Representation of Nonequilibrium Steady States in Large Mechanical Systems

Recently a novel concise representation of the probability distribution of heat conducting nonequilibrium steady states was derived. The representation is valid to the second order in the “degree of nonequilibrium”, and has a very suggestive form where the effective Hamiltonian is determined by the excess entropy production. Here we extend the representation to a wide class of nonequilibrium steady states realized in classical mechanical systems where baths (reservoirs) are also defined in terms of deterministic mechanics. The present extension covers such nonequilibrium steady states with a heat conduction, with particle flow (maintained either by external field or by particle reservoirs), and under an oscillating external field. We also simplify the derivation and discuss the corresponding representation to the full order.     

High-temperature expansion for nonequilibrium steady states in driven lattice gases

We develop a controlled high-temperature expansion for nonequilibrium steady states of the driven lattice gas, the "Ising model" for nonequilibrium physics. We represent the steady state as P(eta) alpha e(-betaH(eta)-psi(eta)) and evaluate the lowest order contribution to the nonequilibrium effective interaction psi(eta). We see that, in dimensions d > or = 2, all models with nonsingular transition rates yield the same summable psi(eta), suggesting the possibility of describing the state as a Gibbs state similar to equilibrium. The models with the Metropolis rule show exceptional behavior.     

Steady State Thermodynamics

The present paper reports our attempt to search for a new universal framework in nonequilibrium physics. We propose a thermodynamic formalism that is expected to apply to a large class of nonequilibrium steady states including a heat conducting fluid, a sheared fluid, and an electrically conducting fluid. We call our theory steady state thermodynamics (SST) after Oono and Paniconi's original proposal. The construction of SST is based on a careful examination of how the basic notions in thermodynamics should be modified in nonequilibrium steady states. We define all thermodynamic quantities through operational procedures which can be (in principle) realized experimentally. Based on SST thus constructed, we make some nontrivial predictions, including an extension of Einstein's formula on density fluctuation, an extension of the minimum work principle, the existence of a new osmotic pressure of a purely nonequilibrium origin, and a shift of coexistence temperature. All these predictions may be checked experimentally to test SST for its quantitative validity.     

Precipitation of radiation belt electrons by magnetospherically reflected (MR) whistlers

We use a test particle simulation model based on gyro-averaged equations of motion to study the influence of oblique magnetospherically reflected (MR) whistlers on the near-loss-cone distribution function of radiation belt electrons. We find that MR whistlers originating in lightning can resonantly interact with radiation belt electrons over a broad range of L-shells and precipitate higher energy electrons from lower L-shells. Electrons in the energy range of 1–2.6 MeV are precipitated from L=2, whereas from L=4 the precipitated electron energy range is 150–220 keV. The precipitated differential electron flux due to this interaction is higher for higher L-shells, and the maximum value ranges from at at L=4. The lifetimes of radiation belt electrons in a given magnetic flux tube around the L-shell on which the interaction takes place are found to be of the order of several days, comparable to lifetimes corresponding to electron loss induced by hiss, which was heretofore assumed to be the dominant loss mechanism [1]. The minimum electron lifetimes vary from 2.47 days for E=1.11 MeV electrons at L=2 to 4.64 days for E=173 keV electrons at L=4.LOLA Research Center, Belgrade, Yugoslavia. STAR Laboratory, Stanford University, Stanford, California. Published in Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 37, No. 6, pp. 727–740, June, 1994.     

Ab-initio calculations of structural,phonon and thermal properties of $$\hbox {Al}_x \hbox {Ga}_{1-x} \hbox {As}$$ alloy

We provide the energy spectrum of an electron in a degenerately doped semiconductor of parabolic band. Knowing the energy spectrum, the density-of-states (DOS) functions are obtained, considering the Gaussian distribution of the potential energy of the impurity states, showing a band tail in them e.g., energy spectrum and density-of-states. Therefore, Fermi integrals (FIs) of DOS functions, having band tail, are developed by the exact theoretical calculations of the same. It is noticed that with heavy dopings in semiconductors, the total FI demonstrates complex functions, containing both real and imaginary terms of different FI functions. Their moduli possess an oscillatory function of \(\eta \) (reduced \(\hbox {Fermi energy} = E_{\mathrm{f}}/k_{\mathrm{B}}T\), \(k_{\mathrm{B}}\) is the Boltzmann constant and T is the absolute temperature) and \(\eta _{e}\) (impurity screening potential), having a series solutions of confluent hypergeometric functions, \(\Phi (a, b; z)\), superimposed with natural cosine functions of angle \(\theta \). The variation of \(\theta \) with respect to \(\eta \) indicated a resonance at \(\eta =1.5\). The oscillatory behaviour of FIs show the existence of ‘band-gaps’, both in the real as well as in the forbidden bands as new band gaps in the semiconductor.     

