  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.
