  For classical discrete systems under constant composition (specifically
substitutional alloys), canonical average acts as a map from a set of many-body
interatomic interactions to a set of configuration in thermodynamic
equilibrium, which is generally nonlinear. In terms of the configurational
geometry (i.e., information about configurational density of states), the
nonlinearity has been measured as special vector on configuration space, which
is extended to Kullback-Leibler (KL) divergence on statistical manifold.
Although they successfully provide new insight into how the geometry of lattice
characterizes the nonlinearity, their application is essentially restricted to
thermodynamic equilibrium. Based on the resource theory (especially,
thermo-majorization), we here extend the applicability of the nonlinearity to
nonequilibrium states obtained through single-shot work on Gibbs state. We
derive the bound for the extended nonlinearity in nonequilibrium state,
characterized by the nonlinearity in equilibrium state, Renyi alpha-divergence
between equilibrium and nonequilibrium distribution, temperature and work.
