Unified First Law and Thermodynamics of Apparent Horizon in FRW Universe

Abstract

In this paper we revisit the relation between the Friedmann equations and the first law of thermodynamics. We find that the unified first law firstly proposed by Hayward to treat the "outer"trapping horizon of dynamical black hole can be used to the apparent horizon (a kind of "inner" trapping horizon in the context of the FRW cosmology) of the FRW universe. We discuss three kinds of gravity theorties: Einstein theory, Lovelock thoery and scalar-tensor theory. In Einstein theory, the first law of thermodynamics is always satisfied on the apparent horizon. In Lovelock theory, treating the higher derivative terms as an effective energy-momentum tensor, we find that this method can give the same entropy formula for the apparent horizon as that of black hole horizon. This implies that the Clausius relation holds for the Lovelock theory. In scalar-tensor gravity, we find, by using the same procedure, the Clausius relation no longer holds. This indicates that the apparent horizon of FRW universe in the scalar-tensor gravity corresponds to a system of non-equilibrium thermodynamics. We show this point by using the method developed recently by Eling {\it et al.} for dealing with the $f(R)$ gravity.

arXiv commentv2: revtex, 23 pages, references added, minor changes, to appear in PRD

References in corpus (23)

• Thermodynamics of Spacetime: The Einstein Equation of State
• The Dynamics of General Relativity
• Quasilocal Energy and Conserved Charges Derived from the Gravitational Action
• First Law of Thermodynamics and Friedmann Equations of Friedmann-Robertson-Walker Universe
• General Laws of Black-Hole Dynamics
• Unified first law of black-hole dynamics and relativistic thermodynamics
• Gravity and the Thermodynamics of Horizons
• Classical and Quantum Thermodynamics of horizons in spherically symmetric spacetimes
• Thermodynamic Behavior of Friedmann Equation at Apparent Horizon of FRW Universe
• Gravitational Energy in Spherical Symmetry
• Non-equilibrium Thermodynamics of Spacetime
• Cosmic Holography
• Friedmann Equations of FRW Universe in Scalar-tensor Gravity, f(R) Gravity and First Law of Thermodynamics
• Thermodynamic route to Field equations in Lanczos-Lovelock Gravity
• A Note on Thermodynamics of Black Holes in Lovelock Gravity
• Dynamic black-hole entropy
• Cosmology and the S-matrix
• Inflation and de Sitter Thermodynamics
• Positivity of Quasilocal Mass
• Transplanckian energy production and slow roll inflation
• Gravity: A New Holographic Perspective
• Black holes in the Brans-Dicke-Maxwell theory
• de Sitter thermodynamics and the braneworld

Cited by in corpus (252)

• f(R) theories
• Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests
• f(T) teleparallel gravity and cosmology
• Thermodynamical Aspects of Gravity: New insights
• Black hole chemistry: thermodynamics with Lambda
• Thermodynamics in f(R,T) Theory of Gravity
• Reconstruction of $f(T)$ gravity: Rip cosmology, finite-time future singularities and thermodynamics
• Thermodynamic Behavior of Field Equations for f(R) Gravity
• Hawking Radiation of Apparent Horizon in a FRW Universe
• Corrected Entropy-Area Relation and Modified Friedmann Equations
• Tunnelling Methods and Hawking's radiation: achievements and prospects
• Friedmann Equations and Thermodynamics of Apparent Horizons
• Deep Connection Between Thermodynamics and Gravity in Gauss-Bonnet Braneworld
• Modified cosmology from extended entropy with varying exponent
• Thermodynamics of interacting holographic dark energy with apparent horizon as an IR cutoff
• Thermodynamics of Apparent Horizon in Brane World Scenario
• Modified Friedmann Equations from Tsallis Entropy
• Black Holes in Gravity with Conformal Anomaly and Logarithmic Term in Black Hole Entropy
• Thermodynamics of cosmological horizons in $f(T)$ gravity
• Probing interaction and spatial curvature in the holographic dark energy model
• Generalized Vaidya Spacetime in Lovelock Gravity and Thermodynamics on Apparent Horizon
• Thermodynamics of apparent horizon and modified Friedman equations
• Horizon Thermodynamics and Gravitational Field Equations in Horava-Lifshitz Gravity
• Surface Density of Spacetime Degrees of Freedom from Equipartition Law in theories of Gravity
• Entropic Corrections to Friedmann Equations
• Influence of Generalized and Extended Uncertainty Principle on Thermodynamics of FRW universe
• Thermodynamics and classification of cosmological models in the Horava-Lifshitz theory of gravity
• The generalized second law of thermodynamics in the accelerating universe
• Generalized second law of thermodynamics in Gauss-Bonnet braneworld
• Thermodynamics in $F(R)$ gravity with phantom crossing
• Is gravitational entropy quantized ?
