Dissipative Diamagnetism—A Case Study for Equilibrium and Nonequilibrium Statistical Mechanics

Using the path integral approach to equilibrium statistical physics the effect of dissipation on Landau diamagnetism is calculated. The calculation clarifies the essential role of the boundary of the container in which the electrons move. Further, the derived result for diamagnetization also matches with the expression obtained from a time-dependent quantum Langevin equation in the asymptotic limit, provided a certain order is maintained in taking limits. This identification then unifies equilibrium and nonequilibrium statistical physics for a phenomenon like diamagnetism, which is inherently quantum and strongly dependent on boundary effects. In addition we have shown that our results are directly connected with fluctuation induced diamagnetic susceptibility of superconducting grains. PACS Number: 03.65.Yz, 05.20.-y, 05.20.Gg, 05.40.-a, 75.20.-g     

Rotational statistics and thermodynamic functions of hydrogen peroxide

Partition functions for both the rotational modes (hindered internal rotation and overall rotation) of the hydrogen peroxide (H₂O₂) molecule in the ground electronic state are studied using quantum and classical Gibbsian statistical mechanics. The partition functions are used to calculate rotational thermodynamic functions (internal energy, enthalpy, Helmholtz free energy, Gibbs free energy and entropy) of a hydrogen peroxide gas of weakly interacting molecules at temperatures above 300 K.     

Letter: Quantum Statistical Entropy of d-Dimensional Horowitz–Strominger Black Hole

By using the method of quantum statistics, we derive directly the partition functions of bosonic and fermionic field in the d-dimensional Horowitz-Strominger black hole. The statistical entropy of black hole is obtained by an improved brick—wall method. When we choose proper parameter in our results, we can obtain that the entropy of the black hole is proportional to the area of the horizon. In our result, there don't exist the left out term and divergent logarithmic term given in the original brick—wall method. We avoid the difficulty in solving the wave equation of scalar and Dirac field. And we offer a simple and direct way of studying entropy of the higher-dimensional complicated black hole.     

General constraints on the ionic eos

Abstract

From statistical mechanics one obtains exactly, relative to zeros of energy and entropy at zero temperature, several terms in the high-temperature expansion for the ionic contribution to the equation of state. By standard thermodynamics we relate the temperature independent terms of the high-temperature expansion for the entropy and internal energy to the -1 and 0 moments, respectively, of the specific heat. If we assume that we understand the solid region, this exact high-temperature information then paradoxically constrains the area and general shape of the specific heat curve in the difficult region above melting but below ideal gas. We outline this reasoning and a model that realizes the constraints.     

Quantum shape effects and novel thermodynamic behaviors at nanoscale

Thermodynamic properties of confined systems depend on sizes of the confinement domain due to quantum nature of particles. Here we show that shape also enters as a control parameter on thermodynamic state functions. By considering specially designed confinement domains, we demonstrate how shape effects alone modify Helmholtz free energy, entropy and internal energy of a confined system. We propose an overlapped quantum boundary layer method to analytically predict quantum shape effects without even solving Schrödinger equation or invoking any other mathematical tools. Thereby we reduce a thermodynamic problem into a simple geometric one and reveal the profound link between geometry and thermodynamics. We report also a torque due to quantum shape effects. Furthermore, we introduce isoformal, shape preserving, process which opens the possibility of a new generation of thermodynamic cycles operating at nanoscale with unique features.     

Thermodynamic properties and the approximate solutions of the Schrödinger equation with the shifted Deng–Fan potential model

With the introduction of a new improved approximation scheme (Pekeris-type approximation) to deal with the centrifugal term, the energy eigenvalues and the wave functions of the Schrödinger equation of the shifted Deng–Fan molecular potential are obtained, via the asymptotic iteration method. Rotational–vibrational energy eigenvalues of some diatomic molecules are presented, these results are in good agreement with other results in the literature. For these selected diatomic molecules, energy eigenvalues obtained are in much better agreement with the results obtained from the rotating Morse potential model for moderate values of rotational and vibrational quantum numbers. Furthermore, thermodynamic properties such as the vibrational mean U, specific heat C, free energy F and entropy S for the pure vibrational state in the classical limit for these energy eigenvalues are studied.     

Quantum State Merging and Negative Information

We consider a quantum state shared between many distant locations, and define a quantum information processing primitive, state merging, that optimally merges the state into one location. As announced in [Horodecki, Oppenheim, Winter, Nature 436, 673 (2005)], the optimal entanglement cost of this task is the conditional entropy if classical communication is free. Since this quantity can be negative, and the state merging rate measures partial quantum information, we find that quantum information can be negative. The classical communication rate also has a minimum rate: a certain quantum mutual information. State merging enabled one to solve a number of open problems: distributed quantum data compression, quantum coding with side information at the decoder and sender, multi-party entanglement of assistance, and the capacity of the quantum multiple access channel. It also provides an operational proof of strong subadditivity. Here, we give precise definitions and prove these results rigorously.     

Statistical-Mechanical Entropy of Garfinkle-Horowitz-Strominger Black Hole

Taking WKB approximation to solve the scalar field equation in the Garfinkle-Horowitz-Strominger (GHS) black hole spacetime, we can get the classical momenta. Substituting the classical momenta into state density equation corrected by the generalized uncertainty principle, we will obtain the number of quantum states with energy less than ω. It is convergent in the neighborhood of the horizon. Then, it is used to calculate the statistical-mechanical entropy of the scalar field in the GHS black hole spacetime. The calculation shows that the entropy is proportional to the horizon area.     

