  A theory for the thermodynamic properties of steps on faceted crystalline
surfaces is presented. The formalism leads to the definition of step excess
quantities, including an excess step stress that is the step analogy of surface
stress. The approach is used to develop a relationship between the temperature
dependence of the step free energy ($\gamma^\mathrm{st}$) and step excess
quantities for energy and stress that can be readily calculated by atomistic
simulations. We demonstrate the application of this formalism in
thermodynamic-integration (TI) calculations of the step free energy, based on
molecular-dynamics simulations, considering $\left< 110 \right>$ steps on the
$\{111\}$ surface of a classical potential model for elemental Cu. In this
application we employ the Frenkel-Ladd approach to compute the reference value
of $\gamma^\mathrm{st}$ for the TI calculations. Calculated results for excess
energy and stress show relatively weak temperature dependencies up to a
homologous temperature of approximately 0.6, above which these quantities
increase strongly and the step stress becomes more isotropic. From the
calculated excess quantities we compute $\gamma^\mathrm{st}$ over the
temperature range from zero up to the melting point ($T_\mathrm{m}$). We find
that $\gamma^\mathrm{st}$ remains finite up to $T_\mathrm{m}$, indicating the
absence of a roughening temperature for this $\{111\}$ surface facet, but
decreases by roughly fifty percent from the zero-temperature value. The
strongest temperature dependence occurs above homologous temperatures of
approximately 0.6, where the step becomes configurationally disordered due to
the formation of point defects and appreciable capillary fluctuations.
