scholarly journals EQUIPARTITION OF ENERGY AND THE FIRST LAW OF THERMODYNAMICS AT THE APPARENT HORIZON

2011 ◽  
Vol 20 (04) ◽  
pp. 553-559 ◽  
Author(s):  
FU-WEN SHU ◽  
YUNGUI GONG
Keyword(s):  
Apparent Horizon ◽  
Friedmann Equation ◽  
Consistency Check ◽  
First Law Of Thermodynamics ◽  
A Value ◽  
Cosmological Observations ◽  
Equipartition Law ◽  
Equipartition Of Energy ◽  
The Universe ◽  
Friedmann Robertson Walker

We apply the holographic principle and the equipartition law of energy to the apparent horizon of a Friedmann–Robertson–Walker universe and derive the Friedmann equation describing the dynamics of the universe. We also show that the equipartition law of energy can be interpreted as the first law of thermodynamics at the apparent horizon. The consistency check shows that our derivation is correct for –1 < w < –(1/3), a value that matches the recent cosmological observations.

scholarly journals Thermodynamics in Loop Quantum Cosmology

2009 ◽  
Vol 2009 ◽  
pp. 1-9 ◽  
Author(s):  
Li-Fang Li ◽  
Jian-Yang Zhu
Keyword(s):  
Quantum Cosmology ◽  
Apparent Horizon ◽  
Friedmann Equation ◽  
Gravitational Energy ◽  
Effective Density ◽  
Loop Quantum Cosmology ◽  
Thermodynamic Quantities ◽  
Effective Pressure ◽  
The Universe ◽  
Friedmann Robertson Walker

Loop quantum cosmology (LQC) is very powerful to deal with the behavior of early universe. Moreover, the effective loop quantum cosmology gives a successful description of the universe in the semiclassical region. We consider the apparent horizon of the Friedmann-Robertson-Walker universe as a thermodynamical system and investigate the thermodynamics of LQC in the semiclassical region. The effective density and effective pressure in the modified Friedmann equation from LQC not only determine the evolution of the universe in LQC scenario but also are actually found to be the thermodynamic quantities. This result comes from the energy definition in cosmology (the Misner-Sharp gravitational energy) and is consistent with thermodynamic laws. We prove that within the framework of loop quantum cosmology, the elementary equation of equilibrium thermodynamics is still valid.

Cosmological Friedmann equation in infrared modified Hořava–Lifshitz gravity via generalized Misner–Sharp mass

2016 ◽  
Vol 31 (23) ◽  
pp. 1650123 ◽  
Author(s):  
Molin Liu ◽  
Yuling Yang ◽  
Yu Han ◽  
Zonghua Zhao ◽  
Jianbo Lu
Keyword(s):  
Field Equation ◽  
Apparent Horizon ◽  
Friedmann Equation ◽  
Gravitational Action ◽  
First Law Of Thermodynamics ◽  
Friedmann Equations ◽  
Gravity Theories ◽  
Friedmann Robertson Walker

In various gravity theories, Friedmann equations can be cast to a form of the first law of thermodynamics in a Friedmann–Robertson–Walker (FRW) cosmological setup. However, this result failed in recent infrared (IR) modified Hořava–Lifshitz (HL) gravity. The difficulty stems from the fact that HL gravity is Lorentz-violating. Motivated by this problem, we use the Misner–Sharp mass to investigate the thermodynamics near the apparent horizon in HL cosmology. We find that the Friedmann equations can be derived from the first law of thermodynamics. The Misner–Sharp mass used here inherits the specific properties of HL gravity since it is directly from the gravitational action of HL theory. We also prove that the first law of thermodynamics with logarithmic entropy still holds at the apparent horizon in FRW. The results suggest that the general prescription of deriving the field equation from thermodynamics still works in the HL cosmology.

