In the realm of nanotechnology, statistical mechanics helps in understanding the thermodynamic properties of nanosystems. The Boltzmann distribution is one such equation: \[ f(E) = \frac{1}{e^{(E - \mu)/kT} + 1} \] where \( E \) is the energy, \( \mu \) is the chemical potential, \( k \) is the Boltzmann constant, and \( T \) is the temperature. This distribution is particularly useful in analyzing the behavior of electrons in nanomaterials.
