Entropy Of Quantum State Research Articles

Hypergraph min-cuts from quantum entropies

The von Neumann entropy of pure quantum states and the min-cut function of weighted hypergraphs are both symmetric submodular functions. In this article, we explain this coincidence by proving that the min-cut function of any weighted hypergraph can be approximated (up to an overall rescaling) by the entropies of quantum states known as stabilizer states. We do so by constructing a novel ensemble of random quantum states, built from tensor networks, whose entanglement structure is determined by a given hypergraph. This implies that the min-cuts of hypergraphs are constrained by quantum entropy inequalities, and it follows that the recently defined hypergraph cones are contained in the quantum stabilizer entropy cones, which confirms a conjecture made in the recent literature.

Entropy of Quantum States

Given the algebra of observables of a quantum system subject to selection rules, a state can be represented by different density matrices. As a result, different von Neumann entropies can be associated with the same state. Motivated by a minimality property of the von Neumann entropy of a density matrix with respect to its possible decompositions into pure states, we give a purely algebraic definition of entropy for states of an algebra of observables, thus solving the above ambiguity. The entropy so-defined satisfies all the desirable thermodynamic properties and reduces to the von Neumann entropy in the quantum mechanical case. Moreover, it can be shown to be equal to the von Neumann entropy of the unique representative density matrix belonging to the operator algebra of a multiplicity-free Hilbert-space representation.

Quantum statistical vibrational entropy and enthalpy of formation of helium-vacancy complex in BCC W

High-temperature advance-reactor design and operation require knowledge of in-reactor materials properties far from the thermal ground state. Temperature-dependence due to the effects of lattice vibrations is important to the understanding and formulation of atomic processes involved in irradiation-damage accumulation. In this paper, we concentrate on the formation of He-V complex. The free-energy change in this regard is derived via thermodynamic integration from the phase-space trajectories generated from MD simulations based on the quantum fluctuation-dissipation relation. The change of frequency distribution of vibration modes during the complex formation is properly accounted for, and the corresponding entropy change avoids the classical ln(T) divergence that violates the third law. The vibrational enthalpy and entropy of formation calculated this way have significant effects on the He kinetics during irradiation.

Classical Statistical Entropy of Black Hole

The present article derives an expression for classical statistical entropy of black hole using Maxwell- Boltzmann statistics and shows that the classical statistical entropy is directly proportional to the area of event horizon of black hole leading the result as SbhαA(r). No primary and secondary data is used in this paper. We have designed the work similar to the work of Ren Zhao and Shuang-Qi Hu who obtained the quantum statistical entropy corresponding to the black hole horizon using Femi-Dirac & Bose-Einstein statistics. They have also shown that the entropy corresponding to the black hole horizon surface is the entropy of quantum state near the surface of the horizon. It is completely theoretical based work using Laptop done at Marwari College research laboratory and the residential research chamber of first author.

Entropy of quantum states: Ambiguities

The von Neumann entropy of a generic quantum state is not unique unless the state can be uniquely decomposed as a sum of extremal or pure states. As pointed out to us by Sorkin, this happens if the GNS representation (of the algebra of observables in some quantum state) is reducible, and some representations in the decomposition occur with non-trivial degeneracy. This non-unique entropy can occur at zero temperature. We will argue elsewhere in detail that the degeneracies in the GNS representation can be interpreted as an emergent broken gauge symmetry, and play an important role in the analysis of emergent entropy due to non-Abelian anomalies. Finally, we establish the analogue of an H-theorem for this entropy by showing that its evolution is Markovian, determined by a stochastic matrix.

A new explanation for statistical entropy of charged black hole

Using the Unruh-Verlinde temperature obtained by the idea of entropy force, we directly calculated the partition functions of Boson field in Reissner-Nordstrom spacetime with quantum statistical method. We obtain the expression of the black hole quantum statistical entropy. We find that the term is proportional to the area of black hole horizon and the logarithmic correction term appears. Our result is valid for flat spacetime.

Entanglement entropy of a black hole and isolated horizon

Using Unruh-Verlinde temperature obtained by entropic force, we directly calculate partition functions of quantum field in Schwarzschild spacetime via quantum statistical method and derive the expression of the black hole statistical entropy. In our calculation the lower limit of integral is the location of isolated horizon introduced in loop quantum gravity and the upper limit of integral is infinity. So the obtained entropy is the statistical entropy from isolated horizon to the infinite. In our calculation there are not the cutoff and approximation. The results showed that, as long as proper Immirzi parameters are selected, the entropy obtained by loop quantum gravity is consistent with the quantum statistical entropy outside the black hole horizon. Therefore the black hole entropy is a quantum entanglement entropy outside the isolated horizon.

