Search Results (14)

We consider Onsager’s non-equilibrium thermodynamics from the perspective of the gradient flow in information geometry. Assuming Onsager’s reciprocal relations, we can regard his phenomenological equations as gradient-flow equations and develop two different gradient-flow models. We consider their features and their relations. Both models are applied to the ideal gas and van der Waals gas. Full article

This study examines the thermal conduction resistance in anisotropic bodies using linear extended irreversible thermodynamics. The fulfilment of the Onsager Reciprocal Relations in anisotropic bodies, such as crystals, has been demonstrated. This fulfilment is achieved by incorporating Newton’s heat transfer coefficients into the calculation of the entropy production rate. Furthermore, a basic principle for the transport of heat, similar to the Onsager–Fuoss formalism for the multicomponent diffusion at a constant temperature, was established. This work has the potential to be applied not just in the field of material science, but also to enhance our understanding of heat conduction in crystals. A novel formalism for heat transfer analogous to Onsager–Fuoss model for multicomponent diffusion was developed. It is believed that this work could be applied for educational purposes. Full article

Diffusiophoresis is the isothermal migration of a colloidal particle through a liquid caused by a cosolute concentration gradient. Although diffusiophoresis was originally introduced using hydrodynamics, it can also be described by employing the framework of multicomponent diffusion. This not only enables the extraction of diffusiophoresis coefficients from measured multicomponent-diffusion coefficients but also their theoretical interpretation using fundamental thermodynamic and transport parameters. This review discusses the connection of diffusiophoresis with the 2 × 2 diffusion-coefficient matrix of ternary liquid mixtures. Specifically, diffusiophoresis is linked to the cross-term diffusion coefficient characterizing diffusion of colloidal particles due to cosolute concentration gradient. The other cross-term, which describes cosolute diffusion due to the concentration gradient of colloidal particles, is denoted as osmotic diffusion. Representative experimental results on diffusiophoresis and osmotic diffusion for polyethylene glycol and lysozyme in the presence of aqueous salts and osmolytes are described. These data were extracted from ternary diffusion coefficients measured using precision Rayleigh interferometry at 25 °C. The preferential-hydration and electrophoretic mechanisms responsible for diffusiophoresis are examined. The connection of diffusiophoresis and osmotic diffusion to preferential-interaction coefficients, Onsager reciprocal relations, Donnan equilibrium and Nernst–Planck equations are also discussed. Full article

The Kelvin relation, relating the Seebeck coefficient and the Peltier coefficient, is a theoretical basis of thermoelectricity. It was first derived by Kelvin using a quasi-thermodynamic approach. However, Kelvin’s approach was subjected to much criticism due to the rude neglect of irreversible factors. It was only later that a seemingly plausible proof of the Kelvin relation was given using the Onsager reciprocal relation with full consideration of irreversibility. Despite this, a critical issue remains. It is believed that the Seebeck and Peltier effects are thermodynamically reversible, and therefore, the Kelvin relation should also be independent of irreversibility. Kelvin’s quasi-thermodynamic approach, although seemingly irrational, may well have touched on the essence of thermoelectricity. To avoid Kelvin’s dilemma, this study conceives the physical scenarios of equilibrium thermodynamics to explore thermoelectricity. Unlike Kelvin’s quasi-thermodynamic approach, here, a completely reversible thermodynamic approach is used to establish the reciprocal relations of thermoelectricity, on the basis of which the Kelvin relation is once again derived. Moreover, a direct thermodynamic derivation of the Onsager reciprocal relations for fluxes defined as the time derivative of an extensive state variable is given using the method of equilibrium thermodynamics. The present theory can be extended to other coupled phenomena. Full article

Equilibrium thermodynamics answers the question, “by how much?” Nonequilibrium thermodynamics answers the question “how fast?” The physicochemical mechanics approach presented in this article answers both of these questions. It also gives equilibrium laws and expressions for all major transport coefficients and their relations, which was previously impossible. For example, Onsager’s reciprocal relations only tell us that symmetric transport coefficients are equal, and even for these, the value is often not known. Our new approach, applicable to non-isolated systems, leads to a new formulation of the second law of thermodynamics and agrees with entropy increase in spontaneous processes for isolated systems. Instead of entropy, it is based on a modified Lagrangian formulation which always increases during system evolution, even in the presence of external fields. This article will present numerous examples of physicochemical mechanics can be applied to various transport processes and their equilibriums, including thermodiffusion and different surface processes. It has been proven that the efficiency of a transport process with an actual steady-state flux (as opposed to a reversible process near equilibrium) is 50%. Finally, an analogy between physicochemical mechanics and some social processes is mentioned. Full article

In this work, the linearity axiom of irreversible thermodynamics for diffusion and heat transfer has been re-examined. It is shown that this axiom is compatible with the entropy production invariance principle with respect to a reference quantity for diffusion and heat transfer in the Euclidean space. Moreover, the underlying relations of the other principles of irreversible thermodynamics for multi-component diffusion and heat transfer, such as the quasi-equilibrium and the Onsager reciprocal relations (ORR) with the entropy production invariance, are re-examined. It was shown that the linearity principle postulates for diffusion and heat transfer and could be directly derived from the entropy production invariance axiom. It is believed that this work could not only be used for the drying of polymer coatings but also for pedagogical purposes. It may also be generalized; thus, leading to a generalized framework for irreversible thermodynamics. Full article