• The generalized second law of thermodynamics in generalized gravity theories
• Does the mass of a black hole decrease due to the accretion of phantom energy
• Thermodynamics of Black Holes in Rastall Gravity
• Thermodynamics of flat FLRW universe in Rastall Theory
• Generalized Misner-Sharp Energy in f(R) Gravity
• Thermodynamics of Apparent Horizon in Brane World Scenarios
• Emergent perspective of Gravity and Dark Energy
• Modified cosmology through nonextensive horizon thermodynamics
• Thermodynamic structure of Lanczos-Lovelock field equations from near-horizon symmetries
• Thermodynamics on the apparent horizon in generalized gravity theories
• Equilibrium thermodynamics in modified gravitational theories
• Modified cosmology through Kaniadakis horizon entropy
• Thermodynamics in Rastall Gravity with Entropy Corrections
• Thermodynamics in $f(R)$ gravity in the Palatini formalism
• Thermodynamic analysis of the static spherically symmetric field equations in Rastall theory
• Notes on Entropy Force in General Spherically Symmetric Spacetimes
• Cosmological apparent and trapping horizons
• Black hole entropy in scalar-tensor and f(R) gravity: an overview
• Modified dispersion relations in extra dimensions
• Generalized second law in modified theory of gravity
• Corrections to Hawking-like Radiation for a Friedmann-Robertson-Walker Universe
• Generalized second law of thermodynamics in f(R,T) theory of gravity
• Entropic Corrections to Einstein Equations
• Lovelock black holes with maximally symmetric horizons
• Barrow black hole corrected-entropy model and Tsallis nonextensivity
• Cosmological consequences in the framework of generalized Rastall theory of gravity
• Correspondence of cosmology from non-extensive thermodynamics with fluids of generalized equation of state
• A general maximum entropy principle for self-gravitating perfect fluid
• First law of thermodynamics and Friedmann-like equations in braneworld cosmology
• Universality of P-V Criticality in Horizon Thermodynamics
• Thermodynamic Behavior of particular $f(R,T)$ Gravity Models
• Modified cosmology from the thermodynamics of apparent horizon
• Baryon asymmetry from Barrow entropy: theoretical predictions and observational constraints
• Black holes and black hole thermodynamics without event horizons
• Stringy-Running-Vacuum-Model Inflation: from primordial Gravitational Waves and stiff Axion Matter to Dynamical Dark Energy
• Barrow's black hole entropy and the equipartition theorem
• Gravitational field equations near an arbitrary null surface expressed as a thermodynamic identity
• Viscous dark energy and generalized second law of thermodynamics
• Generalized second law of thermodynamics in warped DGP braneworld
• New explanation for accelerated expansion and flat galactic rotation curves
• Holography in Action
• Viscous Cosmology and Thermodynamics of Apparent Horizon
• Corrected Entropy of Friedmann-Robertson-Walker Universe in Tunneling Method
• Fermions Tunneling from Apparent Horizon of FRW Universe
• Alleviating both $H_0$ and ${\sigma }_8$ tensions in Tsallis cosmology
• Apparent horizon and gravitational thermodynamics of the Universe: Solutions to the temperature and entropy confusions, and extensions to modified gravity
• Thermodynamics of interacting entropy-corrected holographic dark energy in a non-flat FRW universe
• Black Holes in the Universe: Generalized Lemaitre-Tolman-Bondi Solutions
• Considerations on the thermal equilibrium between matter and the cosmic horizon
• Thermodynamics of Fractal Universe
• The Apparent Universe
• Entropic corrections to Friedmann equations and bouncing universe due to the zero-point length
• Misner-Sharp Mass and the Unified First Law in Massive Gravity
• Misner-Sharp Mass in $N$-dimensional $f(R)$ Gravity
• Thermodynamic properties of modified gravity theories
• Generalized second law of thermodynamics in modified FRW cosmology with corrected entropy-area relation
• Universal thermodynamics in different gravity theories: Modified entropy on the horizons
• Thermodynamics of the apparent horizon in the generalized energy-momentum-squared cosmology
• Generalized Second Law of Thermodynamics in $f(T,T_G)$ gravity
• Hawking-like radiation as tunneling from the apparent horizon in a FRW Universe
• Constraints on Tsallis Cosmology from Big Bang Nucleosynthesis and the Relic Abundance of Cold Dark Matter Particles
• The Generalized Uncertainty Principle and the Friedmann equations
• Why Does the Universe Expand ?
