arXiv subjects

G. E. Volovik

Publications and source records attributed to G. E. Volovik.

At least 19 recordsLinked to original sources

arXiv2026

Thermodynamics of homogeneous Universes: de Sitter, Bonnor-Melvin and static Einstein

In the theories, in which dynamic gravitational field emerges from the underlying matter fields, the gravitational field can be considered as a part of matter. Using this approach, we construct the thermodynamics of the homogeneous Universes -- the de Sitter Universe, the Bonnor-Melvin-$Λ$ Universe and the static Einstein Universe. It is demonstrated that although these three Universes have different types of matter fields (ordinary matter, magnetic field, gravitational field and vacuum energy), they have the same thermodynamic properties. Their energy densities obey the same equation, which contains the corresponding matter densities and the pairs of the thermodynamically conjugate variables. In Minkowski vacuum, where the ordinary matter and magnetic and gravitational fields are absent, this thermodynamic approach automatically leads to zero cosmological constant.

gr-qc↗

arXiv2026

From gravastar to central singularity

We consider the model of the regular black hole, which demonstrates that the gravastar is thermodynamically unstable towards the Schwarzschild black hole with singularity.

gr-qc↗

arXiv2026

Quantum and Classical mechanics vs QFT

15 years ago Dmitry Diakonov wrote the paper "Towards lattice-regularized Quantum Gravity", arXiv:1109.0091. In his approach, gravity with metric and tetrads arise from pre-geometric quantum fields leading to unusual dimensions of physical quantities. In particular, particle masses are dimensionless. We are trying to extend the Akama-Diakonov-Wetterich theory by introducing the Planck constants $\hbar$ and ${/\!\!h}=\hbar c$ as elements of the emergent metric. The inverse Planck constant $1/\hbar$ has the dimension of frequency, and, therefore, the mass $M$ of a particle, which has the dimension $\hbarω$, is dimensionless. In this extension, quantum mechanics emerges from the intrinsic quantum fields either in the symmetry breaking mechanism (GUT), or in the opposite mechanism of emergent symmetry in the low-energy corner (anti-GUT). In both cases, quantum mechanics (QM) serves as a bridge between the area of quantum fields (QFT) in the limit $1/\hbar \rightarrow 0$, and the area of classical physics (CM) in the limit $\hbar \rightarrow 0$. In the GUT scheme the inverse Planck constants, $1/\hbar$ and $1/{\\!\!h}$, play the role of the order parameter of the symmetry breaking phase transition from the pre-geometric QFT state to the QM state, in which the quantum mechanics emerges together with the space-time metric. In this phase transition, the integration over field variables in the QFT phase transforms to a path integral formulation of QM, which in turn yields the laws of classical mechanics in the limit $1/\hbar \rightarrow \infty$.

physics.gen-ph↗

arXiv2026

Hawking radiation: black hole vs de Sitter

We discuss the difference between the thermodynamics of black holes and thermodynamics of the de Sitter expansion. Both systems experience the Hawking radiation, but its impact on thermodynamics is different. As distinct from the thermodynamics of black holes, which are finite compact objects, the de Sitter state is the infinite and homogeneous state. The presence of the cosmological horizon provides two sides of the de Sitter thermodynamics: the local thermodynamics and the thermodynamics related to the cosmological horizon. We discuss the connection between these two sides considering the entropy of the Hubble volume in de Sitter spacetime -- the region inside the horizon. On one hand there is the Gibbons-Hawking entropy $S_{\rm GH}=A/4G$ associated with the cosmological horizon. On the other hand this entropy can be obtained by integrating the local entropy density over the Hubble volume. In (3+1) spacetime, these two entropies coincide. This provides physical meaning and a natural explanation to the Gibbons-Hawking entropy -- it is the entropy in the volume $V_H$ bounded by the cosmological horizon. Here we consider whether the Gibbons-Hawking conjecture remains valid for the de Sitter state in general $d+1$ spacetime. To do this, we use the local de Sitter thermodynamics, characterized by a local temperature $T_{\rm dS}=H/π$. This temperature is not related to the horizon: it is the temperature of local activation processes, such as the ionization of an atom in the de Sitter environment, which occur deep within the cosmological horizon. This local temperature is universal and does not depend on dimension $d$, it is twice the Gibbons-Hawking temperature $T_{\rm GH}=H/2π$. We found that the entropy of the Hubble volume is $S_H=(d-1)A/8G$, which modifies the Gibbons-Hawking entropy of horizon. The original form of the Gibbons-Hawking entropy is valid only for $d=3$.

