# Werner O. EbelingRostock University and Humboldt-University Berlin · Institute of Theoretical Physics Department of Physics

Werner O. Ebeling

Dipl.Phys., Dr.rer.nat.habil.

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770

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Introduction

New analytical tools for the calculation of thermodynamical and
transport properties of complex electrolytes including seawater

## Publications

Publications (770)

In 1932 Onsager and Fouss found in a seminal work that the the conductivity of mixtures
of electrolytes depends on specific mixture effects which may be calculated by means
of a matrix theory. Here we formulate the matrix theory of conductivity for seawater. We solve that problem of seawater conductivity for a 6 - component model and show numerical...

In previous work we developed a statistical method for calculating the individual activities of ions including the electrostatic association of ions in a semi-chemical picture. Here we estimate explicitly the ionization constants for pair and triple electrostatic association and calculate the degree of ionization for electrolytic mixtures including...

For universality in the approach, it is customary to appropriately rescale problems to a single or a set of dimensionless equations with dimensionless quantities involved or to rescale the experimental setup to a suitable size for the laboratory conditions. Theoretical results and/or experimental findings are supposed to be valid for both the origi...

Based on methods of statistical mechanics for the calculation of individual activity coefficients for electrolytic solutions we present analytical nonlinear extensions of the standard Debye - Hückel and Mean-Spherical approximations. These extensions, so - called DHX and MSX approximations, respectively, generalize the exact results from cluster th...

A few salient soliton-like wave evolutionary features of one- and two-dimensional lattices of interacting active units are provided here. In the latter case, particular attention is given to the crystal-like triangular lattice. On the one hand, the units are coupled with nearest neighbors anharmonic forces (Morse potential). On the other hand the u...

We consider the dynamics of electrons and holes moving in two-dimensional lattice layers and bilayers. As an example, we study triangular lattices with units interacting via anharmonic Morse potentials and investigate the dynamics of excess electrons and electron–hole pairs according to the Schrödinger equation in the tight binding approximation. W...

The pandemic COVID-19 spread is considered on the basis of mathematical model recently proposed by the authors. Historical and evolutionary aspects of the pandemic are discussed and the perspectives for the end of COVID-19 are formulated based on the statistical data and historical examples.

So far, individual activity coefficients of ions could not be measured directly in electrochemical experiments. Their knowledge is important, however, for the solution of various physical chemical problems, and is particularly of high relevance for understanding and estimating the pH of seawater and related climatological studies. In this paper we...

Zu Marx’ 200. Geburtstag trafen sich 2018 in Berlin Wissenschaftler verschiedenster Fachdisziplinen und Generationen, um sein Denken auf heuristisches Potential für gegenwärtige und künftige Probleme und Entwicklungen hin zu befragen. Sowohl durch positive Anknüpfung als auch durch kritische Distanzierung erarbeiteten sie sich einen Zugang unter de...

First statistical derivation of diffusion equations from the Liouville equation based on Zwanzigs method of projection operators

Selforganization, Valuation and Optimization

Analysis of the connections between selforganization and optimization

Some new and exact results from cluster expansion incuding higher
virial coefficients, methods for estimation of potential parameters

Provided in this paper is a theory of long-range electron transfer with near sound (supersonic or subsonic) velocity along one-dimensional crystal lattices. The theory represents the development of an earlier work by introducing Marcus formulation. To illustrate its application to a realistic case, the theory is used to offer an explanation of two...

Based on statistical methods to calculate individual activity coefficients of ions in electrolyte solutions developed in parts I and II, we present here applications to two simplified seawater models (SWM 2+ and SWM 6+). As in the foregoing parts we start with exact results for the model of hard charged spheres (non-additive radii) obtained from th...

Mobile discrete breathers (MDBs) are here suggested as localized excitations underlying the trapping and transport of charged particles (electron or hole) along a DNA-like molecular wire with anchored ends such as attached to two electrodes. For illustration the Peyrard-Bishop-Dauxois-Holstein (PBDH) model is used. MDBs are excited by imposing appr...

Based on a previous survey of statistical methods to calculate individual activity coefficients of ions in electrolyte solutions (part I, authored with Hartmut Krienke), we present here applications to several components of seawater such as NaCl, KCl and MgCl 2 , MgSO 4 , CaCl 2 , CaSO 4 and Na 2 SO 4. We investigate these components individually,...

