Showing papers in "Physica A-statistical Mechanics and Its Applications in 1983"
TL;DR: In this paper, the authors apply the influence-functional method of Feynman and Vernon to the study of Brownian motion at arbitrary temperature and obtain an explicit expression for the time evolution of the complete density matrix ϱ(x, x, x′, t) when the system starts in a particular kind of pure state.
Abstract: We apply the influence-functional method of Feynman and Vernon to the study of Brownian motion at arbitrary temperature. By choosing a specific model for the dissipative interaction of the system of interest with its environment, we are able to evaluate the influence functional in closed form and express it in terms of a few parameters such as the phenomenological viscosity coefficient. We show that in the limit h→0 the results obtained from the influence functional formalism reduce to the classical Fokker-Planck equation. In the case of a simple harmonic oscillator with arbitrarily strong damping and at arbitrary temperature, we obtain an explicit expression for the time evolution of the complete density matrix ϱ(x, x′, t) when the system starts in a particular kind of pure state. We compare our results with those of other approaches to the problem of dissipation in quantum mechanics.
2,198 citations
TL;DR: In this paper, the concentration dependence of the short-time self-diffusion coefficient Ds for spherical particles in suspension is analyzed and the importance of many-body hydrodynamic interactions between an arbitrary number of spheres can be inferred from the second virial coefficient of Ds.
Abstract: We calculate the concentration-dependence of the short-time self-diffusion coefficient Ds for spherical particles in suspension. Our analysis is valid up to high densities and fully takes into account the many-body hydrodynamic interactions between an arbitrary number of spheres. The importance of these many-body interactions can be inferred from our calculation of the second virial coefficient of Ds.
170 citations
TL;DR: In this paper, the most general multi-component solution of the star-triangle equations under an "ice-type" restriction is considered and the transfer matrix of this model is diagonalized and the eigenvectors are written down explicitly using the quantum inverse scattering formalism.
Abstract: The most general multi-component solution of the star-triangle equations under an “ice-type” restriction is considered. The transfer matrix of this model is diagonalized and the eigenvectors are written down explicitly using the quantum inverse scattering formalism. The eigenvectors are shown to have simple symmetry properties under an exchange of arguments.
131 citations
TL;DR: In this article, the structure of aqueous suspensions of electrostatically interacting submicron polymer spheres is studied as a function of shear, and several models are presented to explain the observed effects.
Abstract: The structure of aqueous suspensions of electrostatically interacting submicron polymer spheres is studied as a function of shear. These model colloidal suspensions exhibit a variety of equilibrium and nonequilibrium structures and phase transitions. Both shear induced melting of solid-like structures and shear induced distortion of liquid-like structures are observed. Several models are presented to explain the observed effects. The analogy between these colloidal suspensions and pure fluid systems is discussed.
126 citations
TL;DR: In this article, a complete synthesis of all the properties-equilibrium as well as transport-of the five noble gases and of the 26 mixtures that can be formed with them is presented, based on a thorough revision of the extended law of corresponding states of Kestin, Ro and Wakeham.
Abstract: This paper contains the background for a complete synthesis of all the properties-equilibrium as well as transport—of the five noble gases and of the 26 mixtures that can be formed with them. The synthesis is valid for the zero-density limit only, but covers the temperature range from absolute zero to the onset of ionization. The synthesis is based on a thorough revision of the two-parameter extended law of corresponding states of Kestin, Ro and Wakeham. The paper recalls the basis for the original corresponding-states principle, identifies the places at which experiment and the theory of statistical mechanics suggest deviations, and proceeds to remove them to a point where almost perfect agreement between calculation and a very large body of diverse experimental data is achieved, in the sense that deviations of experimental data from calculation are of the same order as the uncertainty in the best contemporary measurements. The basis of the revised corresponding-states principle is a set of five parameters which characterize each pair-interaction together with a fully consistent and asymptotically correct set of universal collision integrals and functionals that appear in the rigorous theory. These are reinforced with selected quantum-mechanical calculations applied in regions where they are significant.
122 citations
TL;DR: In this article, the authors show that the Hohenberg-Kohn formalism can be extended to a variation over E-V-representable densities for degenerated ground states.
