On the definition of entropy for non-equilibrium states

In this paper it is demonstrated how the mathematical theory of stability of motion can be applied to kinetic equations, describing irreversible processes in an isolated, homogeneous system. It turns out that functions having all the properties of entropy exist throughout the domain of definition of the kinetic equations. Since the kinetic equations depend only on variables defined outside equilibrium thermodynamics, it is possible to define entropy far beyond the range of validity of the thermodynamics of irreversible processes. It is shown that the commonly assumed properties of entropy are not sufficient, however, to single out just one entropy function.     

Microscopic non-equilibrium structure and dynamical model of entropy flow

The extension of quantum mechanics to a general functional space (“rigged Hilbert space”), which incorporates time-symmetry breaking, is applied to construct extract dynamical models of entropy production and entropy flow. They are illustrated by using a simple conservative Hamiltonian system for multilevel atoms coupled to a time-dependent external force. The external force destroys the monotonicity of the ℋ-function evolution. This leads to a model of the entropy flow that allows a steady nonequilibrium structure of the emitted field around the unstable particles.     

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.     

A comparison of different entransy flow definitions and entropy generation in thermal radiation optimization

In thermal radiation, taking heat flow as an extensive quantity and defining the potential as temperature T or the black body emissive power U will lead to two different definitions of radiation entransy flow and the corresponding principles for thermal radiation optimization. The two definitions of radiation entransy flow and the corresponding optimization prin ciples are compared in this paper. When the total heat flow is given, the optimization objectives of the extremum entransy dissipation principles （EEDPs） developed based on potentials T and U correspond to the minimum equivalent temperature difference and the minimum equivalent blackbody emissive power difference respectively. The physical meaning of the definition based on potential U is clearer than that based on potential T, but the latter one can be used for the coupled heat transfer optimization problem while the former one cannot. The extremum entropy generation principle （EEGP） for thermal radiation is also derived, which includes the minimum entropy generation principle for thermal radiation. When the radiation heat flow is prescribed, the EEGP reveals that the minimum entropy generation leads to the minimum equivalent thermodynamic potential difference, which is not the expected objective in heat transfer. Therefore, the minimum entropy generation is not always appropriate for thermal radiation optimization. Finally, three thermal radiation optimization examples are discussed, and the results show that the difference in optimization objective between the EEDPs and the EEGP leads to the difference between the optimization results. The EEDP based on potential T is more useful in practical application since its optimization objective is usually consistent with the expected one.     

On the definitions of entropy and temperature in the extended thermodynamics of irreversible processes

New definitions of entropy and temperature for uniform systems that fast exchange heat with the environment are considered. Instead of the known local equilibrium hypothesis, a local uniformity hypothesis is proposed. Within the proposed formalism of extended thermodynamics of irreversible processes, dual-phase-lag transfer equations are obtained. To cite this article: S.I. Serdyukov, C. R. Physique 8 (2007).     

The maximum entropy principle for non-equilibrium phase transitions: Determination of order parameters,slaved modes,and emerging patterns

The maximum entropy principle allows one to make guesses on the distribution function of systems by maximizing the information entropy under given constraints. In a previous paper we succeeded to formulate appropriate constraints for systems undergoing nonequilibrium phase transitions, but we had to confine our treatment to the order parameters. In this paper we describe a formalism which does not require any a priori knowledge on the order parameters but rather allows us to determine these as well as the slaved modes and the emerging patterns. The method is applicable also to non-physical systems such as neural nets. Our approach allows us to reconsider the Landau theory of phase transitions from a new point of view. A guess is made on the Fokker-Planck equation underlying the processes which give rise to stationary distribution functions of a single order parameter.     

Interface model for non-equilibrium evaporation

A microscopic interface condition for condensing/evaporating interfaces is developed by combining a velocity dependent condensation probability [T. Tsuruta, H. Tanaka, T. Masuoka, Int. J. Heat Mass Transfer 42 (1999) 4107] and Maxwell type interface conditions with accommodation. Using methods from kinetic theory, macroscopic interface conditions for mass and energy transport across the phase boundary are derived. This model only applies to simple substances, where diffusive effects in the bulk phases are not present. The results are compared to classical non-equilibrium thermodynamics. The interface conditions are considered for the limit of small deviation from equilibrium, and the corresponding Onsager coefficients are computed. These results are useful as boundary conditions for non-equilibrium evaporation and condensation problems, as done previously by our group [M. Bond, H. Struchtrup, Phys. Rev. E 70 (2004) 061605].     

