Jorge Ananias Neto

Considerations on gravity as an entropic force and entangled states

Abstract Verlindeʼs ideas considered gravity as an emergent force originated from entropic concepts. This hypothesis generated a huge number of papers through the last recent years concerning classical and quantum approaches about the issue. In a recent paper Kobakhidze, using ultra-cold neutrons experiment, claimed that Verlindeʼs entropic gravity is not correct. In this Letter, by considering the Tsallis nonadditivity entropy concerning the holographic screen, where we assumed that the bits are entangled states, we showed that it is possible to confirm Verlindeʼs formalism.

New bounds for Tsallis parameter in a noncommutative phase-space entropic gravity and nonextensive Friedmann equations

In this paper, we have analyzed the nonextensive Tsallis statistical mechanics in the light of Verlinde’s formalism. We have obtained, with the aid of a noncommutative phase–space entropic gravity, a new bound for Tsallis nonextensive (NE) parameter (TNP) that is clearly different from the ones present in the current literature. We derived the Friedmann equations in a NE scenario. We also obtained here a relation between the gravitational constant and the TNP.

Fundamental Constants, Entropic Gravity and Nonextensive Equipartition Theorem

By using Verlinde’s formalism, we propose that the positive numerical factor, in which Klinkhamer states that it is necessary to define the fundamental length, can be associated to the parameter q of Tsallis’ nonextensive statistical mechanics.

The Batalin-Tyutin formalism on the collective coordinates quantization of the SU(2) Skyrme model

We apply the Batalin–Tyutin constraint formalism of converting a second class system into a first class system for the rotational quantization of the SU(2) Skyrme model. We obtain the first class constraints, the Hamiltonian in the extended phase space, the Lagrangian that leads the new theory and the spectrum of the extended theory. We observe that with the use of the BT formalism on the collective coordinates quantization of the SU(2) Skyrme model there is an additional term in the usual quantum Hamiltonian.

Nonhomogeneous Cooling, Entropic Gravity and MOND Theory

In this paper, by using the holographic principle, a modified equipartition theorem where we assume that below a critical temperature the energy is not equally divided on all bits, and the Unruh temperature, we derive MOND theory and a modified Friedmann equation compatible with MOND theory. Furthermore, we rederive a modified Newton’s law of gravitation by employing an adequate redefinition of the numbers of bits.

The non-abelian BFFT formalism for the collective coordinates quantization of the SU (2) Skyrme model

The collective coordinates expansion of the Skyrme soliton particle model gives rise to the second class constraints. We use the non-abelian BFFT formalism to convert this system into the one with only first class constraints. Choosing two different structure functions of the non-abelian algebra, we obtain simplified algebraic expressions for the first class non-abelian Hamiltonians. This result shows that the non-abelian BFFT method is, in many aspects, richer than the abelian BFFT formalism. For both of the first class Hamiltonians, we derive the Lagrangians which lead to the new theory. When one puts the extended phase space variables equal to zero, the original Skyrmion Lagrangian is reproduced. The method of the Dirac first class constraints is employed to quantize these two systems. We achieve the same spectrum, a result which confirms the consistency of the non-abelian BFFT formalism.

Thermodynamic aspects of dark energy fluids

In this paper we have investigated the limits imposed by thermodynamics on a dark energy fluid. We have obtained the heat capacities and the compressibilities for a dark energy fluid. The thermal and mechanical stabilities require these quantities to be positive. We have shown that dark energy fluids must satisfy the stability conditions and that such requirement put difficulties in the cosmic fluid models with negative constant EoS parameters. We have also shown that the observational constraints imposed by SN Ia, BAO and

A note on the relations between thermodynamics, energy definitions and Friedmann equations

H(z)

Probing the cosmological viability of non-gaussian statistics

data on a general dark energy fluid with a time-dependent EoS parameter are in conflict with the constraints imposed by thermodynamics. This result indicates that dark energy fluid models are unphysical.

Weyl ordering prescription for the quantum particle on the D-dimensional sphere

In what follows, we investigate the relation between the Friedmann and thermodynamic pressure equations, through solving the Friedmann and thermodynamic pressure equations simultaneously. Our investigation shows that a perfect fluid, as a suitable solution for the Friedmann equations leading to the standard modelling of the universe expansion history, cannot simultaneously satisfy the thermodynamic pressure equation and those of Friedmann. Moreover, we consider various energy definitions, such as the Komar mass, and solve the Friedmann and thermodynamic pressure equations simultaneously to get some models for dark energy. The cosmological consequences of obtained solutions are also addressed. Our results indicate that some of obtained solutions may unify the dominated fluid in both the primary inflationary and current accelerating eras into one model. In addition, by taking into account a cosmic fluid of a known equation of state, and combining it with the Friedmann and thermodynamic pressure equations, we obtain the corresponding energy of these cosmic fluids and face their limitations. Finally, we point out the cosmological features of this cosmic fluid and also study its observational constraints.