Abstract: In the density-functional formalism of Hohenberg and Kohn1), the variation is only allowed over the one-particle densities which are pure-state-V-representable (PS-V-representable). Levy2) and Lieb3) proved that not every ensemble-V-representable (E-V-representable) density is PS-V-representable. Since we show that the Hohenberg-Kohn formalism can be extended to a variation over E-V-representable densities for degenerated ground states, Levy's and Lieb's result is not a counterexample to the universality of the Hohenberg-Kohn theorem. The question whether every N-representable density is E-V-representable has remained open so far. Presenting examples of non-E-V-representable densities we answer this question in the negative. Thus the value of Levy's functional4) for the calculation of ground-state energies is obvious, since this functional only requires the N-representability of the densities. Therefore we transfer two approaches for the calculation of excited-state energies into the framework of Levy's formalism.
121 citations
TL;DR: In this article, a dynamical interfacial model for quenched fluid systems is proposed and all the processes known to take place in critical fluid mixtures are identified for this model.
Abstract: Studies on kinetics of fluctuations in quenched fluid systems are reviewed on the basis of a new dynamical interfacial model. All the processes known to take place in critical fluid mixtures are identified for this model. We briefly discuss the Ostwald ripening and the interface stability with this model. An analogy with fully developed turbulence is noted and a possibility of intermittent states is indicated.
82 citations
TL;DR: Two types of linear inhomogeneous integral equations, which yield solutions of a broad class of nonlinear evolution equations, are investigated in this paper, where the relations between the matrix elements are shown to lead to Miura transformations between the various partial differential equations.
Abstract: Two types of linear inhomogeneous integral equations, which yield solutions of a broad class of nonlinear evolution equations, are investigated. One type is characterized by a two-fold integration with an arbitrary measure and contour over a complex variable k , and thier complex conjugates, whereas the other one has a two-fold integration over one and the same contour. The inhomogeneous term, which may contain an arbitrary function of k , makes it possible to define a matrix structure on the solutions of the integral equations. The elements of these matrices are shown to obey a system of partial differential equations, the special form of which depends on the choice of the dispersion relation occurring in the integral equations. For special elements of the matrices closed partial differential equations can be derived, such as e.g. the nonlinear Schrodinger equation and the (real and complex) modified Korteweg-de Vries and sine-Gordon equations. The relations between the matrix elements are shown to lead to Miura transformations between the various partial differential equations.
65 citations
TL;DR: In this article, the static mobility tensors of an arbitrary number of spheres in a viscous fluid were evaluated to the case of finite frequencies, and the authors extended their work to evaluate the dynamic mobility tensor of a single sphere.
Abstract: We extend our previously developed scheme to evaluate the static mobility tensors of an arbitrary number of spheres in a viscous fluid, to the case of finite frequencies.
63 citations
TL;DR: In this article, the generalized Fokker-Planck equation for the distribution function of coarse-grained densities of conserved quantities is derived from the Liouville equation and then is investigated by using the gradient expansions in the flux correlation matrix.
Abstract: The paper studies nonlinear hydrodynamic fluctuations by the methods of nonequilibrium statistical mechanics. The generalized Fokker-Planck equation for the distribution function of coarse-grained densities of conserved quantities is derived from the Liouville equation and then is investigated by using the gradient expansions in the flux correlation matrix. We have obtained the functional-differential Fokker-Planck equation describing the nonlinear hydrodynamic fluctuations in spatially nonuniform systems to second order in gradients of coarse-grained fluctuating fields. An outline of the derivation of Fokker-Planck equations containing the Burnett terms is also given. The explicit coordinate representation for the hydrodynamic Fokker-Planck equation is discussed in the case of one-component simple fluid. The general scheme of a change of coarse-grained functional variables is developed for hydrodynamic Fokker-Planck equations. The corresponding transformation rules are found for “drift” terms, “diffusion coefficients” and thermodynamic forces. The dynamical equations and stationary conditions for averages of functions (functionals) of hydrodynamic fields are discussed by using the Fokker-Planck operators acting on such functions. The explicit form of these operators are found for various sets of fluctuating fields. As an application of the formalism the calculation of the stationary correlation functions is presented for a simple nonequilibrium steady state.
59 citations
TL;DR: In this paper, the authors used a hydrodynamic correction to give values for an infinite number of particles for the ratio D / D E (D is the self-diffusion coefficient and D E is the Enskog dense fluid diffusion coefficient) for a dense hard-sphere fluid, for the density range corresponding to 1.5 ⩽ V/V 0 ⌽ 4.0 (where V 0 is the volume of close-packed hard spheres), for systems of 128, 250 and 432 particles.
