On the fluctuation-dissipation theorem in a disordered nonequilibrium system

We present a modified perturbational calculation for a model with quenched disorder in nonequilibrium. A systematic way is proposed to obtain corrections to the usual fluctuation-dissipation theorem.     

On the coverage dependence of the surface diffusion constant

The coverage dependence of the surface diffusion constant (DC) of adsorbates is examined statistical-mechanically from the viewpoint of mutual interactions between adsorbates in the one-dimensional lattice gas model. The change in the DC with the coverage is found to become drastic near the half coverage due to the second nearest neighbor attractive interaction between adsorbates. Horiuti-Polanyi's rule concerning the crossing of potential curves does not lead to a large maximum of the DC in the middle range of the coverage.     

Statistical mechanics of a nonequilibrium steady-state classical particle system driven by a constant external force

A classical particle system coupled with a thermostat driven by an external constant force reaches its steady state when the ensemble-averaged drift velocity does not vary with time. In this work, the statistical mechanics of such a system is derived solely based on the equiprobability and ergodicity principles, free from any conclusions drawn on equilibrium statistical mechanics or local equilibrium hypothesis. The momentum space distribution is determined by a random walk argument, and the position space distribution is determined by employing the equiprobability and ergodicity principles. The expressions for energy, entropy, free energy, and pressures are then deduced, and the relation among external force, drift velocity, and temperature is also established. Moreover, the relaxation towards its equilibrium is found to be an exponentially decaying process obeying the minimum entropy production theorem.     

On the absence of diffusion in a semiinfinite one-dimensional system

For obvious reasons, the self-diffusion coefficient in bounded many-body systems must be strictly zero, provided that it is defined as the limit of [R(t)–R(0)]²/(2td) whent grows indefinitely [d is the dimensionality,R() is the position of a given particle at time]. Thus, the time integral of the velocity correlation function is strictly zero. A system of hard points on a half-infinite line with a reflective wall at the origin does exhibit this property of absence of diffusion, since each particle has an average position. We study in detail the difference between the velocity correlation functions of the infinite and of the half-infinite systems.     

Towards a new kilogram definition based on a fundamental constant

The further development of the International System of Units and the redefinition of the mass unit based on a fundamental constant is a priority task of the metrology community. Two main strategies are pursued today, counting atoms and relating mechanical to electrical power. In this article the actual status of the kilogram and the different proposed methods are reviewed. To cite this article: W. Schwitz et al., C. R. Physique 5 (2004).     

On the definition of the pressure of an infinite system

A microcanonical system $\text{L}$^o_Λ is considered together with a manometer $\text{M}$_Λ. The thermodynamic limit Λ → ∞ is taken for the system $\text{L}$_Λ composed of $\text{L}$^o_Λ and $\text{M}$_Λ. This yields a definition of the pressure P(v, ε) of $\text{{}\text{L}{}^{\mathrm{o}}{}_{\mathrm{\Lambda }}\text{; Λ → ∞}}$ for given values ε and v of the energy and particle densities. P(v, ε) is shown to be equal to the thermodynamic function p(z, β) derived from the grand canonical ensemble for almost all values of ε and v provided the appropriate equilibrium values of the temperature β^?1 and the chemical potential μ = β^?1 log z are inserted.     

Einstein's relation between diffusion constant and mobility for a diffusion model

An Ornstein-Uhlenbeck process in a periodic potential inR ^d is considered. It has been shown previously that this process satisfies a central limit theorem in the sense that, by rescaling space and time in a suitable way, the distribution of the process converges to that of a Wiener process with nonsingular diffusion matrix. Here a rigorous proof is given of a version of Einstein's formula for this model, relating the diffusion constant to the mobility of the system.     

Universal behavior of nonequilibrium fluctuations in free diffusion processes

We show that giant nonequilibrium fluctuations are present during the free diffusive remixing occurring in ordinary liquid mixtures and in macromolecular solutions. The static structure factor of the fluctuations is measured by using a quantitative shadowgraph technique. We show that structure factors at different times and from different samples can be rescaled onto a single master curve without any adjustable parameter, thus giving strong evidence that nonequilibrium fluctuations are a universal feature of free diffusion processes.     