Quantum statistical entropy of Schwarzchild-de Sitter spacetime

Using the quantum statistical method, we calculate quantum statistical entropy between the black hole horizon and the cosmological horizon in Schwarzchild spacetime and derive the expression of quantum statistical entropy in de Sitter spacetime. Under the Unruh-Verlinde temperature of Schwarzchild-de Sitter spacetime in the entropic force views, we obtain the expression of quantum statistical entropy in de Sitter spacetime. It is shown that in de Sitter spacetime quantum statistical entropy is the sum of thermodynamic entropy corresponding black hole horizon and the one corresponding cosmological horizon. And the correction term of de Sitter spacetime entropy is obtained. Therefore, it is confirmed that the black hole entropy is the entropy of quantum field outside the black hole horizon. The entropy of de Sitter spacetime is the entropy of quantum field between the black hole horizon and the cosmological horizon.

Statistical entropy of reissner-nordstrm-de sitter black hole by generalized uncertainty principle

Statistical entropy of scalar field outside Reissner-Nordstrm-de Sitter black hole is computed by the equation of state density corrected by the generalized uncertainty principle and by Wentzel-Kramers-Brillouin approximation method. The result shows that the entropy is proportional to the sum of the internal, the external and the cosmological horizon areas, which accords with these calculated by other methods. It shows internal relation between the entropy of black hole and horizon area. The entropy of black hole is the entropy of quantum state on horizon, which is a quantum effect.

Black Hole Entropy of IR Modified Hořava-Lifshitz Gravity in Quantum Statistics Perspective

In this paper we investigate quantum statistical entropy for the Kehagias-Sfetsos black hole in IR modified Hořava-Lifshitz gravity by using t’ Hooft’s brick-wall method and generalized uncertainty principle method. By carefully calculating, we obtain the brick-wall entropy SBWM=A/4 and the generalized uncertainty principle entropy SGUP=A/96πγ. It is found if we view from quantum statistics, the brick-wall entropy and generalized uncertainty principle entropy may possibly is proportional to the event horizon area. This type area entropy is also justified by Wang et al. (Phys. Rev. D 81:083006, 2010). The study of the quantum statistical entropy may shed light on the understand of Hořava-Lifshitz gravity.

Quantum statistical entropy and minimal length of 5D Ricci-flat black string with generalized uncertainty principle

In this paper, we study the quantum statistical entropy in a 5D Ricci-flat black string solution, which contains a 4D Schwarzschild-de Sitter black hole on the brane, by using the improved thin-layer method with the generalized uncertainty principle. The entropy is the linear sum of the areas of the event horizon and the cosmological horizon without any cutoff and any constraint on the bulk's configuration rather than the usual uncertainty principle. The system's density of state and free energy are convergent in the neighborhood of horizon. The small-mass approximation is determined by the asymptotic behavior of metric function near horizons. Meanwhile, we obtain the minimal length of the position {delta}x, which is restrained by the surface gravities and the thickness of layer near horizons.

Entropy of Kerr-Newman Black Hole to All Orders in the Planck Length

Using the quantum statistical method, the difficulty of solving the wave equation on the background of the black hole is avoided. We directly solve the partition functions of Bose and Fermi field on the background of an axisymmetric Kerr-Newman black hole using the new equation of state density motivated by the generalized uncertainty principle in the quantum gravity. Then near the black hole horizon, we calculate entropies of Bose and Fermi field between the black hole horizon surface and the hypersurface with the same inherent radiation temperature measured by an observer at an infinite distance. In our results there are not cutoffs and little mass approximation introduced in the conventional brick-wall method. The series expansion of the black hole entropy is obtained. And this series is convergent. It provides a way for studying the quantum statistical entropy of a black hole in a non-spherical symmetric spacetime.

The dynamic behavior of quantum statistical entropy in 5D Ricci-flat black string with thin-layer approach

In this Letter, the statistical–mechanical entropies of 5D Ricci-flat black string is calculated through the wave modes of the quantum field with improved thin-layer brick-wall method. The modes along the fifth dimension are semi-classically quantized by Randall–Sundrum mass relationship. We use the two-dimensional area to describe this black string's entropy which, in the small-mass approximation, is a linear sum of the area of the black hole horizon and the cosmological horizon. The proportionality coefficients of entropy are discretized with quantized extra dimensional modes. It should be noted that the small-mass approximation used in our calculation is naturally justified by the assumption that the two branes are located far apart.

Quantum statistical entropy corresponding to cosmic horizon in five-dimensional spacetime

The generalized uncertainty relation is introduced to calculate the quantum statistical entropy corresponding to cosmic horizon. By using the new equation of state density motivated by the generalized uncertainty relation, we discuss entropies of Bose field and Fermi field on the background of five-dimensional spacetime. In our calculation, we need not introduce cutoff. There is no divergent logarithmic term in the original brick-wall method. And it is obtained that the quantum statistical entropy corresponding to cosmic horizon is proportional to the area of the horizon. Further it is shown that the entropy corresponding to cosmic horizon is the entropy of quantum state on the surface of horizon. The black hole’s entropy is the intrinsic property of the black hole. The entropy is a quantum effect. In our calculation, by using the quantum statistical method, we obtain the partition function of Bose field and Fermi field on the background of five-dimensional spacetime. We provide a way to study the quantum statistical entropy corresponding to cosmic horizon in the higher-dimensional spacetime.

