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The Entropy Production—as Cornerstone in Applied Nonequilibrium Thermodynamics—Dedicated to Professor Signe Kjelstrup on the Occasion of Her 75th Birthday

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A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Thermodynamics".

Deadline for manuscript submissions: 31 December 2024 | Viewed by 4464

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Special Issue Editors

Prof. Dr. Dick Bedeaux

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Guest Editor

PoreLab, Department of Chemistry, Norwegian University of Science and Technology, 7491 Trondheim, Norway
Interests: nonequilibrium thermodynamics for surfaces; boundary conditions; nonequilibrium statistical mechanics; transport through porous media; nanothermodynamics

Prof. Dr. Fernando Bresme

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Guest Editor

Department of Chemistry, Imperial College London, London W12 0BZ, UK
Interests: nonequilibrium transport phenomena; molecular simulations; nanoscale heat transport; interfacial science; nonequilibrium thermodynamics; soft matter and complex fluids

Prof. Dr. Alex Hansen

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Guest Editor

PoreLab, Department of Physics, Norwegian University of Science and Technology, 7491 Trondheim, Norway
Interests: transport in porous media; multiphase flow in porous media; non-Newtonian fluid flow in porous media; statistical mechanics; fluid mechanics; nonequilibrium thermodynamics
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Special Issue Information

Dear Colleagues,

The entropy production of nonequilibrium transport processes is at the heart of all of Signe Kjelstrup’s contributions to science, from fuel cells and batteries to shock waves. It is always used to define the independent system variables and thus the coupled flux–force relations in the system of interest, whether the system is a homogeneous electrolyte, a heterogeneous electrochemical interface, a catalyst or a porous medium. To her, typical questions concern the following: how many molecules are needed to write thermodynamic equations for a volume element? Local equilibrium conditions, do they apply to evaporation at interfaces? The entropy balance, according to Kjelstrup, is an underused balance equation in the modelling of applications, for instance chemical reactors or batteries. Is that so? Should entropy production, as computed precisely from the flux–force relations, be linked to exergy analysis, say on oil platforms or for liquefaction of air. Entropy production minimization is essential for work on energy efficiency of process plants, and maybe also to understand designs in nature, like in the seal nose.

With this Special Issue, we hope to encourage large effort in this important field. The purpose of the Special Issue is to demonstrate the strength and importance of the theory of nonequilibrium thermodynamics, with its fundamental basis in entropy production, when used to improve the understanding of processes essential to mankind, industry or nature at large. The editors invite original works that elucidate the various aspects of the statements and questions above. They invite authors also to write shorter analyses (Commentaries) from subfields that point to future research and development.

The topics cover fundamental aspects and applications of all sorts, for instance the applications Kjelstrup worked on, fuel cells, batteries, thermoelectric devices, chemical reactors, distillation columns, reindeer or seal noses. Applications or experiments that challenge us for new theory are especially welcome. All topics mentioned are relevant for commentaries to the subfields. Other ideas can be discussed with the editors.

Prof. Dr. Dick Bedeaux
Prof. Dr. Fernando Bresme
Prof. Dr. Alex Hansen
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

entropy production as the proper basis for transport modelling
entropy production and exergy analysis
entropy production for surfaces
entropy production and entropy balance in thermodynamic modelling of industrial processes
entropy production minimization in nature and industry

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Published Papers (7 papers)

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Research

11 pages, 801 KiB

Open AccessArticle

Computing Entropy for Long-Chain Alkanes Using Linear Regression: Application to Hydroisomerization

by Shrinjay Sharma, Richard Baur, Marcello Rigutto, Erik Zuidema, Umang Agarwal, Sofia Calero, David Dubbeldam and Thijs J. H. Vlugt

Entropy 2024, 26(12), 1120; https://doi.org/10.3390/e26121120 (registering DOI) - 21 Dec 2024

Abstract

Entropies for alkane isomers longer than C

_{10}

Entropies for alkane isomers longer than C

_{10}

are computed using our recently developed linear regression model for thermochemical properties which is based on second-order group contributions. The computed entropies show excellent agreement with experimental data and data from Scott’s tables which are obtained from a statistical mechanics-based correlation. Entropy production and heat input are calculated for the hydroisomerization of C

