Phenomenological model of the diffusion of impurity atoms in ultrathin silicon layers with a nonuniform distribution of temperatures

The influence of fluxes of intrinsic nonequilibrium semiconductor defects on impurity diffusion in a nonuniform temperature field is considered in the framework of the phenomenological theory of irreversible processes. The mass transfer coefficient defined as the ratio of the concentrations of nonequilibrium and equilibrium defects is introduced to take the excessive concentration of nonequilibrium defects into account. The introduction of this coefficient into equations for matter and heat fluxes makes it possible to express the parameters of the process of thermal diffusion (the diffusion coefficient and the heat of transport) as a time-dependent function of the excessive concentration of intrinsic nonequilibrium semiconductor defects.     

Average entropy dissipation in irreversible mesoscopic processes

The Clausius inequality is rectified to obtain expressions for the entropy produced as the result of irreversible work and/or heat exchanges. These are combined with the Jarzynski equality and its generalizations to explicitly relate mean (as opposed to transient) entropy dissipation to experimental or simulation observables. The results are extended to nonisothermal processes which begin and end at nonequilibrium steady states, leading to a new exact expression and positive lower bound for the resulting average entropy dissipation. The Carnot engine emerges as a limiting case of a family of irreversible processes arising from an interface between materials at different temperatures, whose mapping onto reversible and irreversible molecular extension experiments is discussed.     

热质的运动和传递-最低热质能耗散原理和热质运动方程

过增元基于质能方程提出了热质的概念.在非平衡热力学中,存在最低能量耗散原理,根据该原理可以导出热传导,扩散及粘性流动等不可逆输运过程的方程式.当采用热质模型对传热现象进行描述时,发现热质的运动也满足最小作用量原理:最低热质能耗散原理,根据该原理可以推导得出热质运动的动量守恒方程。     

The Steady State Fluctuation Relation for the Dissipation Function

We give a proof of transient fluctuation relations for the entropy production (dissipation function) in nonequilibrium systems, which is valid for most time reversible dynamics. We then consider the conditions under which a transient fluctuation relation yields a steady state fluctuation relation for driven nonequilibrium systems whose transients relax, producing a unique nonequilibrium steady state. Although the necessary and sufficient conditions for the production of a unique nonequilibrium steady state are unknown, if such a steady state exists, the generation of the steady state fluctuation relation from the transient relation is shown to be very general. It is essentially a consequence of time reversibility and of a form of decay of correlations in the dissipation, which is needed also for, e.g., the existence of transport coefficients. Because of this generality the resulting steady state fluctuation relation has the same degree of robustness as do equilibrium thermodynamic equalities. The steady state fluctuation relation for the dissipation stands in contrast with the one for the phase space compression factor, whose convergence is problematic, for systems close to equilibrium. We examine some model dynamics that have been considered previously, and show how they are described in the context of this work.     

A graphic approach to include dissipative-like effects in reversible thermal cycles

Since the decade of 1980’s, a connection between a family of maximum-work reversible thermal cycles and maximum-power finite-time endoreversible cycles has been established. The endoreversible cycles produce entropy at their couplings with the external heat baths. Thus, this kind of cycles can be optimized under criteria of merit that involve entropy production terms. Meanwhile the relation between the concept of work and power is quite direct, apparently, the finite-time objective functions involving entropy production have not reversible counterparts. In the present paper we show that it is also possible to establish a connection between irreversible cycle models and reversible ones by means of the concept of “geometric dissipation”, which has to do with the equivalent role of a deficit of areas between some reversible cycles and the Carnot cycle and actual dissipative terms in a Curzon-Ahlborn engine.     

Irreversibility and randomness in linear response theory

Recall that the fluctuation-dissipation theorem connects the response function of a passive linear system and the spectral density of the stationary stochastic process which describes the thermal fluctuations in the system. It is shown that the classical limit (=0) of the fluctuation-dissipation theorem implies a correspondence between systems which are reversible in the sense that the energy used to drive them away from equilibrium is completely recoverable as work and processes which are deterministic in the sense of Wiener's prediction theory, while irreversible systems correspond to nondeterministic processes. This correspondence is expressed by a simple transformation between the operator kernel which determines the optimal choice of the time-dependent force and the linear predictor for the stochastic process. For quantum systems this correspondence does not hold; the fluctuations are always of the deterministic type for any finite temperature, but the system is not necessarily reversible. For irreversible systems a formula is derived for the instantaneous entropy production which is a generalization of the standard one for Markovian dynamics.     