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

2015 ◽  
Vol 30 (13) ◽  
pp. 1550058 ◽  
Author(s):  
Saugata Mitra ◽  
Subhajit Saha ◽  
Subenoy Chakraborty
Keyword(s):  
Hawking Temperature ◽  
Entropic Force ◽  
First Law Of Thermodynamics ◽  
Friedmann Equations ◽  
Equipartition Law ◽  
Frw Model ◽  
Clausius Relation ◽  
Material Bodies ◽  
The Universe ◽  
Friedmann Robertson Walker

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.

scholarly journals THERMODYNAMICS OF FRIEDMANN EQUATION AND MASSLIKE FUNCTION IN GENERAL BRANEWORLD

2009 ◽  
Vol 24 (31) ◽  
pp. 5877-5888 ◽  
Author(s):  
TAO ZHU ◽  
JI-RONG REN ◽  
SHU-FAN MO
Keyword(s):  
Apparent Horizon ◽  
Friedmann Equation ◽  
Curvature Correction ◽  
First Law Of Thermodynamics ◽  
New Type ◽  
Braneworld Model ◽  
The Difference ◽  
Correction Terms

Using the generalized procedure proposed by S. F. Wu et al.23 recently, we construct the first law of thermodynamics on apparent horizon in a general braneworld model with curvature correction terms on the brane and in the bulk, respectively. The explicit entropy formular of apparent horizon in the general braneworld is worked out. We also discuss the masslike function which associated with a new type first law of thermodynamics of the general braneworld in detail. We analyze the difference between the conventional thermodynamics and the new type thermodynamics on apparent horizon. At last, the discussions about the physical meanings of the masslike function have also been given.

A unified picture of cosmological entropy on apparent horizon in F(R, G) gravity

2017 ◽  
Vol 32 (33) ◽  
pp. 1750182 ◽  
Author(s):  
Ali İhsan Keskin ◽  
Irfan Acikgoz
Keyword(s):  
Apparent Horizon ◽  
Second Law Of Thermodynamics ◽  
Hawking Temperature ◽  
Second Law ◽  
Field Equations ◽  
Frw Universe ◽  
Generalized Second Law ◽  
History Of ◽  
The Universe ◽  
Friedmann Robertson Walker

In this study, the validity of the generalized second law of thermodynamics (GSLT) has been investigated in F(R, G) gravity. We consider that the boundary of the universe is surrounded by an apparent horizon in the spatially flat Friedmann–Robertson–Walker (FRW) universe, and we take into account the Hawking temperature on the horizons. The unified solutions of the field equations corresponding to gravity theory have been applied to the validity of the GSLT frame, and in this way, both the solutions have been verified and all the expansion history of the universe has been shown in a unified picture.

scholarly journals Thermodynamic Prescription of Cosmological Constant in the Randall-Sundrum II Brane

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Tanwi Bandyopadhyay
Keyword(s):  
Cosmological Constant ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Friedmann Equation ◽  
Entropy Function ◽  
Flat Universe ◽  
Corrected Entropy ◽  
Cosmological Scenario ◽  
Equipartition Law ◽  
The Universe

In this work, we apply the quantum corrected entropy function derived from the Generalized Uncertainty Principle (GUP) to the holographic equipartition law to study the cosmological scenario in the Randall-Sundrum (RS) II brane. An extra driving term has come up in the effective Friedmann equation for a homogeneous, isotropic, and spatially flat universe. Further, thermodynamic prescription of the universe constraints this term eventually with an order equivalent to that of the cosmological constant.

scholarly journals Thermodynamics in f(T) Gravity with Nonminimal Coupling to Matter

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Tahereh Azizi ◽  
Najibeh Borhani
Keyword(s):  
Apparent Horizon ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Nonminimal Coupling ◽  
Field Equations ◽  
First Law Of Thermodynamics ◽  
Torsion Scalar ◽  
Arbitrary Coupling ◽  
Friedmann Robertson Walker

In the present paper, we study the thermodynamics behavior of the field equations for the generalized f(T) gravity with arbitrary coupling between matter and the torsion scalar. In this regard, we explore the verification of the first law of thermodynamics at the apparent horizon of the Friedmann-Robertson-Walker universe in two different perspectives, namely, the nonequilibrium and equilibrium descriptions of thermodynamics. Furthermore, we investigate the validity of the second law of thermodynamics for both descriptions of this scenario with the assumption that the temperature of matter inside the horizon is similar to that of horizon.