The recent developments in dynamical systems theory and non-equilibrium statistical mechanics have allowed the birth of new challenges and research perspectives. In particular, different frameworks have been proposed for the modeling of complex emerging phenomena occurring in nature and society. This editorial article introduces the topic and the contributions of this Special Issue. This Special Issue focuses, on the one hand, on the development of new methods, frameworks and models coming from dynamical system theory and the equilibrium/non-equilibrium statistical mechanics and, on the other hand, opens problems related to the existing frameworks. The Special Issue also includes applications to physical, biological and engineering systems. Full article

In this survey-cum-expository work, we primarily seek to study many families of the renowned Hurwitz–Lerch Zeta mapping, including the so-called generalized Hurwitz–Lerch Zeta mappings. The purpose of this study is to examine a new subclass of Hurwitz–Lerch Zeta mappings with negative coefficients in the unit disc $U=\{z\in \mathbb{C}:|z|<1\}.$ We explore fundamental characteristics of the defined class, such as coefficient inequality, neighborhoods, partial sums, and integral means properties. Full article

In this work, we investigate the validity of axioms such as Onsager Reciprocal Relations (ORR) for heat transfer in irreversible thermodynamics close to equilibrium. We show that the ORR for this case could be directly derived by introducing the widely accepted concept of heat transfer coefficients into the entropy production rate and by assuming that the thermal conductivity coefficients are uniquely defined. It is believed that this work can not only be used for pedagogical purposes but may also be generalized to other processes beyond heat transfer, thus leading to a generalized framework for transport phenomena and irreversible thermodynamics. Full article

Time reversal invariance (TRI) of particles systems has many consequences, among which the celebrated Onsager reciprocal relations, a milestone in Statistical Mechanics dating back to 1931. Because for a long time it was believed that (TRI) dos not hold in presence of a magnetic field, a modification of such relations was proposed by Casimir in 1945. Only in the last decade, the strict traditional notion of reversibility that led to Casimir’s work has been questioned. It was then found that other symmetries can be used, which allow the Onsager reciprocal relations to hold without modification. In this paper we advance this investigation for classical Hamiltonian systems, substantially increasing the number of symmetries that yield TRI in presence of a magnetic field. We first deduce the most general form of a generalized time reversal operation on the phase space of such a system; secondly, we express sufficient conditions on the magnetic field which ensure TRI. Finally, we examine common examples from statistical mechanics and molecular dynamics. Our main result is that TRI holds in a much wider generality than previously believed, partially explaining why no experimental violation of Onsager relations has so far been reported. Full article

The aim of this work is to apply linear non-equilibrium thermodynamics to study the electrokinetic properties of three cation-exchange membranes of different structures in ethanol-water electrolyte solutions. To this end, liquid uptake and electro-osmotic permeability were estimated with potassium chloride ethanol-water solutions with different ethanol proportions as solvent. Current–voltage curves were also measured for each membrane system to estimate the energy dissipation due to the Joule effect. Considering the Onsager reciprocity relations, the streaming potential coefficient was discussed in terms of ethanol content of the solutions and the membrane structure. The results showed that more porous heterogeneous membrane presented lower values of liquid uptake and streaming potential coefficient with increasing ethanol content. Denser homogeneous membrane showed higher values for both, solvent uptake and streaming coefficient for intermediate content of ethanol. Full article

In the present work, we study a mesoscopic system consisting of a double quantum dot in which both quantum dots or artificial atoms are electrostatically coupled. Each dot is additionally tunnel coupled to two electronic reservoirs and driven far from equilibrium by external voltage differences. Our objective is to find configurations of these biases such that the current through one of the dots vanishes. In this situation, the validity of the fluctuation–dissipation theorem and Onsager’s reciprocity relations has been established. In our analysis, we employ a master equation formalism for a minimum model of four charge states, and limit ourselves to the sequential tunneling regime. We numerically study those configurations far from equilibrium for which we obtain a stalling current. In this scenario, we explicitly verify the fluctuation–dissipation theorem, as well as Onsager’s reciprocity relations, which are originally formulated for systems in which quantum transport takes place in the linear regime. Full article

This paper investigates not fully explained voltage offsets observed by several researchers during the measurement of the Seebeck coefficient of high Z materials. These offsets, traditionally attributed to faulty laboratory procedures, have proven to have an irreducible component that cannot be fully eliminated in spite of careful laboratory procedures. In fact, these offsets are commonly observed and routinely subtracted out of commercially available Seebeck measurement systems. This paper offers a possible explanation based on the spontaneous formation of an adiabatic temperature gradient in the presence of a force field. The diffusion-diffusion heat transport mechanism is formulated and applied to predict two new thermoelectric effects. The first is the existence of a temperature gradient across a potential barrier in a semiconductor and the second is the Onsager reciprocal of the first, that is, the presence of a measureable voltage that arises across a junction when the temperature gradient is forced to zero by a thermal clamp. Suggested future research includes strategies for utilizing the new thermoelectric effects. Full article

A rate equation for a discrete probability distribution is discussed as a route to describe smooth relaxation towards the maximum entropy distribution compatible at all times with one or more linear constraints. The resulting dynamics follows the path of steepest entropy ascent compatible with the constraints. The rate equation is consistent with the Onsager theorem of reciprocity and the fluctuation-dissipation theorem. The mathematical formalism was originally developed to obtain a quantum theoretical unification of mechanics and thermodinamics. It is presented here in a general, non-quantal formulation as a part of an effort to develop tools for the phenomenological treatment of non-equilibrium problems with applications in engineering, biology, sociology, and economics. The rate equation is also extended to include the case of assigned time-dependences of the constraints and the entropy, such as for modeling non-equilibrium energy and entropy exchanges. Full article