gr-qc↗

arXiv2026

Massless graviton in de Sitter as second sound in two-fluid hydrodynamics

The concept of gravitons and their masses, clear in the case of Minkowski spacetime, remains ambiguous for de Sitter spacetime. Here, we used a two-fluid approach to de Sitter thermodynamics and found a collective mode that is analogous to second sound in the two-fluid dynamics of the de Sitter state. This mode is massless and propagates at the speed of light. This suggests that this second-sound analog is a massless graviton propagating in de Sitter spacetime. The type of graviton this mode represents requires further consideration.

gr-qc↗

arXiv2026

Non-extensive entropy of Vinen quantum turbulence

In Ref. [1] the statistical structure of the turbulent cascade in the context of non-additive entropy was considered. Here we suggest that the vortex line ensemble in the Vinen quantum turbulence in superfluids is described by the non-extensive Tsallis-Cirto statistics with $δ=3$. This in particular leads to the temperature, which describes the thermodynamics of the Vinen ensemble, $T\sim mv^2$, where $v$ is the velocity of the flow and $m$ is the mass of the atom of the superfluid liquid.

cond-mat.stat-mech↗

arXiv2026

Topological charge of fermions and Landau theory of Fermi liquid

In the fermionic liquids, the Fermi surface is topologically stable,\cite{Volovik2003} which is at the origin of the applicability of the Landau theory of Fermi liquid (LFL). The LFL exists under special condition, when the Green's function has a pole with nonzero residue $Z$. Otherwise one has non-Landau Fermi liquid (NLFL), such as Luttinger liquid, which is described by the same topological invariant. It appears that in general this topological invariant is the property of the fermionic particle, i.e. the particle charge (or the electric charge of electron) is equivalent to the topological charge of the fermion. The conservation of the fermionic charge is equivalent to the conservation of the topological charge. We consider the application of this topological charge to the Landau theory of Fermi liquids. We also consider the application to non-Fermi liquids and crystalline insulators in relation to the Luttinger theorem.

cond-mat.str-el↗

arXiv2026

Thermodynamics of Einstein static Universe with boundary

The de Sitter state and the static Einstein Universe are unique states that have a constant scalar Ricci curvature ${\cal R}$. It was shown earlier that such a unique symmetry of the de Sitter state leads to special thermodynamic properties of this state, which are determined by the local temperature $T=1/(πR)$, where $R$ is the radius of the cosmological horizon. Then, what happens in the static Universe? We consider the original Einstein Universe, i.e. the so-called spherical Universe. It is half of the elliptical Universe $R\times S^3$, which was introduced later. Formally, the original Einstein Universe has a boundary at $r=R$. Here we consider the boundary at $r=R$ as a surface that connects the Einstein Universe with the thermal environment. In this realization of the Einstein Universe, it is characterized by a local temperature $T=1/(πR)$, which is analogous to the local temperature of the de Sitter state. Or, conversely, the temperature of environment heat bath determines the radius of the Universe, $R=1/πT$. The thermodynamics of the bounded Einstein Universe is also analogous to the thermodynamics of the de Sitter state. In particular, the entropy of the bounded Universe satisfies the holographic relation, $S=A/4G$, where $A=2π^2R^2$ is the area of the boundary. This shows that in thermodynamics the physical boundary of the static Einstein Universe plays the same role as the cosmological de Sitter horizon. In this Universe, Zeldovich's stiff matter is also preferred.

gr-qc↗

arXiv2026

Thermodynamics of Kerr black hole: Tsallis-Cirto composition law and entropy quantization

The processes of splitting and merging of black holes obey the composition law generated by the Tsallis-Cirto $δ=2$ statistics. The same composition law expresses the full entropy of the Reissner-Nordström black hole via the entropies of its outer and inner horizons. Here we apply this composition law to the thermodynamics of the Kerr black hole. As distinct from Reissner-Nordström black hole, where the full entropy depends only on mass $M$ and does not depend on its charge $Q$, the entropy of Kerr black hole is the sum of contributions from its mass $M$ and angular momentum $J$, i.e. $S(M,J)=S(M,0) + 4π\sqrt{J(J+1)}$. Here $S(M,0)$ is the entropy of the Schwarzschild black hole. This demonstrates that when the Kerr black hole with $J\gg 1$ absorbs or emits a massless particle with spin $s_z=\pm 1/2$, its entropy changes by $|ΔS| = 2π$. We also considered the quantization of entropy suggested by the toy model, in which the black hole thermodynamics is represented by the ensemble of the Planck-scale black holes -- Planckons. The Tsallis-Cirto composition law is also extended to the thermodynamics of Kerr-Newman black hole.

