{"title":"Analyses of cost of energy and multi-objective optimizations for single-stage thermoelectric coolers","authors":"Yuanwang Li, Yanlin Ge, Lingen Chen, Huijun Feng, Shaojun Xia","doi":"10.1515/jnet-2026-0043","DOIUrl":"https://doi.org/10.1515/jnet-2026-0043","url":null,"abstract":"Based on finite-time thermodynamics and single-stage thermoelectric cooler model from prior literature, this study introduces the cost of energy, it is defined as COE = <jats:italic>Q</jats:italic> <jats:sub> <jats:italic>L</jats:italic> </jats:sub> / <jats:italic>I</jats:italic> , which quantifies heat flux per unit current passing through thermoelectric cooler from cold end, and fills a gap in finite-time thermodynamics as a new thermodynamic index. The cost of energy expression is derived, and the current and area allocation of heat-exchangers are optimized to maximize the cost of energy under fixed total heat-exchanger area. Using NSGA-II, 1- to 4-objective optimizations are performed for cooling load, coefficient of performance, efficient cooling load and cost of energy. TOPSIS, LINMAP and Shannon Entropy methods are used to identify optimal solutions. The maximum cost of energy increases with the thermoelectric unit number and total heat transfer area, but decreases with heat reservoir temperature difference. When external heat-transfer loss is considered, the maximum cost of energy decreases by 22.1 %. For four-objective optimization, the optimal current is distributed between 5 A and 40 A, and optimal heat-exchanger area allocation ratio ranges from 0.5 to 0.63 and clusters mainly between 0.55 and 0.6. Key contributions are cost of energy analysis and four-objective optimization for single-stage thermoelectric cooler by using finite-time-thermodynamics and multi-objective methods.","PeriodicalId":16428,"journal":{"name":"Journal of Non-Equilibrium Thermodynamics","volume":"202 1","pages":""},"PeriodicalIF":6.6,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148870238","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Modeling and multi-objective optimization of an ammonia-fueled protonic ceramic fuel cell/sweeping gas membrane distillation hybrid system for cogeneration of power and freshwater","authors":"Xuewen Yu, Houcheng Zhang, Hui Chen, Changgan Lai, Jianming Li, Shaocheng Lang, Zhaoyang Zhang, Yiwei Zhang","doi":"10.1515/jnet-2026-0040","DOIUrl":"https://doi.org/10.1515/jnet-2026-0040","url":null,"abstract":"This study proposes and investigates a hybrid system that couples an ammonia-fueled protonic ceramic fuel cell (NH <jats:sub>3</jats:sub> -PCFC) with sweeping gas membrane distillation (SGMD) to co-produce electricity and freshwater. A comprehensive steady-state model is developed, incorporating ammonia decomposition kinetics, NH <jats:sub>3</jats:sub> -PCFC electrochemistry, and detailed heat- and mass-transfer within the SGMD module. The NH <jats:sub>3</jats:sub> -PCFC and SGMD submodels are independently validated against published data, providing support for the credibility of the coupled modeling framework. Baseline simulations indicate that the hybrid system achieves a maximum power density of 3,868.26 W m <jats:sup>−2</jats:sup> and an overall energy efficiency of 49.2 %, evidencing a clear synergy between electrochemical conversion and waste-heat-driven desalination. Parametric studies indicate that higher operating temperature and thinner electrolyte significantly enhance power output, while hydrogen and air utilization ratios strongly influence system efficiency and exergy destruction. Moreover, increasing SGMD membrane porosity effectively improves freshwater productivity and thermodynamic performance. Resolving the intrinsic trade-off between power density and energy efficiency, a multi-objective NSGA-II optimization delivers a compromise solution with a power density of 6,732.62 W m <jats:sup>−2</jats:sup> and an energy efficiency of 51.4 % under balanced operating conditions. The findings indicate the potential feasibility of NH <jats:sub>3</jats:sub> -PCFC/SGMD cogeneration and provide design guidance for applications in remote, maritime, and resource-limited settings.","PeriodicalId":16428,"journal":{"name":"Journal of Non-Equilibrium Thermodynamics","volume":"73 1","pages":""},"PeriodicalIF":6.6,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148870237","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Optimization of cooling power of a thermoelectric refrigerator: a unified approach","authors":"Rajeshree Chakraborty, Ramandeep S. Johal","doi":"10.1515/jnet-2026-0044","DOIUrl":"https://doi.org/10.1515/jnet-2026-0044","url":null,"abstract":"We analyze the steady-state formalism for optimizing the cooling power of a thermoelectric refrigerator (TER), unifying the endoreversible and exoreversible approximations within one framework. Although the cooling power is non-optimizable within the endoreversible model based on Newtonian heat-transfer law, we show that the issue can be circumvented in the near-reversible regime where the external thermal conductances are large, but finite. We extend this analysis to optimize the cooling power in the presence of both internal and external irreversibilities and derive a closed-form expression for the coefficient of performance (COP) that depends on the thermoelectric figure of merit and the ratio of internal to external thermal conductances. The model reproduces the endoreversible and the exoreversible