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PubMed2000

Causal entropy bound for a spacelike region.

The identification of a causal-connection scale motivates us to propose a new covariant bound on entropy within a generic spacelike region. This "causal entropy bound," scaling as sqrt[EV], and thus lying around the geometric mean of Bekenstein's S/ER and holographic S/A bounds, is checked in various "critical" situations. In the case of limited gravity, Bekenstein's bound is the strongest while naive holography is the weakest. In the case of strong gravity, our bound and Bousso's holographic bound are stronger than Bekenstein's, while naive holography is too tight, and hence typically wrong.

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PubMed2000

Decoherence and the rate of entropy production in chaotic quantum systems

We show that for an open quantum system which is classically chaotic (a quartic double well with harmonic driving coupled to a sea of harmonic oscillators) the rate of entropy production has, as a function of time, two relevant regimes: For short times it is proportional to the diffusion coefficient (fixed by the system-environment coupling strength). For longer times (but before equilibration) there is a regime where the entropy production rate is fixed by the Lyapunov exponent. The nature of the transition time between both regimes is investigated.

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PubMed2000

Entropy and holography constraints for inhomogeneous universes.

We calculated the entropy of a class of inhomogeneous dust universes. Allowing spherical symmetry, we proposed a holographic principle by reflecting all physical freedoms on the surface of the apparent horizon. In contrast to flat homogeneous counterparts, the principle may break down in some models. We refined fractal parabolic solutions to have a reasonable entropy value for the present observable universe and found that the holographic principle always holds in the realistic cases.

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PubMed2001

Causal boundary entropy from horizon conformal field theory.

The effective quantum theory of near horizon regions of classical four-dimensional spatially flat, Friedman-Robertson-Walker spacetimes is shown to be approximately a two-dimensional conformal field theory. The central charge and expectation value of the Hamiltonian of this theory, and the statistical entropy of horizon states which can be calculated using Cardy's formula, are all proportional to the horizon area in units of Newton's constant. The proportionality constant which is determined by Planck scale physics can be fixed such that the entropy is equal to a quarter of the horizon area in units of Newton's constant, in agreement with thermodynamic considerations.

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PubMed2002

Statistical interpretation of the Bekenstein entropy for systems with a stretched horizon.

For the two-charge extremal holes in string theory we show that the Bekenstein entropy obtained from the area of the stretched horizon has a statistical interpretation as a "coarse graining entropy": different microstates give geometries that differ near r = 0, and the stretched horizon cuts off the metric at r = b where these geometries start to differ.

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PubMed2002

Near-horizon conformal symmetry and black hole entropy.

Near an event horizon, the action of general relativity acquires a new asymptotic conformal symmetry. For two-dimensional dilaton gravity, this symmetry results in a chiral Virasoro algebra, and Cardy's formula for the density of states reproduces the Bekenstein-Hawking entropy. This lends support to the notion that black hole entropy is controlled universally by conformal symmetry near the horizon.

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PubMed2003

Quasinormal modes, the area spectrum, and black hole entropy.

The results of loop quantum gravity concerning geometric operators and black hole entropy are beset by an ambiguity labeled by the Immirzi parameter. We use a result from classical gravity concerning the quasinormal mode spectrum of a black hole to fix this parameter in a new way. As a result we arrive at the Bekenstein-Hawking expression of A/4l(2)(P) for the entropy of a black hole and in addition see an indication that the appropriate gauge group of quantum gravity is SO(3) and not its covering group SU(2).

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PubMed2003

d-dimensional black hole entropy spectrum from quasinormal modes.

Starting from recent observations about quasinormal modes, we use semiclassical arguments to derive the Bekenstein-Hawking entropy spectrum for d-dimensional spherically symmetric black holes. We find that, as first suggested by Bekenstein, the entropy spectrum is equally spaced: S(BH)=kln((m(0))n, where m(0) is a fixed integer that must be derived from the microscopic theory. As shown in O. Dreyer, gr-qc/0211076, 4D loop quantum gravity yields precisely such a spectrum with m(0)=3 providing the Immirzi parameter is chosen appropriately. For d-dimensional black holes of radius R(H)(M), our analysis predicts the existence of a unique quasinormal mode frequency in the large damping limit omega((d))(M)=alpha((d))c/R(H)(M) with coefficient [formula: see text], where m(0) is an integer.

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PubMed2003

Mass, action, and entropy of Taub-Bolt-de Sitter spacetimes.

We apply a recent proposal for defining conserved mass in asymptotically de Sitter spacetimes to the class of Taub-Bolt-de Sitter spacetimes. We compute the action, entropy, and conserved mass of these spacetimes, and find that in certain instances the mass and entropy can exceed that of pure de Sitter spacetime, in violation of recent suggestive conjectures to the contrary.

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PubMed2003

Shannon entropy as an indicator of atomic avoided crossings in strong parallel magnetic and electric fields.

Avoided crossings are the most distinctive atomic spectroscopic features in the presence of magnetic and electric fields. We point out the role of Shannon's information entropy as an indicator or predictor of these phenomena by studying the dynamics of some excited states of hydrogen in the presence of parallel magnetic and electric fields. Moreover, in addition to the well-known energy level repulsion, it is found that Shannon's entropy manifests the informational exchange of the involved states as the magnetic field strength is varied across the narrow region where an avoided crossing occurs.

