Entropy Of Matter Research Articles

Relic gravitational waves and the generalized second law

The generalized second law of gravitational thermodynamics is applied to the present era of accelerated expansion of the Universe. In spite of the fact that the entropy of matter and relic gravitational waves inside the event horizon diminish, the mentioned law is fulfilled provided that the expression for the entropy density of the gravitational waves satisfies a certain condition.

Simple sufficient conditions for the generalized covariant entropy bound

The generalized covariant entropy bound is the conjecture that for any null hypersurface which is generated by geodesics with nonpositive expansion starting from a spacelike 2-surface B and ending in a spacelike 2-surface ${B}^{\ensuremath{'}},$ the matter entropy on that hypersurface will not exceed one quarter of the difference in areas, in Planck units, of the two spacelike 2-surfaces. We show that this bound can be derived from the following phenomenological assumptions: (i) matter entropy can be described in terms of an entropy current ${s}_{a};$ (ii) the gradient of the entropy current is bounded by the energy density, in the sense that $|{k}^{a}{k}^{b}{\ensuremath{\nabla}}_{a}{s}_{b}|<~2\ensuremath{\pi}{T}_{\mathrm{ab}}{k}^{a}{k}^{b}/\ensuremath{\Elzxh}$ for any null vector ${k}^{a}$ where ${T}_{\mathrm{ab}}$ is the stress energy tensor; and (iii) the entropy current ${s}_{a}$ vanishes on the initial 2-surface B. We also show that the generalized Bekenstein bound---the conjecture that the entropy of a weakly gravitating isolated matter system will not exceed a constant times the product of its mass and its width---can be derived from our assumptions. Though we note that any local description of entropy has intrinsic limitations, we argue that our assumptions apply in a wide regime. We closely follow the framework of an earlier derivation, but our assumptions take a simpler form, making their validity more transparent in some examples.

Holography in a radiation-dominated universe with a positive cosmological constant

We discuss the holographic principle in a radiation-dominated, closed Friedmann-Robertson-Walker (FRW) universe with a positive cosmological constant. By introducing a cosmological D-bound on the entropy of matter in the universe, we can write the Friedmann equation governing the evolution of the universe in the form of the Cardy formula. When the cosmological D-bound is saturated, the Friedmann equation coincides with the Cardy-Verlinde formula describing the entropy of radiation in the universe. As a concrete model, we consider a brane universe in the background of Schwarzschild-de Sitter black holes. It is found that the cosmological D-bound is saturated when the brane crosses the black hole horizon of the background. At that moment, the Friedmann equation coincides with the Cardy-Verlinde formula describing the entropy of radiation matter on the brane.

Magnetic Protoneutron Star Winds and [CLC][ITAL]r[/ITAL][/CLC]-Process Nucleosynthesis

Because of their neutron richness and association with supernovae, postexplosion protoneutron star winds are thought to be a likely astrophysical site for rapid neutron-capture nucleosynthesis (the r-process). However, the most recent models of spherical neutrino-driven protoneutron star winds do not produce robust r-process nucleosynthesis for canonical neutron stars with a gravitational mass of 1.4 M☉ and coordinate radius of 10 km. These models fail variously; the flow entropy is too low, the electron fraction is too high, or the dynamical expansion timescale is too long. To date, no models have included the effects of an ordered dipole magnetic field. We show that a strong magnetic field can trap the outflow in the neutrino heating region, thus leading to much higher matter entropy. We estimate both the trapping timescale and the resulting entropy amplification. For sufficiently large energy deposition rates, the trapped matter emerges dynamically from the region of closed magnetic field lines and escapes to infinity. We find that ordered dipoles with surface fields of 6 × 1014 G increase the asymptotic entropy sufficiently for robust r-process nucleosynthesis.

