  Twisted bilayer materials have attracted tremendous attention due to their
unique and novel properties. Here, we derive a thermodynamic model for twisted
bilayer graphene (tBLG) within the framework of the classical statistical
mechanics, based on which, the configuration entropy reflecting the number of
micro-status in moire unit-cells, is directly derived from the Helmholtz free
energy with a clear physical interpretation. More importantly, we show the
configuration entropy of tBLG relative to the AB-stacked bilayer graphene is
proportional to the logarithmic function of the ratio of moire period and the
atomic lattice constant, which we found dominates the Helmholtz free energy of
tBLG and can well explain experimental observations in superlubric contacts.
Our work provides a theoretical foundation for studying moire effect of
incommensurate contact interfaces and could facilitate twisting based
applications such as superlubricity.