Spatial correlations in nonequilibrium systems: The effect of diffusion

We show how the ideas of the fluctuation-dissipation theory can be used to calculate spatial correlations in interacting systems away from equilibrium. The only spatially dependent dissipative process considered is diffusion, and spatial correlations are generated by the nonlocal spatial dependence of the chemical potential. The results are the lowest order in a hierarchy of generalized hydrodynamic type calculations applicable to nonequilibrium systems. We derive equations for the density correlation functions at stationary state supported by diffusive fluxes and show that they have the local equilibrium form. The static correlation function is obtained from the fluctuation-dissipation theorem, which we show to be equivalent to the Ornstein-Zernike integral equation. At equilibrium we demonstrate that the dynamical structure factor obtained by these methods includes the expected wave-vector dependent diffusion constant. Finally we derive a necessary and sufficient condition for local equilibrium to obtain at a stationary state and show by explicit calculation that chemical processes can give rise to significant nonequilibrium correlations.     

Change in the surface concentration during diffusion saturation at a constant rate

Solution of the inverse problem of one-dimensional diffusion with constant coefficient leads to kinetic dependences of the surface concentration which ensure constancy of the rate of diffusion saturation. Numerical calculations are made for saturation of the Ni-Al system with oxygen.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 39–41, March, 1981.     

Friction and diffusion coefficients in coordinate in nonequilibrium nuclear processes

The influence of different sets of friction and diffusion coefficients on the dynamics of a nuclear system is investigated. Taking as an example a dinuclear system we show in a “classic” investigation that with zero diffusion in the coordinate, the uncertainty relation can be violated during short initial times. Sets of diffusion coefficients are found for which the “classic” and quantum diffusion equations give close physical results. The tunneling through an energy barrier is sensitively influenced by the friction and diffusion coefficients in coordinate in the diffusion equation.     

On the nonequilibrium phase transition in protein

Considerations are presented that support the idea that the nonequilibrium phase transition in protein is accompanied by the growth of a colloidal nanocrystal (or the vitrified phase of a liquid crystal). To date, the dynamic transition forms of protein, which are “the source of the catalytic power of enzymes,” have been poorly understood. In our experiments, we observed the dehydration (drying) of the colloid solution of protein in an open (far from thermodynamic equilibrium) one-component protein-water system. The protein in this state is found to acquire properties typical of matter self-organization, including the universal properties of colloidal nanocrystals of different nature, namely, nonequilibrium chaotic dynamics with self-replicability, autocatalysis, coherency, autowave fluctuations, synchronism, fractality, 3D epitaxial growth (stacking) of films, nucleation giving rise to blocks (cells) with shell nuclei, etc. It then follows that our realistic model of the nonequilibrium state of protein during growth of its colloidal nanocrystal provides an opportunity of studying the dynamics of the structural and energy-information features of the transition and solid colloidal nanocrystalline phases of protein. In addition, it allows researchers to gain fundamentally new information about the energy characteristics of protein under abiotic and biotic conditions.     

On the entropy of nonequilibrium states

A definition originally proposed by H. S. Green is used to calculate the entropy of nonequilibrium steady states. This definition provides a well-defined coarse graining of the entropy. Although the dimension of the phase space accessible to nonequilibrium steady states is less than the ostensible dimension of that space, the Green entropy is computed from within the accessible phase space, thereby avoiding the divergences inherent in the fine-grained entropy. It is shown that the Green entropy is a maximum at equilibrium and that away from equilibrium, the thermodynamic temperature computed from the Green entropy is different from the kinetic temperature.     

New branch of intersubband plasmons in a nonequilibrium two-layer system

The plasma oscillation spectrum for 2D electrons in a double quantum well is calculated. It is shown that an additional branch of intersubband plasmons can exist without experiencing Landau damping in the case of nonequilibrium population of subbands. In an asymmetric structure, this branch is responsible for both the emergence of instabilities and the possibility of amplification of plasma waves.