We study the temporal and spatial nonlinear dynamical evolution of a coupled triangular lattice crystal bilayer system where in one layer one excess free electron is injected while an excess positive charge, a hole, is created in the other. The atoms of each of the backbone lattices interact with anharmonic (short range) Morse potentials whereas th...

In this chapter, we will introduce useful tools of Quantum Statistics. Most of them will be used in later chapters of this book to solve concrete problems. Our survey covers, of course, the most prominent methods such as density operators introduced by von Neumann and Landau, Wigner’s phase-space functions method, and Bogolyubov’s method of reduced...

Planck’s theory of radiation which is the origin of quantum statistics, was semi-phenomenological based on concepts of electrodynamics, classical thermodynamics, and classical radiation theory.

Matter appears on our planet, in the solar system and in the rest of Universe in rather different forms.

With increasing density of plasmas, non-ideality effects become more and more apparent. This is of particular importance for plasmas with deep bound states, that is, when the thermal energy is smaller than or of the same order as the ground state energies of the atoms in the plasma. For hydrogen this is the case already for T < 10⁵ K. Then, except...

Quantum statistics is a many body theory describing macroscopic matter. Let us first summarize concepts of classical many body theory and subsequently concepts of many body quantum theory, just what we need in the following. After this we will proceed to the simplest quantum statistical ensembles.

The pioneers of the theory of classical kinetic equations are Rudolf Clausius (1822–1888), James Clerk Maxwell (1831–1879) and Ludwig Boltzmann (1844–1906). Their theories are based on the classical dynamics of particles in the phase space according to Liouville and on detailled studies of the classical mechanics of collisions between neutral molec...

From the classical kinetic theory of gases we know the equation of state of the ideal gas, βp = n (see Chap. 1). For real gases, the interaction forces between the molecules lead to corrections to the ideal gas equation of state. We mention the classical theory by van der Waals and the systematic expansions with respect to density, called virial ex...

In the first part of this work we provide a survey of several methods to estimate the individual activity coefficients of ions in electrolyte solutions in the light of statistical theory. In particular we discuss statistical methods based on the model of hard charged spheres and other simple ionic interaction potentials, such as the Debye-Hückel ap...

We study here the old problem of individual activity coefficients in the light of statistical theory. Several methods are proposed for the estimation of theoretical individual ionic activity coefficients using he model of hard charged spheres and other simple potentials on the basis of virial expansions, DHX-approximations, the analytical solution...

Prof. Werner Ebeling and Rainer Feistel (Germany) understand selforganization as the opposite of normal processes, which show a tendency to dissipate energy, the growth of chaos. As a necessary condition, selforganization requires a supercritical distance from the thermodynamic equilibrium and the provision of high-quality energy. Evolution is a ch...

We construct metastable long-living hexagonal lattices with appropriately modified Morse interactions and show that highly-energetic solitons may be excited moving along crystallographic axes. Studying the propagation, their dynamic changes and the relaxation processes it appears that lump solitons create in the lattice running local compressions....

In 1971, Manfred Eigen extended the principles of Darwinian evolution to chemical processes, from catalytic networks to the emergence of information processing at the molecular level, leading to the emergence of life. In this paper, we investigate some very general characteristics of this scenario, such as the valuation process of phenotypic traits...

The self-organization of information belongs to the basic topics of Haken’s synergetics. The basic statement of this paper is following Eigen and Haken-Krell that information is a product of evolution and: there is no information processing without life, and there is no life without information processing. The origin of information processing is ba...

Localized supersonic long-living nonlinear modes excited in triangular lattices of point particles interacting via potential Morse bonds are studied in a frame of a model with appropriately chosen bonds to rule out redundancy bonds. Numerical simulations on a base of Newtonian equations are performed to define configurations (coordinates and veloci...

The most fundamental approach to study relativistic quantum systems of many particles is currently a quantum field theory (QFT). In these theories, particles are usually considered as elementary excitations of the corresponding field. This approach automatically takes into account the creation and annihilation of particles, and treats interactions...

In this chapter we substantially extend the analysis of the previous chapters to two-component partially ionized Coulomb systems with positive and negative charges and a mass ratio M varying between one and two thousand. While low values of the mass ratio M are directly relevant for semiconductors, we do not consider any special solid state propert...

