Covariant formulation of non-equilibrium statistical thermodynamics

The Fokker Planck equation is considered as the master equation of macroscopic fluctuation theories. The transformation properties of this equation and quantities related to it under general coordinate transformations in phase space are studied. It is argued that all relations expressing physical properties should be manifestly covariant, i.e. independent of the special system of coordinates used. The covariance of the Langevin-equations and the Fokker Planck equation is demonstrated. The diffusion matrix of the Fokker Planck equation is used as a contravariant metric tensor in phase space. Covariant drift vectors associated to the Langevin- and the Fokker Planck equation are found. It is shown that special coordinates exist in which the covariant drift vector of the Fokker Planck equation and the usual non-covariant drift vector are equal.The physical property of detailed balance and the equivalent potential conditions are given in covariant form. Finally, the covariant formulation is used to study how macroscopic forces couple to a system in a non-equilibrium steady state. A general fluctuation-dissipation theorem for the linear response to such forces is obtained.     

On the De Donder-Meixner transformations in non-equilibrium thermodynamics

A characterization of the more general De Donder-Meixner transformations in irreversible thermodynamics was performed, and some new properties of these transformations were obtained.     

Boundary layer analysis for non-equilibrium phase transitions

In this review, we discuss some of the recent developments in understanding various boundary induced phase transitions in asymmetric simple exclusion processes using boundary layer analysis. The boundary layer analysis is shown to be useful in gaining a lot of physical insights regarding the formation of shock, the critical point and the dual boundary transition.     

Non-equilibrium thermodynamics of interfacial systems: II. Boundary conditions for fluids with spin

The theory of non-equilibrium thermodynamics is applied to a system of two immiscible fluids whose molecules possess internal angular momentum (spin) which are separated by an interface. The conservation laws and the Gibbs relation are used to derive the entropy production at the interface. The resulting linear laws relating the fluxes and forces represent boundary conditions on the hydrodynamic equations for the bulk phases. A limiting case is considered and boundary conditions derived by previous authors are obtained.     

Relativistic heavy-ion collisions: An approach based on non-equilibrium thermodynamics

A new theory of particle production in high energy collisions is proposed which is based on non-equilibrium thermodynamics. The non-equilibrium model is a major extension of the equilibrium thermodynamic model of relativistic heavy-ion collisions developed earlier. While the equilibrium thermodynamic theory is appropriate for the formation of light nuclei and for pions, the non-equilibrium theory applies to the creation of particles heavier than the pion, which include such particles as the strange mesons, strange baryons and the anti-nucleons. Using an approach based on the degree of the reaction of kinetic theory, the time evolution of the composition of hadronic systems in incomplete equilibrium is investigated. Densities of produced particles are related to space-time quantities and to the production cross sections of the underlying dynamic processes. An application of the non-equilibrium approach to the production of strange matter is given. The importance of secondary processes, following pion production, in the formation of strange matter is shown. In fact, the secondary production process for kaons is as important as the direct production process arising from initial nucleon-nucleon (NN) collision of a first collision picture. Thus, kaons can be produced in a late stage of the collision of two nuclei and they do not necessarily reflect the early stages of the collision as first thought. Using the experimental number of kaons, the time of reaction is also estimated. No evidence for a long-lived state of the nuclear system is found. Expressions for particle production ratios are developed. The results of an equilibrium theory and a non-equilibrium theory are found to be similar for such ratios. The chemical equilibrium constant is shown to be present in the non-equilibrium theory; the Boltzmann factor in the production threshold energy appears in the equilibrium theory. The K^?/K⁺ ratio is estimated. Surprisingly, reasonable agreement with experiment is found in the K^?/K⁺ ratio using the equilibrium theory, even though the production processes for K⁺'s and K^?'s treated individually, are not ones for which the equilibrium theory applies. It is shown that a fundamental difference between the equilibrium and non-equilibrium theory is lost when particle ratios for non-equilibrium particles are taken. Expressions for the production of complex composite structures made of strange particles are developed. The non-equilibrium model with some modifications may be useful for high energy NN and pion-nucleon collisions.     

