Abstract
We study thermodynamics in f(R) gravity theory with the disformal transformation.The transformation which is applied to the matter Lagrangian has the formγ_μν = A(ϕ,X)*g_μν + B(ϕ,X)*∂_μ{ϕ}∂_ν{ϕ}with the assumption of the Minkowski matter metric γ_μν = η_μν, where ϕ is the disformal scalar and X is the corresponding kinetic term of ϕ. The generalized first and second laws of the thermodynamics in the Friedmann-Lemaître-Robertson-Walker (FLRW) universe could be verified. Through the disformal relation, the Hubble parameter contains the disformal field which defines the effectively varying equation of state for matter.