Plasmas with deep bound states are not well described by density expansions. Here fugacity expansions are a very useful alternative to density expansions. The quantum-statistical theory is formulated in the grand canonical ensemble. This provides representations of the pressure and the densities in terms of the fugacities, which serve as implicit v...

In this chapter we begin by examining simple models of electron hopping between bound states located on sites or atoms. In particular, we investigate electron hopping on classical dynamic lattices. Then we discuss models of molecular dynamics of electrons based on effective potential interactions, including models of Wigner dynamics with coordinate...

As example, we consider application of the theoretical approach discussed in the last chapter to treatment of a partially ionized strongly coupled dense electron-hole plasma. We take into account strong Coulomb correlation effects such as bound states (excitons, bi-excitons, clusters), their modification by the surrounding plasma, and their eventua...

This brief survey of kinetic and transport theory starts with the stochastic approach, which is mathematically simpler than kinetic equations of Boltzmann and Lenard–Balescu type. We continue with Lorentz approximations and then discuss the derivation of quantum Boltzmann equations using the Bogoliubov method. The next topic is fluctuation–dissipat...

The aim of this chapter is to extend the equation of state (EOS) found in the last three chapters to higher densities.

We summarize the physics and the statistical theory of strongly coupled gases. Starting from the binary correlation functions, we develop systematic expansions with respect to the density, the so-called virial expansions, and also fugacity expansions. Further, we discuss solutions of integral equations (PY and HNC) for dense systems. Quantum effect...

The elementary quantum theory of screening effects is described using essentially classical semi-phenomenological methods, and tools developed by Debye-Hückel, Bogoliubov, Mayer, and other pioneers. Following Morita and Kelbg, quantum effects are modeled by nonsingular effective potentials.

Hydrodynamic simulations of relativistic heavy-ion collisions require knowledge, not only of the thermodynamic properties of the QGP, but also of the transport properties. While significant progress in calculations of the thermodynamic properties of QGP has been made in recent years, the transport properties are still poorly accessible using lattic...

As pointed out in Chaps. 1 and 3, the correlations in classical Coulomb systems such as electrolytes and quasi-classical plasmas were first studied by Milner, Debye, Hückel, Wigner, and others. Strictly speaking, there is no classical statistical theory of point charges, due to several divergencies which show when Debye’s limiting laws are not appl...

Here we summarize the most important results in this field of physics, which is growing due to the dominant role of these forms of matter in the cosmos. We describe the progress made in physical studies and the statistical theory of dense gases and nonideal plasmas, including their historical roots in the work of van der Waals, Debye, Saha, Planck,...

It is shown how the ideas based on the concept of selforganization and the new discipline synergetics changed our views. First the basic priciples of selforganization and evolution are explained. Then we show in particular that these ideas played an important role in the social changes in East European countries at the end of the last century. In t...

Dietrich Kremp (1937–2017) made important contributions to statistical physics, especially quantum statistics, plasma physics, and the physics of electrolytes. He was a recognized member of the strongly coupled Coulomb systems and non-ideal plasmas communities, and his text books continue to have a profound influence on these fields.

We summarize the work devoted to plasma thermodynamics and ionization theory performed by two protagonists working at Kiel University: Max Planck and Albrecht Unsöld. First we show that Planck developed, in Kiel, the basis for describing the chemical equilibria between charged particles (ions) and formulated later, in Berlin, the first complete ver...

First we discuss some early work of Ulrike Feudel on structure formation in nonlinear reactions including ions and the efficiency of the conversion of chemical into electrical energy. Then we give some survey about energy conversion from chemical to higher forms of energy like mechanical, electrical and ecological energy. We consider examples of en...

We investigate how an magnetic field influences the ionization equilibrium

We discuss the relation between entropy and information from the physicists point of view differing between bound and free information. The quantitative physical aspects of information flow are given by flows of entropy, which are closely related to the reduction of uncertainty and the predictability of events. Free information is considered as a q...

The aim of this book is the pedagogical exploration of the basic principles of quantum-statistical thermodynamics as applied to various states of matter – ranging from rare gases to astrophysical matter with high-energy density. The reader will learn in this work that thermodynamics and quantum statistics are still the concepts on which even the mo...