Calculating Entropy of Plane Symmetry Black Hole via Generalized Uncertainty Relation

The generalized uncertainty relation is introduced to calculate entropy of the black hole. By using quantum statistical method, we directly obtain the partition function of Bose and Fermi field on the background of the plane symmetry black hole. Then we calculate the entropy of Bose and Fermi field on the background of black hole near the horizon of the black hole. In our calculation, we need not introduce cutoff. There are not the left out term and the divergent logarithmic term in the original brick-wall method. And it is obtained that the entropy of the black hole is proportional to the area of the horizon. The inherent contact between the entropy of black hole and the area of horizon is opened out. Further it is shown the entropy of black hole is entropy of quantum state on the surface of horizon. The black hole’s entropy is the intrinsic property of the black hole. The entropy is a quantum effect.

The generalized uncertainty relation and Dirac field entropy of black hole with an internal global monopole

The generalized uncertainty relation is considered in the new equation of state density. Using the WKB approximation, Dirac field entropy of the horizon of the black hole with an internal global monopole is calculated directly. The result shows that the black hole entropy is proportional to the horizon area, which brings to light the relationship between the black hole entropy and the entropy of quantum state near the event horizon. The difference from the brick-wall model is that the present result is convergent without any cutoff. It is indicated that this method can be used to calculate the entropy of the scale field of black hole, and it can be extended to calculate the entropy of Dirac field.

Quantum Statistic Entropy of Three-Dimensional BTZ Black Hole

Using the new equation of state density motivated by the generalized uncertainty relation in the quantum gravity, we investigate entropy of a black line on the background of the three-dimensional BTZ. In our calculation, we need not introduce cutoff and can remove the divergent term in the original brick-wall method via the new equation of state density. And it is obtained that the entropy of the black line is proportional to the area of the horizon (perimeter). Further it is shown the entropy of black line is the entropy of quantum state on the surface of horizon (perimeter). The black line entropy is the intrinsic property of the black hole. The entropy is a quantum effect. By using quantum statistical method, we directly obtain the partition function of Bose field and fermi field on the background of the black line. The difficulty to solve wave equation of various particles is avoided. We offer a new simple and direct way for calculating the entropy of various spacetime black holes (black plane, black line and black column).

Quantum Statistical Entropy of Five-Dimensional BlackHole

The generalized uncertainty relation is introduced to calculatequantum statistic entropy of a black hole. By using thenew equation of state density motivated by the generalizeduncertainty relation, we discuss entropies of Bose field and Fermifield on the background of the five-dimensional spacetime. In ourcalculation, we need not introduce cutoff. There is not thedivergent logarithmic term as in the original brick-wall method. Andit is obtained that the quantum statistic entropy corresponding toblack hole horizon is proportional to the area of the horizon.Further it is shown that the entropy of black hole is the entropy ofquantum state on the surface of horizon. The black hole's entropyis the intrinsic property of the black hole. The entropy is aquantum effect. It makes people further understand the quantum statistic entropy.

Total Quantum Statistical Entropy of Reissner–Nordstrom Black Holes:in Dirac Field Case

The total quantum statistical entropy of Reissner–Nordstromblack holes in Dirac field case is evaluated in this article.The space-time of the black holes is divided into three regions:region 1 (r>ro), region 2 (ro>r>ri), andregion 3 (ri>r>0), where ro is theradius of the outer event horizon, and ri is the radius of theinner event horizon. The total quantum statistical entropy ofReissner–Nordstrom black holes is S = S1+S2+S3,where Si (i = 1,2,3) is the entropy, contributed by regions1,2,3. The detailed calculation shows that S2 is neglectfullysmall. S1 = wt(π2/45)kb(Ao/ϵ2β3), S3 = −wt(π2/45)kb(Ai/ϵ2β3),where Ao and Ai are, respectively, the areas of theouter and inner event horizons, wt = 2s[1−2−(s+1)],s = d/2, d is the space-time dimension, here d = 4, s = 2. Asri approaches ro in the extreme case the totalquantum statistical entropy of Reissner–Nordstrom black holes approaches zero.

Quantum Entropy of Black Hole with Internal Global Monopole

Using the generalized uncertainty relation, the new equation of statedensity is obtained, and then the entropy of black hole with an internalglobal monopole is discussed. The divergence that appears in black holeentropy calculation through original brick-wall model is overcome. Theresult of the direct proportion between black hole entropy and its eventhorizon area is drawn and given. The result shows that the black holeentropy must be the entropy of quantum state near the event horizon.