limits as special cases. We conclude that for small temperature differences, the combined irreversibilities reduce the COP to values below 1/2, which aligns with the observed performance of the single-stage TER, and can provide realistic estimates for the COP.","PeriodicalId":16428,"journal":{"name":"Journal of Non-Equilibrium Thermodynamics","volume":"6 1","pages":""},"PeriodicalIF":6.6,"publicationDate":"2026-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148821193","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"About the dissipative dynamical law of Newton","authors":"Peter Ván","doi":"10.1515/jnet-2026-0034","DOIUrl":"https://doi.org/10.1515/jnet-2026-0034","url":null,"abstract":"The thermodynamic basis of classical mechanics is presented. In this framework, ideal Newtonian mechanics emerges as the zero-dissipation limit of a more general, dissipative theory. The thermodynamic approach predicts a novel dissipative contribution to the momentum that depends on the applied force, leading to a damping coefficient with a specific, experimentally testable dependence on the inertial mass and the spring constant. A torsion balance experiment with variable moment of inertia has been designed to measure this effect. Several known equations, including a thermodynamic version of the Eliezer-Ford-O’Connell equation of radiation reaction, are recovered as special cases.","PeriodicalId":16428,"journal":{"name":"Journal of Non-Equilibrium Thermodynamics","volume":"27 1","pages":""},"PeriodicalIF":6.6,"publicationDate":"2026-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148821196","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Work extraction via local gates and phase transitions in open quantum systems","authors":"Grazia Di Bello","doi":"10.1515/jnet-2026-0025","DOIUrl":"https://doi.org/10.1515/jnet-2026-0025","url":null,"abstract":"In this mini-review, we discuss work extraction under restricted control, where only the system is accessible while other degrees of freedom remain uncontrolled. In this setting, <jats:italic>local ergotropy</jats:italic> is the maximum work extractable by cyclic unitaries on the system, and it can differ strongly from “switch-off” extraction after quenching the system-environment coupling. We review two settings where correlations and many-body effects shape local work. First, in a two-qubit quantum Rabi model, dissipation induces a Berezinskii–Kosterlitz–Thouless quantum phase transition. A gate-based charge-store-extract protocol uses a decoherence-free state to stabilize storage and makes strong system-bath coupling a resource, yielding local ergotropy above switch-off extraction and making its dynamics transition-dependent, also in relative fluctuations. Second, in a disordered XXZ chain where the first two spins form a battery coupled to an interacting spin bath, local ergotropy shows distinct long-time behavior across Anderson, many-body localized, and ergodic regimes, linking extractable work to localization transitions. Overall, the examples reviewed here show that local ergotropic observables quantify quantum-battery performance under local control and probe collective phenomena.","PeriodicalId":16428,"journal":{"name":"Journal of Non-Equilibrium Thermodynamics","volume":"5 1","pages":""},"PeriodicalIF":6.6,"publicationDate":"2026-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148836231","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Performance optimization of a thermally integrated pumped thermal electricity storage system based on finite time thermodynamics","authors":"Zhikang Yu, Liutao Zhu, Zhu Jiang, Yuji Du, Zhigang Song, Xukai Yang, Xiaosong Zhang, Shifang Huang","doi":"10.1515/jnet-2026-0001","DOIUrl":"https://doi.org/10.1515/jnet-2026-0001","url":null,"abstract":"The performance of thermally integrated pumped thermal electricity storage is fundamentally governed by internal thermodynamic irreversibilities. This study establishes a rigorous finite-time thermodynamic framework to analyze and optimize a system coupling a high-temperature heat pump with an organic Rankine cycle. By incorporating finite-rate heat transfer and annualized capital cost constraints, a comprehensive model is developed to evaluate the system’s round-trip efficiency. Parametric investigations demonstrate that the round-trip efficiency reaches a maximum of 71.29 % under optimal operating temperatures, though it remains highly sensitive to variations in storage temperature. The charge-discharge duration ratio is identified as a governing determinant, with the round-trip efficiency exhibiting a declining trend as this ratio increases. Furthermore, the synergy of internal heat transfer matching, quantified by specific conductance coefficients, proves crucial for performance enhancement. Global irreversibility is minimized under a symmetric configuration where the heat transfer conductance of the heat pump and the power cycle are balanced. Thermoeconomic optimization reveals a distinct performance peak, with the round-trip efficiency reaching 63.59 % at optimal dimensionless cost coefficients, forming a narrow “efficiency ridge” in the design space. This work provides a foundational theoretical basis for the optimization of irreversible pumped thermal electricity storage systems within the realm of non-equilibrium thermodynamics.","PeriodicalId":16428,"journal":{"name":"Journal of Non-Equilibrium Thermodynamics","volume":"73 