Verlinde's Proposal Research Articles

Implications, Consequences and Interpretations of Generalized Entropy in the Cosmological Setups

Recently, it was argued (Eur. Phys. J. C {\bf73}, 2487 (2013)) that the total entropy of a gravitational system should be related to the volume of system instead of the system surface. Here, we show that this new proposal cannot satisfy the unified first law of thermodynamics and the Friedmans equation simultaneously, unless the effects of dark energy candidate on the horizon entropy are considered. In fact, our study shows that some types of dark energy candidate may admit this proposal. Some general properties of required dark energy are also addressed. Moreover, our investigation shows that this new proposal for entropy, while combined with the second law of thermodynamics (as the backbone of Verlinde's proposal), helps us in providing a thermodynamic interpretation for the difference between the surface and bulk degrees of freedom which, according to Padmanabhan's proposal, leads to the emergence of spacetime and thus the universe expansion. In fact, our investigation shows that the entropy changes of system may be equal to the difference between the surface and bulk degrees of freedom falling from surface into the system volume. Briefly, our results signal us that this new proposal for entropy may be in agreement with the thermodynamics laws, the Friedmann equation, Padmanabhan's holographic proposal for the emergence of spacetime and therefore the universe expansion. In fact, this new definition of entropy may be used to make a bridge between Verlinde's and Padmanabhan's proposals.

Einstein equations and MOND theory from Debye entropic gravity

Verlinde's proposal on the entropic origin of gravity is basedstrongly on the assumption that the equipartition law of energyholds on the holographic screen induced by the mass distributionof the system. However, from the theory of statistical mechanicswe know that the equipartition law of energy does not hold in thelimit of very low temperature. Inspired by the Debye model for theequipartition law of energy in statistical thermodynamics andadopting the viewpoint that gravitational systems can be regardedas a thermodynamical system, we modify Einstein field equations.We also perform the study for Poisson equation and modifiedNewtonian dynamics (MOND). Interestingly enough, we find that theorigin of the MOND theory can be understood from Debye entropicgravity perspective. Thus our study may fill in the gap existingin the literature understanding the theoretical origin of MONDtheory. In the limit of high temperature our results reduce totheir respective standard gravitational equations.

An entropic understanding of Coulomb force

Exploiting Verlinde's proposal on the entropic understanding of Newton's law, we show that Coulomb force could also be understood as an entropically emergent force (rather than as a fundamental force). We apply Kaluza-Klein idea to Verlinde's formalism to obtain Coulomb interaction in the lower dimensions. The kinematics concerning the Kaluza-Klein momenta separates the interaction due to the momentum flow from the gravitational interaction. The momentum-charge conversion relation results in the precise form of Coulomb interaction.

Hidden Symmetries for Thermodynamics and Emergence of Relativity

Erik Verlinde recently proposed an idea about the thermodynamic origin of gravity. Though this is a beautiful idea, which may resolve many long standing problems in the theories of gravity, it also raises many other problems. In this article I will comment on some of the problems of Verlinde's proposal with special emphasis on the thermodynamical origin of the principle of relativity. It is found that there is a large group of hidden symmetries of thermodynamics, which contains the Poincare group of the spacetime for which space is emergent. This explains the thermodynamic origin of the principle of relativity.