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This article reports a study on variable-generalised Chaplygin gas (VGCG) interacting with pressureless dark matter (DM) with interaction term  Q  chosen in the form  Q =3 Hδρ  Λ , where  ρ  Λ  denotes the density of the VGCG. Detailed cosmology of the interacting VGCG has been studied and a quintom behaviour of the equation of state (EoS) parameter has been observed. A statefinder analysis has shown attainment of ΛCDM fixed point by the interacting VGCG. Subsequently, a reconstruction scheme for  f ( T ) gravity has been presented based on the interacting VGCG with power-law form of scale factor. The EoS parameter corresponding to the reconstructed  f ( T ) has shown quintom behaviour. Finally, we have studied the generalised second law (GSL) of thermodynamics in reconstructed  f ( T ) cosmology considering the universe as a closed bounded system with future event horizon as the cosmological boundary. We have associated two different entropies with the cosmological horizons with a logarithmic correction term and a power-law correction term. We have studied the validity of the GSL for both of these corrections.

Reconstruction of f ( T ) Gravity with Interacting Variable-Generalised Chaplygin Gas and the Thermodynamics with Corrected Entropies