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PubMed2004

Universal canonical black hole entropy.

Nonrotating black holes in three and four dimensions are shown to possess a canonical entropy obeying the Bekenstein-Hawking area law together with a leading correction (for large horizon areas) given by the logarithm of the area with a universal finite negative coefficient, provided one assumes that the quantum black hole mass spectrum has a power-law relation with the quantum area spectrum found in nonperturbative canonical quantum general relativity. The thermal instability associated with asymptotically flat black holes appears in the appropriate domain for the index characterizing this power-law relation, where the canonical entropy (free energy) is seen to turn complex.

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PubMed2004

Information entropy in cosmology.

The effective evolution of an inhomogeneous cosmological model may be described in terms of spatially averaged variables. We point out that in this context, quite naturally, a measure arises which is identical to a fluid model of the Kullback-Leibler relative information entropy, expressing the distinguishability of the local inhomogeneous mass density field from its spatial average on arbitrary compact domains. We discuss the time evolution of "effective information" and explore some implications. We conjecture that the information content of the Universe-measured by relative information entropy of a cosmological model containing dust matter-is increasing.

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PubMed2004

Boundary entropy of one-dimensional quantum systems at low temperature.

The boundary beta function generates the renormalization group acting on the universality classes of one-dimensional quantum systems with boundary which are critical in the bulk but not critical at the boundary. We prove a gradient formula for the boundary beta function, expressing it as the gradient of the boundary entropy s at fixed nonzero temperature. The gradient formula implies that s decreases under renormalization, except at critical points (where it stays constant). At a critical point, the number exp((s) is the "ground-state degeneracy," g, of Affleck and Ludwig, so we have proved their long-standing conjecture that g decreases under renormalization, from critical point to critical point. The gradient formula also implies that s decreases with temperature, except at critical points, where it is independent of temperature. It remains open whether the boundary entropy is always bounded below.

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PubMed2004

Maximum Renyi entropy principle for systems with power-law Hamiltonians.

The Renyi distribution ensuring the maximum of Renyi entropy is investigated for a particular case of a power-law Hamiltonian. Both Lagrange parameters alpha and beta can be eliminated. It is found that beta does not depend on a Renyi parameter q and can be expressed in terms of an exponent kappa of the power-law Hamiltonian and an average energy U. The Renyi entropy for the resulting Renyi distribution reaches its maximal value at q=1/(1+kappa) that can be considered as the most probable value of q when we have no additional information on the behavior of the stochastic process. The Renyi distribution for such q becomes a power-law distribution with the exponent -(kappa+1). When q=1/(1+kappa)+epsilon (0<epsilon<<1) there appears a horizontal head part of the Renyi distribution that precedes the power-law part. Such a picture corresponds to some observed phenomena.

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PubMed2005

Curie law, entropy excess, and superconductivity in heavy fermion metals and other strongly interacting fermi liquids.

Low-temperature thermodynamic properties of strongly interacting Fermi liquids with a fermion condensate are investigated. We demonstrate that the spin susceptibility of these systems exhibits the Curie-Weiss law, and the entropy contains a temperature-independent term. The excessive entropy is released at the superconducting transition, enhancing the specific heat jump deltaC and rendering it proportional to the effective Curie constant. The theoretical results are favorably compared with the experimental data on the heavy-fermion metal CeCoIn5, as well as 3He films.

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PubMed2006

Boundary effects in the critical scaling of entanglement entropy in 1D systems.

We present exact diagonalization and density matrix renormalization group results for the entanglement entropy of critical spin-1/2 XXZ chains. We find that open boundary conditions induce an alternating term in both the energy density and the entanglement entropy which are approximately proportional, decaying away from the boundary with a power law. The power varies with anisotropy along the critical line and is corrected by a logarithmic factor, which we calculate analytically, at the isotropic point. A heuristic resonating valence bond explanation is suggested.

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PubMed2006

Nonanalyticities of entropy functions of finite and infinite systems.

In contrast to the canonical ensemble where thermodynamic functions are smooth for all finite system sizes, the microcanonical entropy can show nonanalytic points also for finite systems. The relation between finite and infinite system nonanalyticities is illustrated by means of a simple classical spinlike model which is exactly solvable for both finite and infinite system sizes, showing a phase transition in the latter case. The microcanonical entropy is found to have exactly one nonanalytic point in the interior of its domain. For all finite system sizes, this point is located at the same fixed energy value epsilon(c)(finite), jumping discontinuously to a different value epsilon(c)(infinite) in the thermodynamic limit. Remarkably, epsilon(c)(finite) equals the average potential energy of the infinite system at the phase transition point. The result indicates that care is required when trying to infer infinite system properties from finite system nonanalyticities.

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PubMed2006

Configurational electronic entropy and the phase diagram of mixed-valence oxides: the case of LixFePO4.

We demonstrate that configurational electronic entropy, previously neglected, in ab initio thermodynamics of materials can qualitatively modify the finite-temperature phase stability of mixed-valence oxides. While transformations from low-T ordered or immiscible states are almost always driven by configurational disorder (i.e., random occupation of lattice sites by multiple species), in FePO4-LiFePO4 the formation of a solid solution is almost entirely driven by electronic rather than ionic configurational entropy. We argue that such an electronic entropic mechanism may be relevant to most other mixed-valence systems.

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