a), i.e., $S_{\text{tBLG}}-S_{\text{AB}}=12k_B\ln (a_m/a)$. Finally, based on the observation that the out-of-plane deformation follows the evolution of Moiré patterns, a possible dissipation mechanism in the interlayer sliding of tBLG is discussed. This work provides a theoretical guidance for studying the Moiré effect of incommensurate contact interfaces such as tribology.

扭曲的双层材料由于其独特而新颖的特性而引起了极大的关注。在这项工作中，我们在经典统计力学的框架内推导出了扭曲双层石墨烯 (tBLG) 的热力学模型。层间扭曲的影响是由依赖于莫尔的面外变形引入的，在此基础上量化了扭曲相关的亥姆霍兹自由能。此外，反映莫尔晶胞中微状态数量的配置熵直接来自亥姆霍兹自由能和玻尔兹曼熵方程，具有清晰的物理解释。我们展示了 tBLG 相对于 AB 堆叠双层石墨烯的构型熵与莫尔周期比率的对数函数成正比（${\mathrm{一个}}_{米}$) 和晶格常数 ( a )，即${\mathrm{小号}}_{\text{tBLG}}-{\mathrm{小号}}_{\text{AB}}=12{ķ}_{乙}\ln ({\mathrm{一个}}_{米}/\mathrm{一个})$. 最后，基于面外变形跟随莫尔图案演变的观察，讨论了tBLG层间滑动中可能的耗散机制。该工作为研究摩擦学等不相称接触界面的莫尔效应提供了理论指导。