_{7}

isomers in various zeolites (FAU-, ITQ-29-, BEA-, MEL-, MFI-, MTW-, and MRE-types) at 500 K at chemical equilibrium. Small variations in these properties are observed because of the differences in reaction equilibrium distributions for these zeolites. The effect of chain length on heat input and entropy production is also studied for the hydroisomerization of C

_{7}

, C

_{8}

, C

_{10}

, and C

_{14}

isomers in MTW-type zeolite at 500 K. For longer chains, both heat input and entropy production increase. Enthalpies and absolute entropies of C

_{7}

hydroisomerization reaction products in MTW-type zeolite increase with higher temperatures. These findings highlight the accuracy of our linear regression model in computing entropies for alkanes and provide insight for designing and optimizing zeolite-catalyzed hydroisomerization processes. Full article

(This article belongs to the Special Issue The Entropy Production—as Cornerstone in Applied Nonequilibrium Thermodynamics—Dedicated to Professor Signe Kjelstrup on the Occasion of Her 75th Birthday)

9 pages, 297 KiB

Open AccessArticle

Internal Energy, Fundamental Thermodynamic Relation, and Gibbs’ Ensemble Theory as Emergent Laws of Statistical Counting

by Hong Qian

Entropy 2024, 26(12), 1091; https://doi.org/10.3390/e26121091 - 13 Dec 2024

Viewed by 419

Abstract

Statistical counting ad infinitum is the holographic observable to a statistical dynamics with finite states under independent and identically distributed N sampling. Entropy provides the infinitesimal probability for an observed empirical frequency

\hat{ν}

with respect to a probability prior

p

, when [...] Read more.

\hat{ν}

with respect to a probability prior

p

, when

\hat{ν} \neq p

N \to \infty

. Following Callen’s postulate and through Legendre–Fenchel transform, without help from mechanics, we show that an internal energy

u

emerges; it provides a linear representation of real-valued observables with full or partial information. Gibbs’ fundamental thermodynamic relation and theory of ensembles follow mathematically.

u

is to

\hat{ν}

what chemical potential

μ

is to particle number N in Gibbs’ chemical thermodynamics, what

β = T^{- 1}

is to internal energy U in classical thermodynamics, and what

ω

is to t in Fourier analysis. Full article

24 pages, 916 KiB

Open AccessArticle

An Instructive CO₂ Adsorption Model for DAC: Wave Solutions and Optimal Processes

by Emily Kay-Leighton and Henning Struchtrup

Entropy 2024, 26(11), 972; https://doi.org/10.3390/e26110972 - 13 Nov 2024

Viewed by 679

Abstract

We present and investigate a simple yet instructive model for the adsorption of CO₂ from air in porous media as used in direct air capture (DAC) processes. Mathematical analysis and non-dimensionalization reveal that the sorbent is characterized by the sorption timescale and capacity, while the adsorption process is effectively wavelike. The systematic evaluation shows that the overall adsorption rate and the recommended charging duration depend only on the wave parameter that is found as the ratio of capacity and dimensionless air flow velocity. Specifically, smaller wave parameters yield a larger overall charging rate, while larger wave parameters reduce the work required to move air through the sorbent. Thus, optimal process conditions must compromise between a large overall adsorption rate and low work requirements. Full article

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20 pages, 1519 KiB

Open AccessArticle

Transported Entropy of Ions and Peltier Coefficients in 8YSZ and 10Sc1CeSZ Electrolytes for Solid Oxide Cells

by Aydan Gedik and Stephan Kabelac

Entropy 2024, 26(10), 872; https://doi.org/10.3390/e26100872 - 17 Oct 2024

Viewed by 653

Abstract

In this study, the transported entropy of ions for 8YSZ and 10Sc1CeSZ electrolytes was experimentally determined to enable precise modeling of heat transport in solid oxide cells (SOCs). The Peltier coefficient, crucial for thermal management, was directly calculated, highlighting reversible heat transport effects in the cell. While data for 8YSZ are available in the literature, providing a basis for comparison, the results for 10Sc1CeSZ show slightly smaller Seebeck coefficients but higher transported ion entropies. Specifically, at

