  We extend the work of Kannan et al. and derive the cumulant generating
function for the alternating mass harmonic chain consisting of N particles and
driven by heat reservoirs. The main result is a closed expression for the
cumulant generating function in the thermodynamic large N limit. This
expression is independent of N but depends on whether the chain consists of an
even or an odd number of particles, in accordance with the results obtained by
Kannan el al. for the heat current. This result is in accordance with the
absence of local thermodynamic equilibrium in a linear system.