A phenomenological non-equilibrium theory for the thermodynamics of Kelvin bodies

From a generalized Gibbs equation and a general form for entropy flux, we develop a non-linear theory for the thermodynamics of several rheological bodies, known as Kelvin bodies. In accordance with irreversible extended thermodynamics, we deduce a non-stationary transport equation which contains new cross effect terms; in so doing, we obtain a complete hyperbolic system which describes the evolution of the above bodies.     

非平衡热力学中传热过程熵产表达式的修正

熵产是非平衡热力学中的核心物理量,传统上表示为广义力(驱动力)与广义流的乘积.这种表达存在两方面缺陷:一是广义力与广义流的拆分具有任意性;更重要的是,以其计算热波传递时熵产可以为负值,从而违反热力学第二定律.本文基于热质理论分析表明,传热过程的熵产实质上是由热质流体的热质能耗散引起的,所以熵产中的力不是驱动力而是阻力,并且具有力的量纲.由此提出的熵产修正表达式,不仅在计算热波传递过程中熵产恒为正值,与扩展不可逆热力学中的熵产表达式一致,而且不存在力和流拆分的任意性.     

Solitons and solar cells: The non-equilibrium thermodynamics of the photovoltaic effect in polyacetylene

The production of photovoltages by trans-(CH)_x based devices is analyzed in terms of the non-equilibrium thermodynamics of the photovoltaic effect and compared with the model of photogenerated charged soliton pairs. It is concluded that the source of (CH)_x photovoltages is a photo-reaction channel in which photoexcitations remain as band electrons and holes for appreciable lifetimes.     

Oxide solid electrolytes under non-equilibrium conditions — Interfaces and ageing

This paper gives an overview of the materials transport processes which occur in oxide solid electrolytes subjected to a generalized thermodynamical potential gradient. The general equations allowing to describe the transport processes on the anionic and cationic sublattices are given. Kinetic demixing processes and microstructural changes leading to surface instabilities are analysed. Experimental results obtained with yttria-doped zirconia and gadolinium doped ceria illustrate the importance of these phenomena on the transport properties of the materials but also on their long term stability in operating conditions. Paper presented at the Patras Conference on Solid State Ionics — Transport Properties, Patras, Greece, Sept. 14–18, 2004.     

Entropy identity and equilibrium conditions in relativistic thermodynamics

Starting out with the balance equations for energy-momentum, spin, particle and entropy density, an approach is considered which represents a framework for special- and general-relativistic continuum thermodynamics. A general entropy density 4-vector, containing particle, energy-momentum, and spin density contributions, is introduced. This makes possible, firstly, to test special entropy density 4-vectors used by other authors with respect to their generality and validity and, secondly, to determine entropy supply and entropy production. Using this entropy density 4-vector, material-independent equilibrium conditions are discussed. While in literature, generally thermodynamic equilibrium is determined by introducing a variety of conditions by hand, the present approach proceeds as follows: For a comparatively wide class of space–time geometries, the necessary equilibrium conditions of vanishing entropy supply and vanishing entropy production are exploited. Because these necessary equilibrium conditions do not determine the equilibrium, supplementary conditions are added systematically motivated by the requirement that also all parts of the necessary conditions have to be fixed in equilibrium.     

Effective mass of surface electrons in helium under non-equilibrium conditions

The mass shift of surface electrons in helium has been investigated theoretically caused by electron-ripplon interaction as a function of electromagnetic field power absorbed by a system. It is shown that the mass shift is negative at weak powers of external field but it increases as the power increases and changes its sign. The results of calculation and comparison with the experimental data testify to the favourable role of two-ripplon scattering processes in energy relaxation of surface electrons above helium.     