The excitation of solitons and discrete breathers (pinned or otherwise, also known as intrinsic localized modes, DB/ILM) in a one-dimensional lattice, also denoted as a chain, is considered when both on-site and inter-site vibrations, coupled together, are governed by the empirical Morse interaction. We focus attention on the transformation of the...

We present computational evidence of the possibility of fast, supersonic or subsonic, nearly loss-free ballistic-like transport of electrons bound to lattice solitons (a form of electron surfing on acoustic waves) along crystallographic axes in two-dimensional anharmonic crystal lattices. First we study the structural changes a soliton creates in t...

We investigate the relation between entropy and the possibility to find shorter representations (compressibility) of sequences consisting of letters etc.

Adam Smith, Charles Darwin, Rudolf Clausius, and Léon Brillouin considered certain “values” as key quantities in their descriptions of market competition, natural selection, thermodynamic processes, and information exchange, respectively. None of those values can be computed from elementary properties of the particular object they are attributed to...

It is shown that in DNA-like molecules containing added, excess charges, such as electrons and holes (cation-radicals), it is possible by highly energetic, local, mechanical excitation at definite places of the chain to control the creation of breathers/bubbles and hence to control the long-range transfer of charges moving along the chain in a defi...

We study here several simple models of the electron transfer (ET) in a one-dimensional nonlinear lattice between a donor and an acceptor and propose a new fast mechanism of electron surfing on soliton-like excitations along the lattice. The nonlinear lattice is modeled as a classical one-dimensional Morse chain and the dynamics of the electrons are...

We study by means of numerical simulation collisions of quasi-one-dimensional solitonic excitations in a 2D lattice of particles interacting via Morse potential forces. Local mobile excitations arise as a result of strong kicks for one or some selected particles stimulating motion of compression of density along crystallographic axes. It is shown t...

Wie Hermann Haken in seinem Beitrag zu diesem Band dargelegt hat (Haken, 2015), fanden die ersten Tagungen auf dem Gebiet in Westeuropa Ende der 60er Jahre statt, insbesondere „Theoretical Physics and Biology“ in Versailles 1967 und die erste Synergetik-Tagung in Elmau 1972. Die ersten uns bekannten Seminare in Osteuropa fanden in den frühen 70er J...

Die Ursprünge der Synergetik und der physikalisch orientierten Theorie der Selbstorganisation liegen in den Arbeiten verschiedener wissenschaftlicher Schulen, die sich in den 60er und 70er Jahren des 20. Jahrhunderts herausgebildet haben. Wie Hermann Haken in seinem Beitrag zu diesem Band dargelegt hat (Haken, 2014), gab es bereits in den 60er Jahr...

We summarize life and work on nonideal plasma thermodynamics of the late Fazylkhan Baimbetov. Analyzing Baimbetovs method of pseudo potentials we develop several extensions. First we optimize the parameter choice by comparing with recent exact results for thermodynamics. We compare the result of the pseudopotential method with the available exact r...

Dynamic entropies, long range correlations and fluctuations in linear structures, symbolic sequances.

Arbeitskreis "Prinzip Einfachheit" der Leibniz-Sozietät der Wissenschaften zu Berlin , Wissenschaftliche Vorträge 2010 - 2015

Die Autoren geben als aktiv Beteiligte erstmalig aus ihrem persönlichen Erleben eien Einblick auf die ersten zwei Jahrzehnte der Synergetik-Geschichte. Hermenn Haken führt in die Begrifflichkeit der Synergetik ein und verdeutlicht die Schwierigkeiten, ein neues Denken in der Wissenschaft zu etablieren. Peter Plath geht exemplarisch auf die Vorgesch...

In a recent paper [Phys. Rev. E 91, 013108 (2015)PLEEE81539-375510.1103/PhysRevE.91.013108], Kraeft et al. criticize known exact results on the equation of state of quantum plasmas, which have been obtained independently by several authors. They argue about a difference in the definition of the direct two-body function Q(x), which appears in virial...

We consider the wave dynamics of a one-dimensional lattice where both on-site and inter-site vibrations, coupled together, are governed by Morse interactions. We focus attention on the onset of lattice solitons and discrete breathers (DBs, aka intrinsic localized modes, ILM). We show how varying the relative strength of the on-site potential to tha...