scholarly journals Thermodynamics in new model of loop quantum cosmology

2021 ◽  
Vol 81 (2) ◽  
Author(s):  
Xiangdong Zhang
Keyword(s):  
Quantum Cosmology ◽  
Apparent Horizon ◽  
Friedmann Equation ◽  
High Energy ◽  
Effective Density ◽  
Loop Quantum Cosmology ◽  
Thermodynamic Quantities ◽  
Effective Pressure ◽  
New Model ◽  
The Universe

AbstractThe thermodynamic properties of loop quantum cosmology (LQC) without considering the Lorentz term were established in Li and Zhu (Adv High Energy Phys 2009:905705, 2009). In this paper, we extend this result to the recent proposed new model of LQC with the Lorentz term. We investigate the thermodynamics of LQC on the apparent horizon of the Friedmann–Lematre–Robertson–Walker universe. The result shows that the effective density and effective pressure in the modified Friedmann equation of LQC not only determines the evolution of the universe but can also serve as the thermodynamic quantities. Moreover, with the help of the Misner–Sharp energy, the first law of thermodynamics of the LQC is still valid as expected. This in turn endows precise physical meaning to the effective matter density $$\rho _{eff}$$ ρ eff and the effective pressure $$P_{eff}$$ P eff .

Thermodynamics of the FRW universe in rainbow gravity

2017 ◽  
Vol 26 (13) ◽  
pp. 1750139 ◽  
Author(s):  
Akram Sadat Sefiedgar ◽  
Majid Daghigh
Keyword(s):  
High Energy Physics ◽  
Apparent Horizon ◽  
Friedmann Equation ◽  
High Energy ◽  
Suitable Model ◽  
Frw Universe ◽  
Thermodynamical Properties ◽  
Generalized Second Law ◽  
Friedmann Robertson Walker ◽  
Energy Physics

Rainbow gravity can be a suitable model to study the Friedmann–Robertson–Walker (FRW) universe in the realm of high energy physics. In rainbow gravity the radius of the apparent horizon is modified and it is used to derive the surface gravity and the temperature on the horizon. Inspired by the modified Friedmann equation in rainbow gravity and adopting the viewpoint that there is a deep connection between Friedmann equation and the first law of thermodynamics, the entropy on the horizon is obtained. It is interesting to be noted that the thermodynamical properties of the FRW universe depend on the energy of the probe, which is used by an observer to investigate the spacetime. Finally, it is shown that the validity of the generalized second law (GSL) of thermodynamics can be considered as a useful instrument to restrict the choice of rainbow gravity functions.

scholarly journals Generalized Misner–Sharp energy in generalized Rastall theory

2020 ◽  
Vol 98 (9) ◽  
pp. 853-856
Author(s):  
H. Moradpour ◽  
M. Valipour
Keyword(s):  
Apparent Horizon ◽  
Second Law Of Thermodynamics ◽  
Spherically Symmetric ◽  
Coupling Coefficients ◽  
Field Equations ◽  
Frw Universe ◽  
Einstein Theory ◽  
First Law Of Thermodynamics ◽  
Horizon Entropy ◽  
Friedmann Robertson Walker

Employing the unified first law of thermodynamics and the field equations of the generalized Rastall theory, we get the generalized Misner–Sharp mass of space–times for which gtt = –grr = –f(r). The obtained result differs from those of the Einstein and Rastall theories. Moreover, using the first law of thermodynamics, the obtained generalized Misner–Sharp mass, and the field equations, the entropy of static spherically symmetric horizons are also addressed in the framework of the generalized Rastall theory. In addition, by generalizing the study to a flat Friedmann–Robertson–Walker (FRW) universe, the apparent horizon entropy is also calculated. Considering the effects of applying the Newtonian limit to the field equations on the coupling coefficients of the generalized Rastall theory, our study indicates (i) the obtained entropy–area relation is the same as that of the Rastall theory, and (ii) the Bekenstein entropy is recovered when the generalized Rastall theory reduces to the Einstein theory. The validity of the second law of thermodynamics is also investigated in the flat FRW universe.

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