• Thermodynamics and Perturbative Analysis of Some Newly Developed $\mathcal{F}(R,L_m,T)$ Theories Under the Scenario of Conserved Energy-momentum Tensor
• Lovelock gravity from entropic force
• Thermodynamic of the Ghost Dark Energy Universe
• Thermodynamics of scalar-tensor theory with non-minimally derivative coupling
• The P-V Phase Transition of the FRW Universe
• Accelerated Expansion of the Universe based on Emergence of Space and Thermodynamics of the Horizon
• Clausius relation and Friedmann equation in FRW universe model
• Phenomenological Fluids from Interacting Tachyonic Scalar Fields
• Thermodynamical description of the interacting new agegraphic dark energy
• Generalized Second Law of Thermodynamics in Extended Theories of Gravity
• Emergence of spacetime dynamics in entropy corrected and braneworld models
• Does the second law hold at cosmic scales?
• Thermodynamics of the apparent horizon in infrared modified Horava-Lifshitz gravity
• Hawking radiation from the cosmological horizon in a FRW universe
• Thermodynamics of FRW Universe: Heat Engine
• A Study of Generalized Second Law of Thermodynamics in Magnetic Universe in the light of Non-Linear Electrodynamics
• Trapping Horizons of the Evolving Charged Wormhole and Black Bounce
• Thermodynamics of Lemaitre-Tolman-Bondi Model
• Validity of the Generalized Second Law of Thermodynamics of the Universe Bounded by the Event Horizon in Brane Scenario
• Horizon Thermodynamics and Gravitational Field Equations in Quasi-Topological Gravity
• Thermodynamical description of the ghost dark energy model
• Modified Friedmann Equations From Debye Entropic Gravity
• Schwarzschild solution as a result of thermodynamics
• First Principle Study of Gravitational Pressure and Thermodynamics of FRW Universe
• Quasilocal energy in modified gravity
• Generalized holographic Ricci dark energy and generalized second law of thermodynamics in Bianchi Type I universe
• Phase space analysis of the bouncing universe with stringy effects
• Dynamical horizon entropy and equilibrium thermodynamics of generalized gravity theories
• The generalized second law in chameleon cosmology
• Thermodynamics of Friedmann Equation and Masslike Function in General Braneworld
• Friedmann equations from nonequilibrium thermodynamics of the Universe: A unified formulation for modified gravity
• Generalized entropies and the expansion law of the universe
• More on the conformal mapping of quasi-local masses: The Hawking-Hayward case
• Modified Friedmann equations from fractional entropy
• Thermodynamic of universe with a varying dark energy component
• Deriving the gravitational field equation and horizon entropy for arbitrary diffeomorphism-invariant gravity from spacetime solid
• Cosmological equations and Thermodynamics on Apparent Horizon in Thick Braneworld
• Thermodynamical properties of dark energy with the equation of state
• Phase Transitions and Critical Phenomena for the FRW Universe in an Effective Scalar-Tensor Theory
• Emergence of cosmic space and its connection with thermodynamic principles
• The Hawking-Page-like Phase Transition from FRW Spacetime to McVittie Black Hole
• Modified Friedmann equations from DSR-GUP
• Thermodynamics of scale-dependent Friedmann equations
• Emergent Universe in the Braneworld Scenario
• From the Komar Mass and Entropic Force Scenarios to the Einstein Field Equations on the Ads Brane
• Evolution of thermodynamic quantities on cosmological horizon in $\Lambda (t)$ model
• Investigation of generalised uncertainty principle effects on FRW cosmology
• Thermodynamics in Loop Quantum Cosmology