Building upon the findings of Muto et al. [Phys. Lett. A 136, 33 (1989)] and
Marchesoni and Lucheroni [Phys. Rev. E 44, 5303 (1991)] about the growth of
the number of (anharmonic) lattice solitons with increasing temperature and using a recent
transport theory developed by the present authors [A.P. Chetverikov, W. Ebeling, G. Röpke,
M.G. Velarde, E...

We model electron transfer from donor to acceptor with a lattice with non-uniform electron on-site energies. The electron motion is described in a tight binding approximation and the lattice site dynamics follows the Morse potential. We focus on the transition time from donor to acceptor which is first determined analytically for a rigid lattice an...

The pairing of electrons in harmonic and anharmonic one-dimensional lattices is studied with account of the electron-lattice interaction. It is shown that in harmonic lattices binding of electrons in a bound localized state called bisoliton, takes place. It is also shown that bisolitons in harmonic lattices can propagate with velocity below the vel...

We study solitons and solectrons and their time and space evolution in triangular and quadratic anharmonic lattices with Morse interactions. First we offer computational evidence of the possibility of long lasting, supersonic lattice solitons moving along crystallographic axes. On the basis of the dispersion equations we postulate appropriate evolu...

The efficiency of a simple model of a motor converting chemical into mechanical energy is studied analytically. The model motor shows interesting properties corresponding qualitatively to motors investigated in experiments. The efficiency increases with the load and may for low loss reach high values near to 100 percent in a narrow regime of optima...

We presnt the result of MD simulations of the electric microfield in symmetrical plasmas

Following the spirit of the late John Nicolis, the purpose of this paper is to develop an evolutionary approach for the basic problem of generation, storage and dissipation of information in physical and biological systems via dynamical processes. After analysing the relation of entropy and information we develop our view that information is in gen...

We study the linear and nonlinear conductivity of plasma by solution of Fokker-Planck equations

The problems of high linear conductivity in an electric field, as well as
nonlinear conductivity, are considered for plasma-like systems.
First, we recall several observations of nonlinear fast charge transport in
dusty plasma, molecular chains, lattices, conducting polymers and semiconductor
layers. Exploring the role of noise we introduce the gen...

Mnay models situated in the current research landscape of modelling and
simulating social processes have roots in physics. This is visible in the name
of specialties as Econophysics or Sociophysics. This chapter describes the
history of knowledge transfer from physics, in particular physics of
self-organization and evolution, to the social sciences...

The quantum statistics of electrons interacting with nonlinear excitations of a classical heated nonlinear lattice of atoms is studied. By using tight-binding approximation, Wigner momentum distributions and computer simulations we show the existence of quite fast and nearly loss-free motions of charges along crystallographic axes and estimate the...

We provide here a theory to account for the thirty-year-old outstanding experimental results by Donovan and Wilson on the electron transport in polydiacetylene (PDA) single crystals. Both supersonic and subsonic velocities are described. In the former case we predict that the velocity is field independent for several decades of the field strength i...

We study here localized excitations in a Morse lattice model of two-dimensional CuO
2 layers (cuprates in short). The Cu-atoms are positioned motionless in a square lattice and the oxygen atoms are able to oscillate around originally equilibrium positions on another superposed square lattice. After studying regular oxygen lattices we investigate la...

We study the quantum dynamics and statistics of electrons interacting with nonlinear excitations of a classical thermal lattice of atoms on a semi-phenomenological basis. By theoretical estimates based on tight-binding approximations, Wigner distributions and computer simulations we show the existence of fast and nearly loss-free motions of electro...

After recalling features of solitons in the Toda (more precisely an adapted Morse-Toda) lattice a succint discussion is provided about the stability of such solitons when the lattice is heated up to physiological temperatures for values of parameters typical of bio-macro-molecules. Then the discussion is focused on the soliton trapping of an added...

We analyze the dynamics of driven translations or rotations based on models with internal oscillations. In particular we discuss several new mechanisms of motors driven by chemical energy. First we study the simple depot model and give analytical solutions including efficiency and stochastic effects. Then we introduce internal oscillations based on...

We study soliton-like excitations and their time and space evolution in several two-dimensional anharmonic lattices with Morse interactions: square lattices including ones with externally fixed square lattice frame (cuprate model), and triangular lattices. We analyze the dispersion equations and lump solutions of the Kadomtsev-Petviashvili equation...