Abstract: Molecular dynamics calculations of the ratio D / D E (where D is the self-diffusion coefficient and D E is the Enskog dense fluid diffusion coefficient) for a dense hard-sphere fluid, have been done for the density range corresponding to 1.5 ⩽ V / V 0 ⩽ 4.0 (where V 0 is the volume of close-packed hard spheres), for systems of 128, 250 and 432 particles. Values of D / D E at a given density do not differ significantly for 250 and 432 particles, and the values are significantly smaller than those obtained for the same densities by Alder, Gass and Wainwright via application of a hydrodynamic correction to give values for an infinite number of particles. The D / D E values for 250 or 432 particles lead to a much better correlation between the Chandler hard-spheres theory and experimental diffusion data for methane than was obtained previously using the infinite system values of D / D E .
TL;DR: In this article, the melting transition of the two-dimensional, three-state, asymmetric or chiral clock model is examined, and the chiral symmetry-breaking operator is relevant at the symmetric (or pure Potts) critical point with a crossover exponent of o ≈ 0.2.
Abstract: The melting transition of the two-dimensional, three-state, asymmetric or chiral clock model is examined. Evidence from scaling arguments and analysis of perturbation series is presented, indicating that the chiral symmetry-breaking operator is relevant at the symmetric (or pure Potts) critical point with a crossover exponent of o ≈ 0.2. The remainder of the commensurate-disordered phase boundary therefore appears to be in a new universality class, distinct from the pure three-state Potts transition. An interfacial wetting transition that plays an important role in the crossover between the two types of critical behavior is discussed. The location and exponents of this wetting transition are obtained both in a low-temperature limit using generating function techniques and in a systematic low-temperature expansion of the transfer matrix.
TL;DR: Newton's Lagrange's and Hamilton's equations of motion have been modified to include the effects of constraints, nonequilibrium fluxes, and gradients as discussed by the authors, and these nonclassical equations provide estimates of the linear transport coefficients and, through nonlinear dissipative terms, can also simulate none-quilibrium steady states.
Abstract: Newton's Lagrange's and Hamilton's equations of motion have been modified to include the effects of constraints, nonequilibrium fluxes, and gradients. These nonclassical equations provide estimates of the linear transport coefficients and, through nonlinear dissipative terms, can also simulate nonequilibrium steady states. To illustrate the modified equations of motion, we apply them to a simple three-oscillator problem. The new methods have also been used to study nonlinear problems with large coupled gradients. We describe two examples: the coupling of heat flow with rotation and the simulation of strong shockwaves in dense fluids.
TL;DR: In this paper, the authors investigate the instabilities which can occur when a layer of a mixture of two miscible fluids in a porous medium is heated from below or from above, and they find that either a stationary instability or an oscillatory instability can occur as the first bifurcation depending on the sign and the magnitude of the Soret coefficient.
Abstract: We investigate the instabilities which can occur when a layer of a mixture of two miscible fluids in a porous medium is heated from below or from above. We find that either a stationary instability or an oscillatory instability can occur as the first bifurcation depending on the sign and the magnitude of the Soret coefficient. The possibility of an oscillatory convective instability when heating is done from above is pointed out for the first time. In addition, we discuss the mechanism of these instabilities using energy balance considerations.
TL;DR: An improved kinetic theory for the domain size distribution function of interacting kink systems in one-dimensional ordering kinetics is presented in this paper, where the correlation of two adjacent domains, which has been ignored previously, is found to have appreciable effects on quantitative aspects of the results obtained such as the ratio of the cutoff to average domain sizes.
Abstract: An improved kinetic theory for the domain size distribution function of interacting kink systems in one-dimensional ordering kinetics is presented. The correlation of two adjacent domains, which has been ignored previously, is found to have appreciable effects on quantitative aspects of the results obtained such as the ratio of the cut-off to average domain sizes. The theory leads to a new physical picture of one-dimensional domain growth in which the major role is played by coalescences of domains by rapid annihilations of the smallest domains with increasing cut-off size. The theory gives the scaled domain size distribution which is in remarkable agreement with that of molecular dynamics.
TL;DR: In this article, non-linear irreversible thermodynamics successfully relates a number of non-Newtonian effects observed, very far from equilibrium, outside the regime of local thermodynamic equilibrium.