1","pages":""},"PeriodicalIF":6.6,"publicationDate":"2026-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148821192","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Constitutive settings with regard to energy- and entropy-balances in non-equilibrium thermodynamics: the thermodynamical verification","authors":"Wolfgang Muschik","doi":"10.1515/jnet-2026-0074","DOIUrl":"https://doi.org/10.1515/jnet-2026-0074","url":null,"abstract":"Constitutive equations have to be in agreement with the energy- and entropy-balances. For achieving that, the procedure of thermodynamical verification is introduced: Because heat flux and entropy flux as well as the time differentials of internal energy and entropy are not independent of each other, energy- and entropy-balances are connected with each other by so-called internal settings laying down the theoretical frame of the applied material description which is characterized by additional constitutive settings.. For elucidating the procedure of thermodynamical verification, three examples are considered which use different settings.","PeriodicalId":16428,"journal":{"name":"Journal of Non-Equilibrium Thermodynamics","volume":"348 1","pages":""},"PeriodicalIF":6.6,"publicationDate":"2026-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148809958","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Carlos Gabarrete, Ana Laura García-Perciante, Olivier Sarbach
{"title":"Kinetic theory for a relativistic charged gas: mathematical foundations of the hydrodynamic limit and first-order results within the projection method","authors":"Carlos Gabarrete, Ana Laura García-Perciante, Olivier Sarbach","doi":"10.1515/jnet-2026-0049","DOIUrl":"https://doi.org/10.1515/jnet-2026-0049","url":null,"abstract":"This work derives first-order constitutive equations for a relativistic charged gas using the Chapman–Enskog expansion of near-equilibrium solutions to the Boltzmann equation, implemented via a novel projection method. The analysis is performed in an arbitrary fixed background spacetime with an external electromagnetic field. Based on a detailed study of the linearized collision operator, we identify the trace-fixed particle frame as the most natural choice for constructing dissipative relativistic fluid theories from kinetic theory. In this frame, the state variables are defined by matching the lowest order moments of the one-particle distribution function with those of the Jüttner equilibrium distribution. The corresponding constitutive relations are obtained, and the associated transport coefficients are shown to be frame-independent when properly defined. We also identify an additional freedom, referred to as representation freedom, and show how both the representation and frame freedoms can be implemented at the microscopic level within the projection method. This allows for a systematic derivation of general first-order constitutive equations starting from the ones obtained in the trace-fixed particle frame. For suitable parameter choices, the resulting fluid theory is strongly hyperbolic, causal, and admits stable global equilibrium states.","PeriodicalId":16428,"journal":{"name":"Journal of Non-Equilibrium Thermodynamics","volume":"22 1","pages":""},"PeriodicalIF":6.6,"publicationDate":"2026-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148322061","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the role of non-constant material parameters in the Guyer–Krumhansl heat equation","authors":"Carmelo F. Munafó","doi":"10.1515/jnet-2025-0156","DOIUrl":"https://doi.org/10.1515/jnet-2025-0156","url":null,"abstract":"Fourier’s law is widely used in engineering field to describe the heat conduction problems, but it leads to an infinite heat propagation velocity and ignores memory/inertial effects. These limitations reduce its accuracy in the modeling of fast or small-scale thermal processes. However, the Guyer–Krumhansl equation offers a more general and accurate framework, especially when complex or non-local heat transport phenomena are involved. Originally derived from phonon hydrodynamics at low temperatures, the Guyer–Krumhansl equation has since been successfully applied to heterogeneous materials and room-temperature problems using a continuum approach. This generalization is promising and could be the standard model in future engineering practice, but it would not be possible without a thorough investigation and understanding of its mathematical properties and the study of nonlinear effects resulting from non-constant material parameters. For this reason, this work investigates the nonlinear formulation of the Guyer–Krumhansl equation, focusing on the effects of temperature-dependent material parameters such as thermal conductivity and relaxation time. These nonlinearities are very essential for capturing real behaviors and ensuring thermodynamic consistency. The study is based on an analysis of the mathematical structure of the model and numerical results, illustrating the influence of non-constant material parameters. These insights contributes to extend the applicability of the Guyer–Krumhansl model in engineering field and guides future experimental validations.","PeriodicalId":16428,"journal":{"name":"Journal of Non-Equilibrium Thermodynamics","volume":"38 1","pages":""},"PeriodicalIF":6.6,"publicationDate":"2026-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148314369","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}