The strong and weak holographic principles

We review the different proposals which have so far been made for the holographic principle and the related entropy bounds and classify them into the strong, null and weak forms. These are analyzed, with the aim of discovering which may hold at the level of the full quantum theory of gravity. We find that only the weak forms, which constrain the information available to observers on boundaries, are implied by arguments using the generalized second law. The strong forms, which go further and posit a bound on the entropy in spacelike regions bounded by surfaces, are found to suffer from serious problems, which give rise to counterexamples already at the semiclassical level. The null form, proposed by Fischler, Susskind, Bousso and others, in which the bound is on the entropy of certain null surfaces, appears adequate at the level of a bound on the entropy of matter in a single background spacetime, but attempts to include the gravitational degrees of freedom encounter serious difficulties. Only the weak form seems capable of holding in the full quantum theory. The conclusion is that the holographic principle is not a relationship between two independent sets of concepts: bulk theories and measures of geometry vrs boundary theories and measures of information. Instead, it is the assertion that in a fundamental theory the first set of concepts must be completely reduced to the second.

Generalized second law of black hole thermodynamics and quantum information theory

We propose a quantum version of a gedanken experiment which supports the generalized second law of black hole thermodynamics. A quantum measurement of particles in the region outside of the event horizon decreases the entropy of the outside matter due to the entanglement of the inside and outside particle states. This decrease is compensated, however, by the increase in the detector entropy. If the detector is conditionally dropped into the black hole depending on the experimental outcome, the decrease of the matter entropy is more than compensated by the increase of the black hole entropy via the increase of the black hole mass which is ultimately attributed to the work done by the measurement.

Positive vacuum energy and the N-bound

We argue that the total observable entropy is bounded by the inverse of the cosmological constant. This holds for all space-times with a positive cosmological constant, including cosmologies dominated by ordinary matter, and recollapsing universes. The argument involves intermediate steps which may be of interest in their own right. We note that entropy cannot be observed unless it lies both in the past and in the future of the observer's history. This truncates space-time to a diamond-shaped subset well-suited to the application of the covariant entropy bound. We further require, and derive, a novel Bekenstein-like bound on matter entropy in asymptotically de Sitter spaces. Our main result lends support to the proposal that universes with positive cosmological constant are described by a fundamental theory with only a finite number of degrees of freedom.

Numerical Uncertainties in the Simulation of Reversible Isentropic Processes and Entropy Conservation

Abstract A challenge common to weather, climate, and seasonal numerical prediction is the need to simulate accurately reversible isentropic processes in combination with appropriate determination of sources/sinks of energy and entropy. Ultimately, this task includes the distribution and transport of internal, gravitational, and kinetic energies, the energies of water substances in all forms, and the related thermodynamic processes of phase changes involved with clouds, including condensation, evaporation, and precipitation processes. All of the processes noted above involve the entropies of matter, radiation, and chemical substances, conservation during transport, and/or changes in entropies by physical processes internal to the atmosphere. With respect to the entropy of matter, a means to study a model’s accuracy in simulating internal hydrologic processes is to determine its capability to simulate the appropriate conservation of potential and equivalent potential temperature as surrogates of dry and moi...

Cosmology versus holography

The most radical version of the holographic principle asserts that all information about physical processes in the world can be stored on its surface. This formulation is at odds with inflationary cosmology, which implies that physical processes in our part of the universe do not depend on the boundary conditions. Also, there are some indications that the radical version of the holographic theory in the context of cosmology may have problems with unitarity and causality. Another formulation of the holographic principle, due to Fischler and Susskind, implies that the entropy of matter inside the post-inflationary particle horizon must be smaller than the area of the horizon. Their conjecture was very successful for a wide class of open and flat universes, but it did not apply to closed universes. Bak and Rey proposed a different holographic bound on entropy which was valid for closed universes of a certain type. However, as we will show, neither proposal applies to open, flat and closed universes with matter and a small negative cosmological constant. We will argue, in agreement with Easther, Lowe, and Veneziano, that whenever the holographic constraint on the entropy inside the horizon is valid, it follows from the Bekenstein-Hawking bound on the black hole entropy. These constraints do not allow one to rule out closed universes and other universes which may experience gravitational collapse, and do not impose any constraints on inflationary cosmology.