Acoustic field and the entropy mode induced by it in a waveguide filled with some non-equilibrium gases

The non-linear propagation of an acoustic beam in a rectangular waveguide is considered. The medium of sound propagation, is a gas where thermodynamically non-equilibrium processes take place: such as exothermic chemical reactions or excitation of vibrational degrees of a molecule’s freedom. The incident and reflected compounds of the acoustic field do not interact in the leading order in the case of periodic weakly nonlinear sound with zero mean value of velocity. The acoustic heating or cooling in a waveguide is discussed.     

Trajectory reweighting for non-equilibrium steady states

Modern methods for sampling rugged landscapes in state space mainly rely on knowledge of the relative probabilities of microstates, which is given by the Boltzmann factor for equilibrium systems. In principle, trajectory reweighting provides an elegant way to extend these algorithms to non-equilibrium systems, by numerically calculating the relative weights that can be directly substituted for the Boltzmann factor. We show that trajectory reweighting has many commonalities with Rosenbluth sampling for chain macromolecules, including practical problems which stem from the fact that both are iterated importance sampling schemes: for long trajectories the distribution of trajectory weights becomes very broad and trajectories carrying high weights are infrequently sampled, yet long trajectories are unavoidable in rugged landscapes. For probing the probability landscapes of genetic switches and similar systems, these issues preclude the straightforward use of trajectory reweighting. The analogy to Rosenbluth sampling suggests though that path-ensemble methods such as PERM (pruned-enriched Rosenbluth method) could provide a way forward.     

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.     

Sharp continuity bounds for entropy and conditional entropy

<正>The von Neumann entropy captures many operational quantities in the quantum information theory such as quantum capacity of the communication channel.Von Neumann entropy is continuous and is represented by Fannes inequality,which was originally given in ref.[1].Quantum correlations such as entanglement and quantum discord etc.,are important resources in quantum information processing.In the last year enormous progress on the generation,concentration,detection and quantification of entanglement has been achieved     

Cumulants in perturbation expansions for non-equilibrium field theory

The formulation of perturbation expansions for a quantum field theory of strongly interacting systems in a general non-equilibrium state is discussed. Non-vanishing initial correlations are included in the formulation of the perturbation expansion in terms of cumulants. The cumulants are shown to be the suitable candidate for summing up the perturbation expansion. Also a linked-cluster theorem for the perturbation series with cumulants is presented. Finally, a generating functional of the perturbation series with initial correlations is studied. We apply the methods to a simple model of a fermion-boson system.     

Two types of definitions for Rayleigh range

A comparison of the Rayleigh range between the two types of definitions (defined by the mean-squared beam width and the effective radius of curvature) is studied analytically and numerically, where the propagation of partially coherent beams both in free space and in atmospheric turbulence are considered. It is shown that the two types of the Rayleigh range definitions are consistent in free space. However, in turbulence the Rayleigh range defined by the mean-squared beam width is smaller than that defined by the effective radius of curvature. The main results obtained in this paper are illustrated by numerical calculation examples, where partially coherent Hermite–Gaussian (PCH–G) beams are considered.     

Techniques for analysis of stability of non-equilibrium system dynamics

Two techniques for practical analysis of non-equilibrium system stability, which were demonstrated using an example of dynamics of a charged subsystem in an electrical field, are presented. Analytical formulas of possible instabilities determining their well-known and unknown mechanisms are derived. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 34–39, October, 2006.     

An identity for the non-equilibrium phase space distribution function

A new identity satisfied by the phase space distribution function is derived and the Zubarev statistical operator is obtained as an approximation to this identity.     

A reduced model for nanoparticle coating in non-equilibrium plasma

In this Letter, a reduced model is developed based on the full model presented earlier [Yarin et al., J. Appl. Phys. 99 (6) (2006) 064310] for the deposition of amorphous hydrogenated carbon onto particles in a methane–hydrogen plasma. The reduced model is developed based on the assumption that, under certain conditions, chemistry may be decoupled from transport. The results from the reduced model are compared to the results from the full model for particle charge and growth rate of the deposited layer. It is shown that the two models are in good agreement for submicron particles that are of interest in nanoparticle coating in low-pressure plasma reactors. The reduced model is computationally far less expensive as compared to the full model and can be implemented for simulation of a large number of nanoparticles in plasma reactors.