• Apparent dark matter as a non-local manifestation of emergent gravity
• Validity of Generalized Second Law of Thermodynamics in the Logamediate and Intermediate scenarios of the Universe
• Unified First Law and Thermodynamics of Dynamical Black Hole in n-dimensional Vaidya Spacetime
• Maximum Entropy Principle for Self-gravitating Perfect Fluid in Lovelock Gravity
• Universal thermodynamics in different gravity theories: Conditions for generalized second law of thermodynamics and thermodynamical equilibrium on the horizons
• New holographic dark energy model inspired by the DGP braneworld
• Thermodynamics of $f(R)$ Gravity with Disformal Transformation
• Cosmological FLRW phase transitions and micro-structure under Kaniadakis statistics
• A Study of Universal Thermodynamics in Brane World Scenario
• First Law of Thermodynamics and Emergence of Cosmic Space in a Non-Flat Universe
• A note on the Hawking radiation calculated by the quasi-classical tunneling method
• Local entropy of a nonequilibrium fermion system
• Thermodynamics of Evolving Lorentzian Wormhole at Apparent and Event Horizons
• Varying constants entropic--$\Lambda$CDM cosmology
• Insight into the Microstructure of FRW Universe from a $P$-$V$ Phase Transition
• Emergent Cosmos in Einstein-Cartan Theory
• Quantum computational complexity, Einstein's equations and accelerated expansion of the Universe
• Cosmological Constraints on Entropic Cosmology with Matter Creation
• The thermal entropy density of spacetime
• Entropy of the FRW cosmology based on the brick wall method
• Scalar-Tensor Theory of Gravity and Generalized Second Law of Thermodynamics on the Event Horizon
• Hawking Radiation as tunneling and the unified first law of thermodynamics for a class of dynamical black holes
• Thermodynamics in a Modified Gravity Involving Higher-Order Torsion Derivative Terms
• First law of thermodynamics and entropy of FLRW universe in modified gravity
• Thermodynamical analysis on a braneworld scenario with curvature corrections
• Equation of State and Joule-Thomson Expansion for the FRW Universe in the Brane World Scenario
• Thermodynamics of FRW Universe With Chaplygin Gas Models
• Fluctuations of the flux of energy on the apparent horizon
• Emergent Dark Matter in Late Time Universe on Holographic Screen
• A Study of Universal Thermodynamics in Lanczos-Lovelock gravity
• A Universe with a generalized ghost dark energy and Van der Waals fluid interacting with a fluid
• Entropy of the FRW universe based on the generalized uncertainty principle
• Thermodynamic Origin of the Cardassian Universe
• On topological charged braneworld black holes
• Thermodynamic analysis of universes with the initial and final de-Sitter eras
• Modified Bekenstein-Hawking system in $f(R)$ gravity
• Renyi Entropy Correction to Expanding Universe
• Thermodynamics of general scalar-tensor theory with non-minimally derivative coupling
• Thermodynamics in Quasi-Spherical Szekeres Space-Time
• Thermodynamic analysis of gravitational field equations in Lyra manifold
• An exact black hole spacetime with scalar field and its shadow together with quasinormal modes
• Phase transitions, critical behavior and microstructure of the FRW universe in the framework of higher order GUP
• Cosmological model based on both holographic-like connection and Padmanabhan's holographic equipartition law
• Revisiting the Birkhoff theorem from a dual null point of view
• The Unified First law in "Cosmic Triad" Vector Field Scenario
• Does the particle creation mechanism favour the formation of a black hole or a naked singularity?