Unconstrained Hamiltonian formulation of general relativity with thermo-elastic sources

A new formulation of the Hamiltonian dynamics of the gravitational field interacting with (non-dissipative) thermo-elastic matter is discussed. It is based on a gauge condition which allows us to encode the six degrees of freedom of the `gravity + matter'-system (two gravitational and four thermo-mechanical ones), together with their conjugate momenta, in the Riemannian metric and its conjugate ADM momentum . These variables are not subject to constraints. We prove that the Hamiltonian of this system is equal to the total matter entropy. It generates uniquely the dynamics once expressed as a function of the canonical variables. Any function U obtained in this way must fulfil a system of three, first-order, partial differential equations of the Hamilton - Jacobi type in the variables . These equations are universal and do not depend upon the properties of the material: its equation of state enters only as a boundary condition. The well posedness of this problem is proved. Finally, we prove that for vanishing matter density, the value of U goes to infinity almost everywhere and remains bounded only on the vacuum constraints. Therefore the constrained, vacuum Hamiltonian (zero on constraints and infinity elsewhere) can be obtained as the limit of a `deep potential well' corresponding to non-vanishing matter. This unconstrained description of Hamiltonian general relativity can be useful in numerical calculations as well as in the canonical approach to quantum gravity.

Kinetic theory of fluidized granular matter

In this paper, we present a statistical treatment of fluidized, elastic granular matter and a kinetic equation that describes the evolution of macroscopic properties of such matter. The present kinetic theory recognizes that the effects of excluded volume become dominant in the dynamic evolution of an assembly of granules and accordingly takes them into account in the formulation. On the basis of the equilibrium solution of the kinetic equation, a thermodynamics-like mathematical structure is constructed for the Boltzmann entropy of granular matter. The meaning of temperature in this mathematical structure is fixed by the shear rate. The equilibrium solution is shown to yield a density distribution comparable with the experimental data of Clement et al. [Europhys. Lett. 16, 133 (1991)]. The shear viscosity of granular matter is shown to increase with the packing fraction. This behavior is in qualitative agreement with experimental result by Hanes et al. [J. Fluid Mech. 150, 357 (1985)]. The viscosity also increases with the shear rate since the 'temperature' increases with the shear rate in the case of granular matter. Consequently, the granular matter is shown to be dilatant, as is experimentally known.

Entropy for extremal Reissner-Nordstrom black holes

We find in the brick wall model that the entropy of scalar matter in an extremal Reissner-Nordstrom background does not vanish and in fact has a stronger divergence than usual. We also interpret earlier results on the classical action of these black holes to argue that the mass may be a measure of the gravitational entropy, somewhat like in string models.

Horizon divergences of fields and strings in black hole backgrounds.

General arguments based on curved space-time thermodynamics show that any extensive quantity, like the free energy or the entropy of thermal matter, always has a divergent boundary contribution in the presence of event horizons, and this boundary term comes with the Hawking-Bekenstein form. Although the coefficients depend on the particular geometry we show that intensive quantities, like the free energy density are universal in the vicinity of the horizon. {} From the point of view of the matter degrees of freedom this divergence is of infrared type rather than ultraviolet, and we use this remark to speculate about the fate of these pathologies in String Theory. Finally we interpret them as instabilities of the Canonical Ensemble with respect to gravitational collapse via the Jeans mechanism.

Entropy production and kinetic effects of light.

We study the production of total entropy in the situation where light has kinetic effects on atoms or molecules. The radiation entropy has the standard form of boson entropy, and the matter entropy is the sum of Boltzmann entropies for excited and nonexcited particles. The matter entropy density is separated into three parts, corresponding to the total velocity distribution, the distribution over internal states, and the correlation between the two. Each of these parts can be changed by the interaction with light. We calculate explicitly the production of both matter and photon entropy in several cases where light is known to induce macroscopic flows in gases. The production rate of matter entropy is expressed in macroscopic quantities. Some other examples, such as laser cooling, are considered briefly. In all cases, the increase of photon entropy is found to be several orders of magnitude larger than the decrease of matter entropy.

Nonsingular cosmological model with matter creation and entropy production

The study of nonsingular cosmological models [4] based on a theory of gravitation in flat space-times [1] is continued. For a radiation free universe the solution of the model is given analytically. Under the assumption that entropy cannot decrease the cosmological constant must be zero. At the beginning of the universe all energy is in the form of gravitation. The universe contracts. Matter and radiation are created out of gravitational energy and entropy is produced. The contraction stops and then the universe expands without limit. The creation of matter continues producing entropy but today the production of matter and entropy is negligible. The density parameter Ω0 ≈ 1, i.e. there must be “missing mass” in the universe. The “flatness” and the “homogeneity” problem are solved.