Segregation by thermal diffusion in moderately dense granular mixtures

A theory based on a solution of the inelastic Enskog equation that goes beyond the weak dissipation limit is used to determine the thermal diffusion factor of a binary granular mixture under gravity. The Enskog equation that aims to describe moderate densities neglects velocity correlations but retains spatial correlations arising from volume exclusion effects. As expected, the thermal diffusion factor provides a segregation criterion that shows the transition between the Brazil-nut effect (BNE) and the reverse Brazil-nut effect (RBNE) by varying the parameters of the system (masses, sizes, composition, density and coefficients of restitution). The form of the phase diagrams for the BNE/RBNE transition is illustrated in detail in the tracer limit case, showing that the phase diagrams depend sensitively on the value of gravity relative to the thermal gradient. Two specific situations are considered: i) absence of gravity, and ii) homogeneous temperature. In the latter case, after some approximations, our results are consistent with previous theoretical results derived from the Enskog equation. Our results also indicate that the influence of dissipation on thermal diffusion is more important in the absence of gravity than in the opposite limit. The present analysis, which is based on a preliminary short report of the author (Phys. Rev. E 78, 020301(R) (2008)), extends previous theoretical results derived in the dilute limit case.     

Local nonequilibrium mass transfer in a two-component system under external pulsed irradiation with energy fluxes

The nonisothermal mass transfer in metal materials under irradiation with concentrated energy fluxes is studied in the one-dimensional approximation. Local nonequilibrium equations of extended irreversible thermodynamics are used to describe the transfer phenomena. It is established that, for short times (on the order of the time required for relaxation of the diffusion flow to its local-equilibrium value), the wave mechanism for mass transfer is dominant over the diffusion one, ensuring that the impurity-concentration profiles have a nonmonotonous form. The degree of influence of the space-time nonlocality of the transfer processes on the formation of concentration profiles is estimated, and the model results are compared with the experimental data.     

Marginal Effect of Structural Defects on the Nonequilibrium Critical Behavior of the Two-Dimensional Ising Model

The influence of various initial magnetizations m0 and structural defects on the nonequilibrium critical behavior of the two-dimensional Ising model is numerically simulated by Monte Carlo methods. Based on analysis of the time dependence of magnetization and the two-time dependences of autocorrelation function and dynamic susceptibility, we revealed the influence of logarithmic corrections and the crossover phenomena of percolation behavior on the nonequilibrium characteristics and the critical exponents. Violation of the fluctuation–dissipation theorem is studied, and the limiting fluctuation–dissipation ratio is calculated for the case of high-temperature initial state. The influence of various initial states on the limiting fluctuation–dissipation ratio is investigated. The nonequilibrium critical dynamics of weakly disordered systems with spin concentrations p ≥ 0.9 is shown to belong to the universality class of the nonequilibrium critical behavior of the pure model and to be characterized by the same critical exponents and the same limiting fluctuation–dissipation ratios. The nonequilibrium critical behavior of systems with p ≤ 0.85 demonstrates that the universal characteristics of the nonequilibrium critical behavior depend on the defect concentration and the dynamic scaling is violated, which is related to the influence of the crossover effects of percolation behavior.     

Extension of the fluctuation-dissipation theorem to non-equilibrium systems

The fluctuation-dissipation theorem is generalized to the case of nonequilibrium (albeit in a stable steady state) systems. The relationship between the correlation function of the current fluctuations and the average energy absorbed by the system as a consequence of dissipation is used. For a nonequilibrium classical system, the responce function is connected with the correlation function in which the averaging is over the derivative of the energy distribution function. Using the spectrum of the electromagnetic fluctuations, inverting the fluctuation-dissipation relation one can find the permittivity of the medium.     