Nonlinear Dynamics and Fluctuations of Dissipative Toda Chains

The dynamics of a ring of masses including dissipative forces (passive or active friction) and Toda interactions between the masses is investigated. The characteristic attractor structure and the influence of noise by coupling to a heat bath are studied. The system may be driven from the thermodynamic equilibrium to far from equilibrium states by including negative friction. We show, that over-critical pumping with free energy may lead to a partition of the phase space into attractor regions corresponding to several types of collective motions including uniform rotations, one- and multiple soliton-like excitations and relative oscillations. The distribution functions in the phase space and the correlation functions of the forces and the spectra of nonlinear excitations are calculated. We show that a finite-size Toda ring with weak thermal coupling develops at intermediate temperatures a broadband colored noise spectrum with an 1/f tail at low frequencies.     

Ambiguities on the Quantization of a One-Dimensional Dissipative System with Position Depending Dissipative Coefficient

For a one-dimensional dissipative system with position depending coefficient, two constant of motion are deduce. These constants of motion bring about two Hamiltonians to describe the dynamics of same classical system. However, their quantization describe the dynamics of two completely different quantum systems. PACS numbers: 03.20.+i; 03.30.+ p; 03.65.-w     

Correction to Entropy of Schwarzschild Black Hole by Modified Dispersion Relation

Taking WKB approximation to solve the scalar field equation in the Schwarzschild black hole spacetime, we can get the classical momenta. Substituting the classical momenta into state density equation corrected by the modified dispersion relation, we will obtain the number of quantum states with energy less than ω. Then, it is used to calculate the statistical-mechanical entropy of the scalar field in the Schwarzschild black hole spacetime. By taking exact method, we obtained the leader term of entropy which is proportional to the event horizon area and correction terms take the forms of ln A, A ⁻¹ln A, A ⁻¹ and so on.     

Growing Classical and Quantum Entropies in the Early Universe

Following the idea that the global and local arrow of time has a cosmological origin, we define an entropy in the classical and in the quantum periods of the universe evolution. For the quantum period a semi-classical approach is adopted, modelling the universe with Wheeler-De Witt equation and using WKB. By applying the self-induced decoherence to the state of the universe it is proved that the quantum universe becomes a classical one. This allows us to define a conditional entropy which, in our simplified model, is proportional to e ^{2γ t} where γ is the dumping factor associated with the interaction potential of the scalar fields. Finally we find both Gibbs and thermodynamical entropy of the universe based in the conditional entropy.     

Dissipative or just nonextensive hydrodynamics? — Nonextensive/dissipative correspondence

We argue that there is correspondence between the perfect nonextensive hydrodynamics and the usual dissipative hydrodynamics, which we call nonextensive/dissipative correspondence (NexDC). It leads to simple expression for dissipative entropy current and allows for predictions for the ratio of bulk and shear viscosities to entropy density, ζ/s and η/F.     

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). PACS 04.20.Dw; 97.60.Lf     

Adiabatic Theorems and Reversible Isothermal Processes

Isothermal processes of a finitely extended, driven quantum system in contact with an infinite heat bath are studied from the point of view of quantum statistical mechanics. Notions like heat flux, work and entropy are defined for trajectories of states close to, but distinct from states of joint thermal equilibrium. A theorem characterizing reversible isothermal processes as quasi-static processes (“isothermal theorem”) is described. Corollaries concerning the changes of entropy and free energy in reversible isothermal processes and on the 0th law of thermodynamics are outlined.*Supported by the Swiss National Foundation.     

The Free Energy and Entropy of Schwarzschild Black Hole Due to Scalar Field

Using the thin film brick-wall model,taking into account the effect of the generalized uncertainty principle on the equation of the density of the states, we calculate the free energy and entropy of schwarzschild black hole due to scalar field, we obtain the entropy proportional to the event horizon area without cutoff. This implies that quantum theory of gravity can remove the divergence of the state density on the event horizon and avoid the cutoff in the original brick-wall model, these results also mean that the thin film brick-wall model is universal. PACS: 0420;9760L.     

Dissipative Future Universe Without Big Rip

The present study deals with dissipative future universe without big rip in context of Eckart formalism. The generalised Chaplygin gas, characterised by equation of state p=-\fracAr^\frac1ap=-\frac{A}{\rho^{\frac{1}{\alpha}}}, has been considered as a model for dark energy due to its dark-energy-like evolution at late time. It is demonstrated that, if the cosmic dark energy behaves like a fluid with equation of state p=ωρ; ω<−1 as well as Chaplygin gas simultaneously then the big rip problem does not arise and the scale factor is found to be regular for all time.     

Generalized Teleportation of a <Emphasis Type="Italic">d</Emphasis>-Level <Emphasis Type="Italic">N</Emphasis>-Particle GHZ State with One Pair of Entangled Particles as the Quantum Channel

With one pair of entangled particles as the quantum channel, we present an explicit generalized protocol for perfectly teleporting a d-level N-particle GHZ state from a sender to a receiver. This protocol has the advantage of transmitting much less particles and classical information for teleporting the d-level N-particle GHZ state than others.