gr-qc↗

arXiv2025

From Landau two-fluid model to de Sitter Universe

The condensed matter analogs are useful for consideration of the phenomena related to the quantum vacuum. This is because in condensed matter we know physics both in the infrared and in the ultraviolet limits, while in particle physics and gravity the physics at trans-Planckian scale is unknown. One of the corner stones of the connections between the non-relativistic condensed matter and the modern relativistic theories is the two-fluid hydrodynamics of superfluid helium. The dynamics and thermodynamics of the de Sitter state of the expansion of the Universe bear some features of the multi-fluid system. There are actually three components: the quantum vacuum, the gravitational component and relativistic matter. The expanding de Sitter vacuum serves as the thermal bath with local temperature, which is twice the Gibbons-Hawking temperature related to the cosmological horizon. This local temperature leads to the heating of matter component and the gravitational component. The latter behaves as Zel'dovich stiff matter and represents the dark matter. In equilibrium and in the absence of the conventional matter the positive partial pressure of dark matter compensates the negative partial pressure of quantum vacuum. That is why in the full equilibrium the total pressure is zero. This is similar to the superfluid and normal components in superfluids, which together produce the zero pressure of the liquid in the absence of environment. If one assumes that in dynamics, the gravitational dark matter behaves as the real Zel'dovich stiff matter, one obtains that both components experience the power law decay due to the energy exchange between these components. Then it follows that their values at present time have the correct order of magnitude. We also consider the other problems through the prism of condensed matter physics, including the black holes and Planck constant.

gr-qc↗

arXiv2025

Thermodynamic and quantum fluctuations of horizon area

The event horizon is a source of irreversibility, analogous to statistical irreversibility. This is why for systems with an event horizon there is no difference between quantum and thermal fluctuations. Quantum processes of quantum tunneling determine the thermodynamics of these systems, their temperatures, entropies and fluctuations. We considered three examples of entropy variance that support this point of view: (i) the variance of the area of the black hole horizon, obtained by consideration of quantum fluctuations; (ii) the variance of the entropy of the Hubble volume in the de Sitter state, obtained by consideration of thermal fluctuations; and (iii) the variance of entropy in integers in the Planckon model, determined by the Poisson distribution.

gr-qc↗

arXiv2025

Extended Tsallis-Cirto entropy for black and white holes

In reference [1] we considered the black hole thermodynamics with the non-extensive entropy. This entropy obeys the composition rule which coincides with the composition rule in the non-extensive Tsallis-Cirto $δ=2$ statistics. Here we extend this approach to the thermodynamics of white holes. The entropy of the white hole is negative as follows from the rate of macroscopic quantum tunneling from black hole to white hole. The white hole entropy is with the minus sign the entropy of the black hole with the same mass, $S_{\rm WH}(M)=-S_{\rm BH}(M)$. This reflects the anti-symmetry with respect to time reversal, at which the shift vector in the Arnowitt-Deser-Misner formalism changes sign. This symmetry allows one to extend the Tsallis-Chirto entropy by adding a minus sign to the Tsallis-Chirto formula applied to white hole. As a result, the composition rule remains the same, with the only difference being that instead of entropy it contains the entropy modulus. The same non-extensive composition rule is obtained for the entropy of the Reissner-Nordström black hole. This entropy is formed by the positive entropy of the outer horizon and the negative entropy of the inner horizon. The model of the black hole formed by "black hole atoms" with Planck-scale mass is also extended to include the negative entropy of white holes.

gr-qc↗

arXiv2025

Thermodynamics of black and white holes in ensemble of Planckons

The Tsallis-Cirto non-extensive statistics with $δ=2$ describes the processes of splitting and merging of black holes and their thermodynamics. Here we consider a toy model, which matches this generalized statistics and extends it by providing the integer valued entropy of the black hole, $S_{\rm BH}(N)=N(N-1)/2$. In this model the black hole consists of $N$ the so-called Planckons -- objects with reduced Planck mass $m_{\rm P}=1/\sqrt{8πG}$ -- so that its mass is quantized, $M=Nm_{\rm P}$. The entropy of each Planckon is zero, but the entropy of black hole with $N$ Planckons is provided by the $N(N-1)/2$ degrees of freedom -- the correlations between the gravitationally attracted Planckons. This toy model can be extended to a charged Reissner-Nordström (RN) black hole, which consists of charged Planckons. Despite the charge, the statistical ensemble of Planckons remains the same, and the RN black hole with $N$ Planckons has the same entropy as the electrically neutral hole, $S_{\rm RNBH}(N)=N(N-1)/2$. This is supported by the adiabatic process of transformation from the RN to Schwarzschild black hole by varying the fine structure constant. The adiabaticity is violated in the extreme limit, when the gravitational interaction between two Planckons is compensated by the repulsion between their electric charges, and the RN black hole loses stability. The entropy of a white hole formed by the same $N$ Planckons has negative entropy, $S_{\rm WH}(N)=-N(N-1)/2$.