• The new higher-order generalized uncertainty principle and primordial big bang nucleosynthesis
• Quasilocal mass in scalar-tensor gravity: spherical symmetry
• Kaniadakis entropy-based characterization of IceCube PeV neutrino signals
• Entropic Gravity and Cosmology in Kaniadakis Statistics
• Thermodynamics of Quasi-Topological Cosmology
• Barrow Cosmology and Big-Bang Nucleosynthesis
• Thermodynamical study of FRW universe in Quasi-Topological Theory
• Accretion of Holographic Dark Energy : Dependency only upon Horizon Radius of Expanding Universe
• Cosmic scenarios in $f(R)$ gravity: a complete evolution
• Unified first law and some general prescription: a redefinition of surface gravity
• Note on nonsingular cyclic universes in the deformed Horava-Lifshitz gravity
• Cosmological horizons as new examples of membrane paradigm
• Quasilocal energy and thermodynamic equilibrium conditions
• Emergence of cosmic space and the maximization of horizon entropy
• Cyclic universe due to phantom and quintessence
• Dark Energy Accretion onto Van der Waal's Black Hole
• Spacetime mappings of the Brown-York quasilocal energy
• A Study of Universal Thermodynamics in Massive Gravity: Modified Entropy on the Horizons
• Thermodynamics of the inhomogeneous perfect fluid LTB model: Modified Bekenstein-Hawking system
• Exponential correction to Friedmann equations
• Thermodynamics in new model of loop quantum cosmology
• Thermodynamics of the Primordial Universe
• Invariance of the Hamilton-Jacobi tunneling method for black holes and FRW model
• The generalized second law of thermodynamics in f(R) gravity for various choices of scale factor
• Thermodynamics of a Non-canonical $f(\bar{R},\bar{T})$ gravity
• Modified cosmology through generalized mass-to-horizon entropy: observational constraints from DESI DR2 BAO data
• Generalized Vaidya spacetime for cubic gravity
• For a flat Universe, $C_P/C_V=-q$ : another coincidence in Cosmology?
• Holographic thermodynamic relation for dissipative and non-dissipative universes in a flat FLRW cosmology
• Apparent horizon and gravitational thermodynamics of Universe in the Eddington-Born-Infeld theory
• A general thermodynamical description of the event horizon in the FRW universe
• Misner-Sharp Energy and P-V Criticality in Quasi-Topological Cosmology
• Observational constraints and dynamical analysis of Kaniadakis horizon-entropy cosmology
• Thermodynamics in Little Rip cosmology in the framework of a type of f(R,T) gravity
• Thermodynamics of scalar field models with kinetic corrections
• Friedmann equations from GUP-modified equipartition law
• Thermodynamics of the arbitrary dimensional FRW universe: Joule-Thomson expansion
• Cosmological Tensions with Non-Extensive Entropic Cosmology: A Modified Stress-Energy Approach
• Implications of maximum acceleration on dynamics
• On the correspondence between energy conservation and energy-momentum tensor conservation in cosmology
• Estimation of temperature of cosmological apparent horizons: a new approach
• Effective Pressure of the FRW Universe
• Modified cosmology through generalized mass-to-horizon entropy: implications for structure growth and primordial gravitational waves
• Generalized Brans-Dicke theory from Verlinde's entropic gravity
• Cosmological scenario based on the first and second laws of thermodynamics: Thermodynamic constraints on a generalized cosmological model
• Cooling-Heating Properties of the FRW Universe in Gravity with a Generalized Conformal Scalar Field
• Thermodynamics of sign-switching dark energy models
• The Einstein equation of state as the Clausius relation with an entropy production
• Constraints on the radiation temperature before inflation
• Observational constraints on the modified cosmology inspired by string T-duality
• Cosmological QCD phase transition in steady non-equilibrium dissipative Hořava-Lifshitz early universe
• Thermodynamical aspects of modified holographic dark energy model
• Observational constraints on Luciano-Saridakis entropic cosmology
• Generalized Second Law of Thermodynamics on the Event Horizon for Interacting Dark Energy
• Generalized Second Law and Thermodynamical Aspects of $f(Q,\mathcal{T})$ Gravity
• Thermodynamic aspects of FLRW Universe in Einstein-Gauss-Bonnet domains
• Statistical physics on Euclidean Snyder space: connections with the GUP and cosmological implications
• Thermodynamics of Apparent Horizon and Friedmann Equations in Big Bounce Universe
• Background instability of quintessence model in light of entropy and distance conjecture
• Heat Capacity and the Violation of Scaling Laws in Gravitational System
• Cosmology with Logarithmic Corrected Horizon Entropy According to the Generalized Entropy and Variable-G Correspondence
• Modified Cosmology from Mass-to-Horizon Relation: Background Evolution
• The trace of field equations for higher-derivative gravity and an equality associating the Lagrangian density with a divergence term
• Dynamical axisymmetric compact objects in General Relativity