Heat flow in a linear harmonic chain: An information-theoretic approach to the nonequilibrium stationary state

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Abstract
The methods of information theory are applied to the problem of describing the transport of internal energy along a linear harmonic chain in a stationary state. It is shown that the average energy flux along the chain is a constant of the motion which can be directly incorporated into the canonical formalism. The classical probability distribution in phase space is constructed and used to evaluate the partition function in the thermodynamic limit. Thermodynamic relationships between the undetermined multipliers and the given information are explicitly determined, as are the singlet- and pair-distribution functions in configuration and momentum space and the correlation of the momentum of a specific particle in time. For a given system energy there is an upper bound for the mean rate of energy transport. As this limit is closely approached, both the range and duration of correlations become large. This behavior, as well as some other features of the model, is reminiscent of that near a critical point.