Crossover from attractive to repulsive Casimir forces and vice versa

Systems described by an O(n) symmetrical varphi;{4} Hamiltonian are considered in a d-dimensional film geometry at their bulk critical points. The critical Casimir forces between the film's boundary planes B_{j}, j=1,2, are investigated as functions of film thickness L for generic symmetry-preserving boundary conditions partial differential_{n}phi=c[over composite function]_{j}phi. The L-dependent part of the reduced excess free energy per cross-sectional area takes the scaling form f_{res} approximately D(c_{1}L;{Phi/nu},c_{2}L;{Phi/nu})/L;{d-1} when d<4, where c_{i} are scaling fields associated with the variables c[over composite function]_{i} and Phi is a surface crossover exponent. Explicit two-loop renormalization group results for the function D(c_{1},c_{2}) at d=4- dimensions are presented. These show that (i) the Casimir force can have either sign, depending on c_{1} and c_{2}, and (ii) for appropriate choices of the enhancements c[over composite function]_{j}, crossovers from attraction to repulsion and vice versa occur as L increases.     

Steady-state thermodynamics for heat conduction: microscopic derivation

Starting from microscopic mechanics, we derive thermodynamic relations for heat conducting nonequilibrium steady states. The extended Clausius relation enables one to experimentally determine nonequilibrium entropy to the second order in the heat current. The associated Shannon-like microscopic expression of the entropy is suggestive. When the heat current is fixed, the extended Gibbs relation provides a unified treatment of thermodynamic forces in the linear nonequilibrium regime.     

Extended Clausius Relation and Entropy for Nonequilibrium Steady States in Heat Conducting Quantum Systems

Recently, in their attempt to construct steady state thermodynamics (SST), Komatsu, Nakagawa, Sasa, and Tasaki found an extension of the Clausius relation to nonequilibrium steady states in classical stochastic processes. Here we derive a quantum mechanical version of the extended Clausius relation. We consider a small system of interest attached to large systems which play the role of heat baths. By only using the genuine quantum dynamics, we realize a heat conducting nonequilibrium steady state in the small system. We study the response of the steady state when the parameters of the system are changed abruptly, and show that the extended Clausius relation, in which “heat” is replaced by the “excess heat”, is valid when the temperature difference is small. Moreover we show that the entropy that appears in the relation is similar to von Neumann entropy but has an extra symmetrization with respect to time-reversal. We believe that the present work opens a new possibility in the study of nonequilibrium phenomena in quantum systems, and also confirms the robustness of the approach by Komatsu et al.     

The Role of Spin-Flipping Terms in Hadronic Transitions of {\Upsilon (4S)}

Recent experimental data on the \({\Upsilon(4S)\to\Upsilon(1S)\eta}\) and \({\Upsilon(4S)\to h_{b}(1P)\eta}\) processes seem to contradict the naive expectation that hadronic transitions with spin-flipping terms should be suppressed with respect those without spin-flip. We analyze these transitions using the QCD multipole expansion (QCDME) approach and within a constituent quark model framework that has been applied successfully to the heavy-quark sectors during the last years. The QCDME formalism requires the computation of hybrid intermediate states which has been performed in a natural, parameter-free extension of our constituent quark model based on the quark confining string (QCS) scheme. We show that (i) the M1–M1 contribution in the decay rate of the \({\Upsilon(4S)\to\Upsilon(1S)\eta}\) is important and its suppression until now is not justified; (ii) the role played by the \({L=0}\) hybrid states, which enter in the calculation of the M1–M1 contribution, explains the observed enhancement in the \({\Upsilon(4S)\to\Upsilon(1S)\eta}\) decay width; and (iii) the anomalously large decay rate of the \({\Upsilon(4S)\to h_{b}(1P)\eta}\) transition has the same physical origin.     

Existence of Nonequilibrium Steady State for a Simple Model of Heat Conduction

This paper contains rigorous results for a simple stochastic model of heat conduction similar to the KMP (Knipnis–Marchiori–Presutti) model but with possibly energy-dependent interaction rates. We prove the existence and uniqueness of nonequilibrium steady states, their relation to Lebesgue measure, and exponential convergence to steady states from suitable initial conditions.     

Monotonic return to steady nonequilibrium

We propose and analyze a new candidate Lyapunov function for relaxation towards general nonequilibrium steady states. The proposed functional is obtained from the large time asymptotics of time-symmetric fluctuations. For driven Markov jump or diffusion processes it measures an excess in dynamical activity rates. We present numerical evidence and we report on a rigorous argument for its monotonic time dependence close to the steady nonequilibrium or in general after a long enough time. This is in contrast with the behavior of approximate Lyapunov functions based on entropy production that when driven far from equilibrium often keep exhibiting temporal oscillations even close to stationarity.     