gr-qc↗

arXiv2025

Black hole thermodynamics and topology

Recently the difference between the Gibbons-Hawking temperature $T_{\rm GH}$ attributed to the Hawking radiation from the de Sitter cosmological horizon and the twice as high local temperature of the de Sitter state, $T=H/π=2T_{\rm GH}$, has been discussed by Hughes and Kusmartsev from the topological point of view (see arXiv:2505.05814). According to their approach, this difference is determined by the Euler characteristic $χ({\cal M})$ of the considered spacetime with Euclidean time. The invariant $χ({\cal M})$ is different for the global spacetime ${\cal M}=S^4$ and for the manifold limited to a region near the horizon, ${\cal M}=D^2\times S^2$. Here we consider the application of the topological approach to Reissner-Nordström (RN) black holes with two horizons. Both the outer and inner horizons are characterized by their near-horizon topology, which determines the corresponding horizon temperatures. As a result of the correlation between the horizons, the entropy of the RN black hole is independent of its electric charge, being completely determined by the mass of the black hole. This demonstrates the applicability of the topological approach to the multi-horizon systems.

gr-qc↗

arXiv2025

First law of de Sitter thermodynamics

The de Sitter state has a special symmetry: it is homogeneous, and its curvature is constant in space. Since all the points in the de Sitter space are equivalent, this state is described by local thermodynamics. This state has the local temperature $T=H/π$ (which is twice the Gibbons-Hawking temperature), the local entropy density, the local energy density, and also the local gravitational degrees of freedom -- the scalar curvature ${\cal R}$ and the effective gravitational coupling $K$. On the other hand, there is the cosmological horizon, which can be also characterized by the thermodynamic relations. We consider the connections between the local thermodynamics and the thermodynamics of the cosmological horizon. In particular, there is the holographic connection between the entropy density integrated over the Hubble volume and the Gibbons-Hawking entropy of the horizon, $S_{\rm volume}=S_{\rm horizon}=A/4G$. We also consider the first law of thermodynamics in these two approaches. In the local thermodynamics, on the one hand, the first law is valid for an arbitrary volume $V$ of de Sitter space. On the other hand, the first law is also applicable to the thermodynamics of the horizon. In both cases, the temperature is the same. This consideration is extended to the contracting de Sitter with its negative entropy, $S_{\rm volume}=S_{\rm horizon}=-A/4G$.

gr-qc↗

arXiv2025

Proton decay in de Sitter environment

The decay of proton in the de Sitter environment is governed by the temperature $T=H/π$, where $H$ is the Hubble parameter. This temperature is twice larger than the Gibbons-Hawking temperature $T_{\rm GH}=H/2π$. This demonstrates the physical difference of two processes. The temperature $T=H/π$ determines the proton decay rate in the local process which takes well inside the cosmological horizon. While the Gibbons-Hawking temperature can be related to the processes which involve the Hawking photons or other particles radiated from the cosmological horizon. The same temperature $T=H/π$ determines the radiation of electron-positron pairs by positron or by other object in the de Sitter environment. Creation of matter and its thermalization in the de Sitter heat bath leads to the energy exchange between matter and quantum vacuum and finally to the decay of the de Sitter state towards the Minkowski vacuum. The lesson for the Unruh effect is also discussed. One may expect the similar separation of effects governed by two different temperatures: the effects related to the Rindler horizon with the Unruh temperature $T_{\rm U}=a/2π$ and the local radiation with $T=a/π=2T_{\rm U}$.

gr-qc↗

arXiv2024

Tsallis-Cirto entropy of black hole and black hole atom

The quantum tunneling processes related to the black hole determine the black hole thermodynamics. The Hawking temperature is determined by the quantum tunneling processes of radiation of particles from the black hole. On the other hand, the Bekenstein-Hawking entropy of the black hole is obtained by consideration of the macroscopic quantum tunneling processes of splitting of black hole to the smaller black holes. These tunneling processes also determine the composition rule for the black hole entropy, which coincides with the composition rule for the nonextensive Tsallis-Cirto $δ=2$ entropy. This composition rule suggests that the mass spectrum of the black hole is equidistant, $M=NM_0$. Here $N$ is an integer number and $M_0=\sqrt{2}m_{\rm P}$ is the mass quantum expressed via the reduced Planck mass $m_{\rm P}$. The Bekenstein-Hawking entropy of the black hole with mass $M=NM_0$ is $S_{\rm BH}(N)=N^2$.

physics.gen-ph↗

arXiv2024

Schwinger vs Unruh

It is shown that the temperatures which characterise the Unruh effect, the Gibbons-Hawking radiation from the de Sitter cosmological horizon and the Hawking radiation from the black hole horizon acquire the extra factor 2 compared with their traditional values. The reason for that is the coherence of different processes. The combination of the coherent processes also allows us to make the connection between the Schwinger pair production and the Unruh effect.

gr-qc↗