Thermodynamics of f(R) Gravity with Disformal Transformation

We study thermodynamics in [Formula: see text] gravity with the disformal transformation. The transformation applied to the matter Lagrangian has the form of [Formula: see text] with the assumption of the Minkowski matter metric [Formula: see text] , where [Formula: see text] is the disformal scalar and X is the corresponding kinetic term of [Formula: see text]. We verify the generalized first and second laws of thermodynamics in this disformal type of [Formula: see text] gravity in the Friedmann-Lemaître-Robertson-Walker (FLRW) universe. In addition, we show that the Hubble parameter contains the disformally induced terms, which define the effectively varying equations of state for matter.