离子-电子非平衡机制降低中心热斑点火条件

提出通过离子-电子非平衡物理模型来降低惯性约束聚变中心热斑点火的聚变点火条件。在该物理模型中,强调离子比电子具备更高的温度,从而使得热斑的热核聚变反应增强,轫致辐射和电子热传导造成的能量漏失相对降低。通过对中心热斑的自加热分析和热斑燃烧动力学分析,发现相对于平衡聚变点火模型,非平衡模型可以显著扩大聚变点火区在热斑面密度和热斑温度空间的范围。同时采用LARED-S程序的数值模拟,研究了通过尖峰脉冲波形、二次冲击物理机制强化中心热斑聚变点火的非平衡性。     

Renormalization group analysis of polymer cyclization with non-equilibrium initial conditions

We develop a renormalization group approach for cyclizing polymers for the case when chain ends are initially close together (ring initial conditions). We analyze the behavior at times much shorter than the longest polymer relaxation time. In agreement with our previous work (Europhys. Lett. 73, 621 (2006)) we find that the leading time dependence of the reaction rate k(t) for ring initial conditions and equilibrium initial conditions are related, namely k _ring(t) ∝ t ^-δ and k _eq(t) ∝ t ^1-δ for times less than the longest polymer relaxation time. Here δ is an effective exponent which approaches δ = 5/4 for very long Rouse chains. Our present analysis also suggests a “sub-leading” term proportional to (ln t)/t which should be particularly significant for smaller values of the renormalized reaction rate and early times. For Zimm dynamics, our RG analysis indicates that the leading time dependence for the reaction rate is k(t) ∼ 1/t for very long chains. The leading term is again consistent with the expected relation between ring and equilibrium initial conditions. We also find a logarithmic correction term which we “exponentiate” to a logarithmic form with a Landau pole. The presence of the logarithm is particularly important for smaller chains and, in the Zimm case, large values of the reaction rate.     

离子-电子非平衡机制降低中心热斑点火条件

提出通过离子-电子非平衡物理模型来降低惯性约束聚变中心热斑点火的聚变点火条件。在该物理模型中,强调离子比电子具备更高的温度,从而使得热斑的热核聚变反应增强,轫致辐射和电子热传导造成的能量漏失相对降低。通过对中心热斑的自加热分析和热斑燃烧动力学分析,发现相对于平衡聚变点火模型,非平衡模型可以显著扩大聚变点火区在热斑面密度和热斑温度空间的范围。同时采用LARED-S程序的数值模拟,研究了通过尖峰脉冲波形、二次冲击物理机制强化中心热斑聚变点火的非平衡性。     

Boundary conditions of gyrotropic materials

We discuss the form of the electromagnetic constitutive equations for the boundary of gyrotropic materials. As an application we consider reflection of light at isotropic materials. It is shown that for Π- and σ-polarized incident light the ellipticity of the reflected light is determined by the optical rotatory power.     

Boundary conditions as Dirac constraints

In this article we show that boundary conditions can be treated as Lagrangian and Hamiltonian constraints. Using the Dirac method, we find that boundary conditions are equivalent to an infinite chain of second class constraints, which is a new feature in the context of constrained systems. Constructing the Dirac brackets and the reduced phase space structure for different boundary conditions, we show why mode expanding and then quantizing a field theory with boundary conditions is the proper way. We also show that in a quantized field theory subjected to the mixed boundary conditions, the field components are non-commutative. Received: 16 October 2000 / Revised version: 8 January 2001 / Published online: 23 February 2001     

Boundary conditions for differential approximations

Low order spherical harmonic (P-N) approximations are applied to a radiative transfer Marshak wave problem. A modified Milne boundary condition is developed for the P-2 approximation, similar to one suggested earlier for the P-1 approximation. Comparison with exact Monte Carlo results suggests that this modified P-2 method may be an accurate and generally applicable differential approximation to the equation of transfer. The Monte Carlo results presented should be useful for testing other approximate formulations of radiative transfer and validating time dependent numerical solution methods for the equation of transfer.