The partition function, denoted as \(Z\), is calculated using the formula: \[ Z = \sum_{i} e^{-\beta E_i} \] where \(E_i\) represents the energy levels of the system, and \(\beta\) is the inverse temperature (\(\beta = 1/k_BT\)). For nanoscale systems, these energy levels can be significantly influenced by quantum effects, requiring precise calculations often involving quantum mechanics and computational methods.
