Large deviations in the alternating mass harmonic chain

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.