Equilibrium thermodynamics in modified gravitational theories

Abstract

We show that it is possible to obtain a picture of equilibrium thermodynamics on the apparent horizon in the expanding cosmological background for a wide class of modified gravity theories with the Lagrangian density f (R, φ, X), where R is the Ricci scalar and X is the kinetic energy of a scalar field φ. This comes from a suitable definition of an energy momentum tensor of the "dark" component that respects to a local energy conservation in the Jordan frame. In this framework the horizon entropy S corresponding to equilibrium thermodynamics is equal to a quarter of the horizon area A in units of gravitational constant G, as in Einstein gravity. For a flat cosmological background with a decreasing Hubble parameter, S globally increases with time, as it happens for viable f (R) inflation and dark energy models. We also show that the equilibrium description in terms of the horizon entropy S is convenient because it takes into account the contribution of both the horizon entropyŜ in non-equilibrium thermodynamics and an entropy production term.

Thermodynamics inf(R,T) theory of gravity

“…It involves derivative of f (R, T ) with respect to the trace of the energy-momentum tensor. Notice that the first law of thermodynamics T h dS h = −dE + W dV holds at the apparent horizon of FRW universe in equilibrium description of modified theories of gravity [26,27,29]. However, in f (R, T ) gravity, this law does not hold due to the presence of an additional term d  S h .…”

“…If we redefine the dark components so that the extra entropy production term is vanished, then such formulation is referred as an equilibrium description. It has been seen so far that the equilibrium description does exist in modified theories of gravity [26,27,29] and extra entropy production term can be removed.…”

Generalized second law of thermodynamic in modified teleparallel theory

“…It is shown that an additional entropy term is produced, to be compared to other modified theories. Later Bamba et al [41,42,60,61] developed the first law of thermodynamics in Palatini f (R), f (T ), f (R, φ, X ) (where X = −1/2g μν ∇ μ φ∇ ν φ is the kinetic term of a scalar field φ) and f (R, φ, X, G) (where G = R 2 − 4R μν R μν + R μνρσ R μνρσ is the Gauss-Bonnet invariant) theories and formulated an additional entropy production term. A similar approach is applied to discuss the thermodynamic laws in f (R, T ), f (R, L m ) and f (R, T, R μν T μν ) theories, and one can see that the presence of non-equilibrium entropy production terms is necessary in such theories [46,47,62].…”

“…A similar approach is applied to discuss the thermodynamic laws in f (R, T ), f (R, L m ) and f (R, T, R μν T μν ) theories, and one can see that the presence of non-equilibrium entropy production terms is necessary in such theories [46,47,62]. Bamba et al [41,42,60,61] have shown that one can manipulate the FRW equations in order to redefine the entropy relation, which results in an equilibrium description of thermodynamics so that the first law of thermodynamics takes the form T dS = dE − W dV . Moreover, in all these theories it has been the case that the usual form of the first law of thermodynamics, i.e., T dS eff = dE − W dV , can be obtained by defining the general entropy relation as a sum of an horizon entropy and an entropy production term.…”

Thermodynamics of gravitationally induced particle creation scenario in DGP braneworld

“…Many people have explored the validity of GSLT of different systems including interaction of two fluid components like DE and dark matter [13][14][15][16], as well as interaction of three components of fluid [17][18][19] in the FRW universe by using simple horizon entropy of the universe. The thermodynamical analysis widely performed in modified theories of gravity [20][21][22][23][24][25].…”