Geometrical Excess Entropy Production in Nonequilibrium Quantum Systems

For open systems described by the quantum Markovian master equation, we study a possible extension of the Clausius equality to quasistatic operations between nonequilibrium steady states (NESSs). We investigate the excess heat divided by temperature (i.e., excess entropy production) which is transferred into the system during the operations. We derive a geometrical expression for the excess entropy production, which is analogous to the Berry phase in unitary evolution. Our result implies that in general one cannot define a scalar potential whose difference coincides with the excess entropy production in a thermodynamic process, and that a vector potential plays a crucial role in the thermodynamics for NESSs. In the weakly nonequilibrium regime, we show that the geometrical expression reduces to the extended Clausius equality derived by Saito and Tasaki (J. Stat. Phys. 145:1275, 2011). As an example, we investigate a spinless electron system in quantum dots. We find that one can define a scalar potential when the parameters of only one of the reservoirs are modified in a non-interacting system, but this is no longer the case for an interacting system.     

Entropy and Nonlinear Nonequilibrium Thermodynamic Relation for Heat Conducting Steady States

Among various possible routes to extend entropy and thermodynamics to nonequilibrium steady states (NESS), we take the one which is guided by operational thermodynamics and the Clausius relation. In our previous study, we derived the extended Clausius relation for NESS, where the heat in the original relation is replaced by its “renormalized” counterpart called the excess heat, and the Gibbs-Shannon expression for the entropy by a new symmetrized Gibbs-Shannon-like expression. Here we concentrate on Markov processes describing heat conducting systems, and develop a new method for deriving thermodynamic relations. We first present a new simpler derivation of the extended Clausius relation, and clarify its close relation with the linear response theory. We then derive a new improved extended Clausius relation with a “nonlinear nonequilibrium” contribution which is written as a correlation between work and heat. We argue that the “nonlinear nonequilibrium” contribution is unavoidable, and is determined uniquely once we accept the (very natural) definition of the excess heat. Moreover it turns out that to operationally determine the difference in the nonequilibrium entropy to the second order in the temperature difference, one may only use the previous Clausius relation without a nonlinear term or must use the new relation, depending on the operation (i.e., the path in the parameter space). This peculiar “twist” may be a clue to a better understanding of thermodynamics and statistical mechanics of NESS.     

The Study of ηc(1S)→ P P ′ $PP^{\prime }$ Decays

International Journal of Theoretical Physics - The ${\eta }_{c}(1S) {\to } PP^{\prime }$ decays are the parity violation modes. These decays can be induced by the weak interactions within the...     

Ergodicity and Energy Distributions for Some Boundary Driven Integrable Hamiltonian Chains

We consider systems of moving particles in 1-dimensional space interacting through energy storage sites. The ends of the systems are coupled to heat baths, and resulting steady states are studied. When the two heat baths are equal, an explicit formula for the (unique) equilibrium distribution is given. The bulk of the paper concerns nonequilibrium steady states, i.e., when the chain is coupled to two unequal heat baths. Rigorous results including ergodicity are proved. Numerical studies are carried out for two types of bath distributions. For chains driven by exponential baths, our main finding is that the system does not approach local thermodynamic equilibrium as system size tends to infinity. For bath distributions that are sharply peaked Gaussians, in spite of the near-integrable dynamics, transport properties are found to be more normal than expected.     

Steady-state thermodynamics of Langevin systems

We study Langevin dynamics describing nonequilibirum steady states. Employing the phenomenological framework of steady-state thermodynamics constructed by Oono and Paniconi [Prog. Theor. Phys. Suppl. 130, 29 (1998)], we find that the extended form of the second law which they proposed holds for transitions between steady states and that the Shannon entropy difference is related to the excess heat produced in an infinitely slow operation. A generalized version of the Jarzynski work relation plays an important role in our theory.     

Chains of twists and induced deformations

Chains of extended twists are composed of factors . The set of Jordanian twists { } can be applied to the initial Hopf algebra . In this case the remaining (transformed) factors of the chain can serve as extensions for such a multijordanian twist. We study the properties of these generalized extensions and the spectra of deformations of the corresponding Heisenberg-like algebras. The results are explicitly demonstrated for the case when .     

The carbon impurity ohmic discharges on particle transport in the HT-7 tokamak

The line-integrated optical measurement of impurity radiation profiles for the study of light impurity transport is performed in the HT-7 tokamak. The carbon impurity line emissivity is obtained by Abel inversion. The radial transport behaviours of carbon impurities at different central line averaged electron densities ne are investigated in ohmic discharges. The diffusion coefficient Dk（r）, the convection velocity Wk（r） and the total flux of the impurity ions Fk decrease with the increase of ne, which shows a reduction in the impurity particle transport at higher electron densities.