Abstract: We review some of the principal results obtained from non-equilibrium molecular dynamics simulations of Couette flow in fluids. The simulations show that even simple fluids exhibit a wide variety of non-Newtonian behaviour (e.g., viscoelasticity, shear thinning and dilatancy, normal stress differences and non-local momentum transport). The asymptotic dispersion relations for each of these effects is consistent with the non-analytic functional forms predicted using “long-time-tail” theories. However in each case, the magnitude of the observed effect is much larger than theoretical predictions. We show that non-linear irreversible thermodynamics successfully relates a number of these non-Newtonian effects observed, very far from equilibrium, outside the regime of local thermodynamic equilibrium.
TL;DR: In this paper, a system consisting of a large number of kinks and antikinks moving under attractive interactions, which are annihilated on contacting each other, is studied using the method of molecular dynamics computer simulation.
Abstract: A system consisting of a large number (up to 40 000) of kinks and antikinks moving under attractive interactions, which are annihilated on contacting each other, is studied using the method of molecular dynamics computer simulation. The average distance between neighboring kinks increases logarithmically in time after a short initial transient period. The size distribution function of domains between neighboring kinks is also computed and found to develop a characteristic cut-off structure. Interpretation of the results in terms of simple kinetic models is given. The results are compared with the recent neutron scattering experiments on layered antiferromagnets by Ikeda.
TL;DR: In this article, a reduction in dielectric friction is calculated for two models: a time-dependent dipole at the center of a sphere, and a moving charge on the axis of a cylinder, each immersed in a dielectoric.
Abstract: Relaxation of nonequilibrium polarization fields in dielectrics is usually theoretically treated solely in terms of the reorientational motion of the polar molecules. If, however, the translational diffusion of these molecules is also taken into account, dielectric relaxation is accelerated. This results in the lowering of the dielectric friction that retards the motion of an ion or dipole in a dielectric. This reduction in dielectric friction is here calculated for two models: a time-dependent dipole at the center of a sphere, and a moving charge on the axis of a cylinder, each immersed in a dielectric. A parameter measuring the relative importance of rotation and diffusion is identified, and a substantial lowering of the dielectric friction is implied in many situations. It is shown that the boundary conditions play a decisive role in the properties of the fields. Directions for a further development of the theory of polarization diffusion are indicated.
TL;DR: In this paper, the authors considered the problem of determining the effective viscosity of dispersed systems (emulsions, suspensions) and derived a series expansion in terms of correlation functions.
Abstract: The problem of the determination of the effective viscosity of disperse systems (emulsions, suspensions) is considered. On the basis of the formal solution of the equations governing creeping flow in a statistically homogeneous dispersion, the effective viscosity is expressed in a series expansion in terms of correlation functions. The contribution of the interfacial tension to the effective viscosity is also considered and finally bounds for the effective viscosity are indicated.
TL;DR: In this article, a new approach to describe fluctuations of reversible chemical reactions in closed systems is proposed, where deterministic rate laws are cast into the form of nonlinear Onsager type closed laws, and a Fokker-Planck equation describing the stochastic process of concentration fluctuations is obtained.
Abstract: The paper proposes a new approach to describe fluctuations of reversible chemical reactions in closed systems. The deterministic rate laws are cast into the form of nonlinear Onsager type closed laws. By means of nonlinear transport theory a Fokker-Planck equation describing the stochastic process of concentration fluctuations is obtained. It is shown that the stochastic formulation reduces to the correct deterministic rate laws in the thermodynamic limit V → ∞ with the concentrations kept fixed. Concrete examples of reactions in ideal mixtures are given and the results of the presented approach are compared with those of the usual approach by means of a birth and death type master equation. It is shown that both approaches lead to the same stationary probability and exhibit the same natural boundaries reflecting the fact of a restricted state space. The proposed Fokker-Planck equation is different from the Fokker-Planck equation obtained from the master equation by truncating its Kramers-Moyal expansion. However, the two equations are shown to have identical Fokker-Planck coefficients in the vicinity of the deterministic equilibrium state. Compared with the usual master equation approach the proposed stochastic modeling of chemical reactions has the advantage of allowing for a straightforward extension to reactions in non-ideal mixtures.
TL;DR: In this paper, the problem of sedimentation and diffusion in a suspension of interacting spherical particles is discussed and the linear response of density and current on the basis of the generalized Smoluchowski equation is derived.
Abstract: We discuss the problem of sedimentation and diffusion in a suspension of interacting spherical particles. We consider external forces acting on the particles and study the linear response of density and current on the basis of the generalized Smoluchowski equation. The theory leads to a natural distinction between a hydrodynamic and a diffusion current. Each of these is defined as an observable in terms of the generalized mobility matrix. We derive general relations for the response functions.
