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Entropy production and heat transport in harmonic chains under time dependent periodic drivings

Using stochastic thermodynamics, the properties of interacting linear chains subject to periodic drivings are investigated. The systems are described by Fokker-Planck-Kramers equation and exact (explicit) solutions are obtained for periodic drivings as functions of the modulation frequency and strength constants. The limit of long chains is analyzed by means of a protocol in which the intermediate temperatures are self-consistently chosen and the entropy production is decomposed as a sum of two individual contributions, one coming from real baths (placed at extremities of lattice) and other from self-consistent baths. The thermal reservoirs lead to a heat flux according to Fourier's law. Explicit expressions for short chains are derived, whose entropy production is written down as a bilinear function of thermodynamic forces and the associated fluxes, from which Onsager coefficients have been evaluated. A comparison between distinct periodic drivings is also performed.