700 ° C

and an oxygen partial pressure of

p_{O_{2}} = 0.21

bar, values of

S_{O^{2 -}}^{*} = 52 \pm 10

J/K·F for 10Sc1CeSZ and

S_{O^{2 -}}^{*} = 48 \pm 9

J/K·F for 8YSZ were obtained. The transported entropy was also validated through theoretical calculations and showed minimal deviations when comparing different cell operation modes (O₂||O²⁻||O₂ and H₂, H₂O||O²⁻||O₂). The influence of the transported entropy of the ions on the total heat generation and the partial heat generation at the electrodes is shown. The temperature has the greatest influence on heat generation, whereby the ion entropy also plays a role. Finally, the Peltier coefficients of 8YSZ for all homogeneous phases agree with the literature values. Full article

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13 pages, 278 KiB

Open AccessArticle

Enhanced Model for the Analysis of Thermoelectric Effects at Nanoscale: Onsager’s Method and Liu’s Technique in Comparison

by Maria Di Domenico and Antonio Sellitto

Entropy 2024, 26(10), 852; https://doi.org/10.3390/e26100852 - 9 Oct 2024

Viewed by 632

Abstract

The aim of this paper is twofold. From the practical point of view, an enhanced model for the description of thermoelectric effects at nanoscale is proposed. From the theoretical point of view, instead, in the particular case of the proposed model, the equivalence between two classical techniques for the exploitation of the second law of thermodynamics is shown, i.e., Onsager’s method and Liu’s technique. An analysis of the heat-wave propagation is performed as well. Full article

8 pages, 225 KiB

Open AccessArticle

On the Elimination of Fast Variables from the Langevin Equation

by Dick Bedeaux

Entropy 2024, 26(10), 821; https://doi.org/10.3390/e26100821 - 26 Sep 2024

Viewed by 535

Abstract

In a multivariable system, there are usually a number of relaxation times. When some of the relaxation times are shorter than others, the corresponding variables will decay to their equilibrium value faster than the others. After the fast variables have decayed, the system can be described with a smaller number of variables. From the theory of nonequilibrium thermodynamics, as formulated by Onsager, we know that the coefficients in the linear flux–force relations satisfy the so-called Onsager symmetry relations. The question we will address in this paper is how to eliminate the fast variables in such a way that the coefficients in the reduced description for the slow variables still satisfy the Onsager relations. As the proof that Onsager gave of the symmetry relations does not depend on the choice of the variables, it is equally valid for the subset of slow variables. Elimination procedures that lead to symmetry breaking are possible, but do not consider systems that satisfy the laws of nonequilibrium thermodynamics. Full article

15 pages, 1126 KiB

Open AccessArticle

Entropy Production and Filling Time in Hydrogen Refueling Stations: An Economic Assessment

by Bruno F. Santoro, David Rincón and Diego F. Mendoza

Entropy 2024, 26(9), 735; https://doi.org/10.3390/e26090735 - 29 Aug 2024

Viewed by 512

Abstract

A multi-objective optimization is performed to obtain fueling conditions in hydrogen stations leading to improved filling times and thermodynamic efficiency (entropy production) of the de facto standard of operation, which is defined by the protocol SAE J2601. After finding the Pareto frontier between filling time and total entropy production, it was found that SAE J2601 is suboptimal in terms of these process variables. Specifically, reductions of filling time from 47 to 77% are possible in the analyzed range of ambient temperatures (from 10 to 40 °C) with higher saving potential the hotter the weather conditions. Maximum entropy production savings with respect to SAE J2601 (7% for 10 °C, 1% for 40 °C) demand a longer filling time that increases with ambient temperature (264% for 10 °C, 350% for 40 °C). Considering average electricity prices in California, USA, the operating cost of the filling process can be reduced between 8 and 28% without increasing the expected filling time. Full article

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Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

1. Dr. Kirill Glavatskiy, The University of Newcastle

2. Prof. Thijs J.H. Vlugt, Delft University of Technology

3. Dr. Thanh Thuat Trinh, Norges Teknisk-Naturvitenskapelige Universitet

4. Dr. Diego Kingston, Universidad de Buenos Aires

5. Prof. Jośe Miguel Rubı́, University of Barcelona

6. Prof. Odne Stokke Burheim, Norges Teknisk-Naturvitenskapelige Universitet

7. Prof. Huijin Xu, Shanghai Jiao Tong Univeristy

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The Entropy Production—as Cornerstone in Applied Nonequilibrium Thermodynamics—Dedicated to Professor Signe Kjelstrup on the Occasion of Her 75th Birthday

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