Additivity of the Entropies of Black Holes and Matterab

The thermodynamic equilibrium between black holes and matter is characterized theoretically, summarizing the results of Martinez and York (1989). Particular attention is given to the problem of gravitational entropy and the nature of the additivity of the entropies of black holes and matter. It is concluded that no extra gravitational entropy arises as a result of the way changes in the gravitational field are produced by static minimally coupled matter, and that black-hole entropy adds directly to the entropy of matter when the two are in thermal equilibrium. The validity of interpreting S(BH) as entropy in the standard sense of statistical thermodynamics is confirmed. 11 refs.

Additivity of the entropies of black holes and matter in equilibrium.

We consider static spherical spacetimes in which a black hole is in equilibrium with surrounding matter. The grand canonical ensemble is defined by the geometry of the boundary of a region of spacetime and the chemical potential evaluated on this boundary. Additivity of the actions of gravity and matter and the principle of equivalence then jointly imply that the total entropy is the simple sum of the accepted black-hole entropy and the ordinary matter entropy. However, energy and thermodynamic potentials exhibit interaction terms and are not simply additive..

The physics of stellar core collapse

The hydrodynamics that develops during the infall of the core of a massive star at the end of its hydrostatic evolutionary epoch can have a profound effect on its subsequent dynamical history. In this paper the important processes governing the infall hydrodynamics are explored both semi-analytically and numerically with the aim of explaining the results of large-scale numerical calculations. We focus in particular on the factors responsible for reducing the mass of the inner core. These factors are found to be mainly associated with general relativistic effects and with the production, equilibration, and transport ofv e 's. Semi-leptonicv e emission and absorption are responsible for virtually all of thev e production. They dominate the energy transfer rate between matter andv e 's, but, with the rates being skewed to high energy, they are an importantv e -matter equilibrator only for the high-energy tail of thev e distribution. Neutrinoelectron scattering (NES) plays the dominant role inv e -matter equilibration with the important result that the equilibration is nearly complete by trapping. A careful examination of conditions where the onset of neutrino trapping is occurring indicates that the trapping density is a function of the enclosed mass, increasing with decreasing distance from the core center, and increasing with the extent of thev e -matter equilibration. Though not the dominant contributor to thev e -matter energy transfer rate, NES dominates the matter entropy production rate with another important result that the electron capture rate on free protons is significantly increased before trapping. The result of all of this is a greatly reduced inner core mass by the time of core turn-around. For numerical calculations employing the LLPR equation of state (or something similar), and for precollapse models having iron cores as small as 1.35M ⊙ (the smallest used by the author), this reduction of the inner core mass leads to the generation of a weak shock which fails to eject mass in a promptffashion. The effect of the small inner core mass on the subsequent dynamical history of the core is unknown.

A model of the universe free of cosmological problems

A cosmological model with an additional term Λ( x) g μν in the energy-momentum tensor is introduced. Its structure is specified by the assumption that the energy density of the universe equals its critical value. The model so determined has k = 1, is singularity-free and does not possess the horizon, entropy, monopole or cosmological-constant problems of the standard hot bang cosmology. The whole universe is found to be causally connected slightly after Planck time. There exists a period of phase transition during part of which the pressure is negative. The model displays a flow of energy from curvature to matter such that the entropy of matter is not conserved.

Impact parameter dependence of the specific entropy and the light particle yield in relativistic heavy ion collision.

The connection between the fragment yield and the associated specific entropy of participant matter produced in the course of a relativistic heavy ion collision is studied within the cascade approach. The essential impact parameter dependence of the fragment yield indicates that the specific entropy increases with impact parameter and that the breakup density is the larger the more central the collision process is. The results show that the bulk equilibrium limit for the entropy production is not reached for such heavy systems as Nb+Nb at 400 MeV/nucleon and that the finite size effects and the dynamical freeze-out process are dominant factors in determining the cluster abundances.