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

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