TL;DR: In this paper, an analytical continuations into the complex energy plane of Dyson-Schmidt type of equations for the calculation of the density of states are constructed for a random alloy model, a liquid metal and for a liquid alloy.
Abstract: Analytic continuations into the complex energy plane of Dyson-Schmidt type of equations for the calculation of the density of states are constructed for a random alloy model, a liquid metal and for a liquid alloy In all these models the characteristic function follows from the solution of this equation Its imaginary part yields the accumulated density of states and its real part is a measure for the inverse of the localization length of the eigenfunctions The equations have been solved exactly for some distributions of the random variables In the random alloy case the strengths of the delta-potentials have an exponential distribution They may also have finite, exponentially distributed values with probability 0 ⪕ p ⪕ 1 and be infinite with probability q = 1 −p In the liquid metal the liquid particles are assumed to behave like hard rods This implies an exponential distribution of the distances between the particles The common electronic potential may be arbitrary, but is assumed to vanish outside the rods In the one-dimensional liquid alloy there is, apart from positional randomness of the liquid particles, a distribution of the strengths of the electronic delta-potentials For Cauchy distributions an argument of Lloyd is extended to obtain the characteristic function from the one in the model with equal strengths For the case of a liquid of point particles a three parameter class of distributions of the strengths is shown to yield a solution in the form of known functions of the equation mentioned above For several cases numerical calculations of the density of states and the inverse localization length of the eigenfunctions are presented and discussed
New results are found: exponential decay of the density of states near special energies in the random alloy and liquid metal; divergence of the density of states at certain energies with non-classical exponent 13 in the random alloy if the average of the potential strengths vanishes; exponentially small broadening of the bound-state levels for low concentrations of the liquid particles; peak in the localization length at the bound-state energies, which becomes exponentially narrow for low concentrations; different exponent in the decay of the inverse localization length at large energies for delta potentials and square-well potentials Further an expression for the grand potential is given, involving a sum over the characteristic function at certain points and divergence of the zero-point energy is found for Cauchy distributions of the delta potential strengths
TL;DR: In this paper, the authors consider linear systems in which some of the variables evolve on a much faster time scale than the remaining ones and extract a reduced dynamics in terms of the slow variables only, valid after an initial transient period.
Abstract: We consider linear systems in which some of the variables evolve on a much faster time scale than the remaining ones. By means of a systematic perturbation theory in the time-scale ratio we extract a reduced dynamics in terms of the slow variables only, valid after an initial transient period. The procedure provides a systematic extension of the usual adiabatic elimination scheme and gives corrections to it. We also find an expression for the long-time behavior of the correlation functions of the slow variables. These asymptotic expressions do not extrapolate back towards the equal-time correlations for t going to zero; the reason for this “initial slip” is given and its magnitude calculated. Method and results are illustrated with a simple example of coupled oscillators.
TL;DR: In this article, the Glauber-model is applied to a spin-one system with two possible orientations and the dynamic equations are solved for a system which has a first order transition.
Abstract: In order to study the dynamic behavior of a lattice gas, it is assumed that the molecules have a “hidden” (ie not directly observable) variable such as two possible orientations This generalization of the Glauber-model to a spin one system is solved using the most probable path method The dynamic equations are solved for a system which has a first order transition The solution is given in the form of a flow diagram and the results for various assumptions about the rate constants are described A method is suggested as to how such a system can become trapped in a metastable state by rapid cooling and by manipulation of the “hidden” variable
TL;DR: In this paper, a survey of experimental data related to the rotational degrees of freedom for the hydrogen isotopes and their mixtures with noble gases below 300 K is given, in as far as possible, expressed in terms of effective cross sections.
Abstract: A survey is given of experimental data related to the rotational degrees of freedom for the hydrogen isotopes and their mixtures with noble gases below 300 K. The results are, in as far as possible, expressed in terms of effective cross sections. The compilation includes experimental data on sound absorption, depolarized Rayleigh and Raman light scattering, flow birefringence, nuclear magnetic relaxation, viscosity, thermal conductivity and the magnetic field effect on transport properties.
TL;DR: A survey of the kinetic theory of transport phenomena in simple fluids is presented in this article, with a critique of the Green-Kubo formulae for the transport coefficients.
