Observational constraints on Tsallis modified gravity

The thermodynamics-gravity conjecture reveals that one can derive the gravitational field equations by using the first law of thermodynamics and vice versa. Considering the entropy associated with the horizon in the form of non-extensive Tsallis entropy, S ∼ Aβ here we first derive the corresponding gravitational field equations by applying the Clausius relation δQ = TδS to the horizon. We then construct the Friedmann equations of Friedmann-Lemaître-Robertson-Walker (FLRW) universe based on Tsallis modified gravity (TMG). Moreover, in order to constrain the cosmological parameters of TMG model, we use observational data, including Planck cosmic microwave background (CMB), weak lensing, supernovae, baryon acoustic oscillations (BAO), and redshift-space distortions (RSD) data. Numerical results indicate that TMG model with a quintessential dark energy is more compatible with the low redshift measurements of large scale structures by predicting a lower value for the structure growth parameter σ8 with respect to ΛCDM model. This implies that TMG model would slightly alleviate the σ8 tension.

Stochastic thermodynamics of a finite quantum system coupled to a heat bath

We consider a situation where an N-level system (NLS) is coupled to a heat bath without being necessarily thermalized. For this situation, we derive general Jarzynski-type equations and conclude that heat and entropy is flowing from the hot bath to the cold NLS and, vice versa, from the hot NLS to the cold bath. The Clausius relation between increase of entropy and transfer of heat divided by a suitable temperature assumes the form of two inequalities which have already been considered in the literature. Our approach is illustrated by an analytical example.

Thermodynamic Analysis of Gravitational Field Equations in Lyra Manifold

Considering the Einstein field equations in Lyra manifold and applying the unified first law of thermodynamics as well as the Clausius relation to the apparent horizon of FRW universe, we find the entropy of apparent horizon in Lyra manifold. In addition, the validity of second law of thermodynamics and its generalized form are also studied. Finally, we use the first law of thermodynamics in order to find the horizon entropy of static spherically symmetric spacetimes. Some results of considering (anti)de-Sitter and Schwarzschild metrics have also been addressed.

Thermodynamic properties of modified gravity theories

We review thermodynamic properties of modified gravity theories, such as [Formula: see text] gravity and [Formula: see text] gravity, where [Formula: see text] is the scalar curvature and [Formula: see text] is the torsion scalar in teleparallelism. In particular, we explore the equivalence between the equations of motion for modified gravity theories and the Clausius relation in thermodynamics. In addition, thermodynamics of the cosmological apparent horizon is investigated in [Formula: see text] gravity. We show both equilibrium and nonequilibrium descriptions of thermodynamics. It is demonstrated that the second law of thermodynamics in the universe can be met, when the temperature of the outside of the apparent horizon is equivalent to that of the inside of it.

Modified Hawking temperature and entropic force: A prescription in FRW model

The idea of Verlinde that gravity is an entropic force caused by information changes associated with the positions of material bodies, is used in the present work for the Friedmann–Robertson–Walker (FRW) model of the Universe. Using modified Hawking temperature, the Friedmann equations are derived on any horizon. For the validity of the first law of thermodynamics (i.e. Clausius relation) it is found that there is modification of Bekenstein entropy on the horizon. However, using equipartition law of energy, Bekenstein entropy is recovered.