Onsager-Machlup Theory and Work Fluctuation Theorem for a Harmonically Driven Brownian Particle

We extend Tooru-Cohen analysis for nonequilibrium steady state (NSS) of a Brownian particle to nonequilibrium oscillatory state (NOS) of Brownian particle by considering time dependent external drive protocol. We consider an unbounded charged Brownian particle in the presence of oscillating electric field and prove work fluctuation theorem, which is valid for any initial distribution and at all times. For harmonically bounded and constantly dragged Brownian particle considered by Tooru and Cohen, work fluctuation theorem is valid for any initial condition (also NSS), but only in large time limit. We use Onsager-Machlup Lagrangian with a constraint to obtain frequency dependent work distribution function, and describe entropy production rate and properties of dissipation functions for the present system using Onsager-Machlup functional.     

Observation of size-dependent thermalization in CdSe nanocrystals using time-resolved photoluminescence spectroscopy

We report heat dissipation times in semiconductor nanocrystals of CdSe. Specifically, a previously unresolved, subnanosecond decay component in the low-temperature photoluminescence decay dynamics exhibits longer decay lifetimes (tens to hundreds of picoseconds) for larger nanocrystals as well as a size-independent, ~25-meV spectral shift. We attribute the fast relaxation to transient phonon-mediated relaxation arising from nonequilibrium acoustic phonons. Following acoustic phonon dissipation, the dark exciton state recombines more slowly via LO-phonon assistance resulting in the observed spectral shift. The measured relaxation time scales agree with classical calculations of thermal diffusion, indicating that interfacial thermal conductivity does not limit thermal transport in these semiconductor nanocrystal dispersions.     

On the evaluation of measurements of small changes in electric resistance

The measurement of small changes in resistance, caused in metal wires by non-equilibrium point defects, meets with many difficulties caused inter alia by changes in temperature, instability of the voltage source and irreversible changes in the electric resistance due to the thermal treatment of the samples. In the first part of the paper, dealing with the d-c bridge method of measurement, the conditions under which the relations given in the literature can be used for calculating small changes in resistance are quantitatively determined on the basis of a detailed analysis of such relations. The second part describes a method of measurement permitting the elimination of irreversible changes in the resistance of thermally treated samples and relations are derived for calculating reversible changes.     

Fundamental aspects of quantum Brownian motion

With this work we elaborate on the physics of quantum noise in thermal equilibrium and in stationary nonequilibrium. Starting out from the celebrated quantum fluctuation-dissipation theorem we discuss some important consequences that must hold for open, dissipative quantum systems in thermal equilibrium. The issue of quantum dissipation is exemplified with the fundamental problem of a damped harmonic quantum oscillator. The role of quantum fluctuations is discussed in the context of both, the nonlinear generalized quantum Langevin equation and the path integral approach. We discuss the consequences of the time-reversal symmetry for an open dissipative quantum dynamics and, furthermore, point to a series of subtleties and possible pitfalls. The path integral methodology is applied to the decay of metastable states assisted by quantum Brownian noise.     

Response function theory for far-from-equilibrium statistical systems

A formalism to determine the response function of a sample in conditions far from thermal equilibrium is presented. It consists in a generalization of scattering theory coupled to the statistical theory of irreversible processes, the nonequilibrium statistical operator method, developed by Zubarev. The scattering cross section is expressed in terms of double-time correlation functions, which are related to appropriate nonequilibrium thermodynamic Green's functions. The latter are also used to treat generalized transport equations, and, as an illustration, the method is applied to the study of the time-resolved Raman spectroscopy of a photoexcited semiconductor plasma.     

Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences

There are only a very few known relations in statistical dynamics that are valid for systems driven arbitrarily far-from-equilibrium. One of these is the fluctuation theorem, which places conditions on the entropy production probability distribution of nonequilibrium systems. Another recently discovered far from equilibrium expression relates nonequilibrium measurements of the work done on a system to equilibrium free energy differences. In this paper, we derive a generalized version of the fluctuation theorem for stochastic, microscopically reversible dynamics. Invoking this generalized theorem provides a succinct proof of the nonequilibrium work relation.     

Equality connecting energy dissipation with a violation of the fluctuation-response relation

In systems driven away from equilibrium, the velocity correlation function and the linear-response function to a small perturbation force do not satisfy the fluctuation-response relation (FRR) due to the lack of detailed balance in contrast to equilibrium systems. In this Letter, an equality between an extent of the FRR violation and the rate of energy dissipation is proved for Langevin systems under nonequilibrium conditions. This equality enables us to calculate the rate of energy dissipation by quantifying the extent of the FRR violation, which can be measured experimentally.