Abstract: A survey of the kinetic theory of transport phenomena in simple fluids is presented. The Chapman-Enskog solution of the Boltzmann equation for dilute gases, the Enskog theory for dense gases, and the current theory for moderately dense gases are discussed. Next, a critique of the Green-Kubo formulae for the transport coefficients is presented. After a discussion of the long time tail contributions to the transport coefficients, recent computer simulations of dense fluids under very severe strain rates or high frequencies are compared with present theory.
TL;DR: In this paper, a method for the calculation of viscosity coefficients describing non-Newtonian flow behavior and the normal pressure differences in a plane Couette symmetry is presented and some remarks on the connection with the linear viscoelasticity are made.
Abstract: After the introduction of viscosity coefficients describing the non-Newtonian flow behavior and the normal pressure differences in a plane Couette symmetry, methods for the calculation of these coefficients are presented and some remarks on the connection with the linear viscoelasticity are made. The nonlinear flow behavior stems from the influence of the vorticity of the flow field and of the symmetric traceless shear rate tensor on the primary shear-rate-induced anisotropy of molecular distribution functions. In the case of molecular liquids the orientational distribution of the molecular axes (alignment) is the most relevant quantity; in simple liquids it is the pair-correlation function. Results are presented which can be inferred from an extended version of irreversible thermodynamics of molecular liquids; from a Fokker-Planck equation approach and for simple liquids, from a kinetic equation of Kirkwood-Smoluchowski type for the pair-correlation function. Finally, some modifications are discussed which lead to a nonanalytic shear-rate and frequency dependence as observed for the viscosity coefficients in the computer simulations.
TL;DR: In this article, it was shown that the solution of the continuous Anisotropic Heisenberg Spin Chain (AHSC) can be obtained from the linear integral equation which was proposed in a previous paper for the solutions of the IHSC and the nonlinear Schrodinger equation.
Abstract: It is shown that the solutions of the continuous Anisotropic Heisenberg Spin Chain (AHSC) can be obtained from the linear integral equation which was proposed in a previous paper for the solutions of the Isotropic Heisenberg Spin Chain (IHSC) and the Nonlinear Schrodinger equation (NLS) An explicit expression is obtained for the Miura transformation which maps the solutions of the AHSC on solutions of the NLS In the second part of the paper we investigate the similarity solutions of these partial differential equations which leads to ordinary differential equations of Painleve type As an application we discuss some new solutions of Painleve IV
TL;DR: In this paper, the dynamics of a one-dimensional classical isotropic Heisenberg ferromagnetic spin system in the presence of a weak relativistic interaction, which causes damping of the spin motion, is considered.
Abstract: The dynamics of a one-dimensional classical continuum isotropic Heisenberg ferromagnetic spin system in the presence of a weak relativistic interaction, which causes damping of the spin motion, is considered. The corresponding evolution equation is identified with a damped nonlinear Schrodinger equation in terms of the energy and current densities of the unperturbed system. A direct perturbation method, along the lines of Kodama and Ablowitz, is developed for the envelope soliton solution of the nonlinear Schrodinger equation and the explicit perturbed solution obtained. This solution is found to be valid in a finite domain of the propagation space. To cover the entire region, a uniform solution is constructed using the matched asymptotic expansion technique. Finally, the spin vectors are constructed using the known procedures in differential geometry and the consequences of damping analysed briefly.
TL;DR: In this paper, Courbage and Prigogine gave the mathematical details and various extensions of the results stated in previous work of Courbage, and extended the theory of transition to Markov processes to such measures.
Abstract: We give the mathematical details and various extensions of the results stated in previous work of Courbage and Prigogine. “Intrinsic random systems” are deterministic and conservative dynamical systems for which we can associate two dissipative Markov processes through a one-to-one “change of representation”, the first leading to equilibrium for t→+∞ and the second for t→-∞. The microscopic formulation of the second principle of thermodynamics permits to lift the degeneracy by the exclusion of all states that do not approach equilibrium for t→+∞. The set of admitted initial conditions D+ is then characterized by a non-equilibrium entropy functional which is infinite for rejected initial states and takes finite values for admitted initial conditions. Thus, rejected initial states correspond to an infinite amount of information. To realize this selection rule we consider general probability measures on phase space that are not necessarily absolutely continuous and we extend the theory of transition to Markov processes to such measures. Owing to the non-invariance of D+ under the time inversion, the evolution of these states in the new representation can only be given by one of the two possible Markov processes.