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Keywords = finite time thermodynamics

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23 pages, 7208 KB  
Article
Spectral Entropy and STFT Analysis of Thermal Signatures for Melt Pool Stability in Laser DED Repair of Complex Structures
by Sai Vempati, Armando José Yáñez Casal, Juan Carlos Becerra Permuy, José Manuel Amado Paz and María José Tobar Vidal
Coatings 2026, 16(6), 686; https://doi.org/10.3390/coatings16060686 - 9 Jun 2026
Viewed by 236
Abstract
The influence of internal substrate geometry on thermal stability during Laser Directed Energy Deposition Repair (DED-R) remains insufficiently understood, particularly for components containing internal cavities and cooling channels. This study investigates the thermal response of solid (Alpha), blind-hole (Bravo), and channeled (Charlie) AISI [...] Read more.
The influence of internal substrate geometry on thermal stability during Laser Directed Energy Deposition Repair (DED-R) remains insufficiently understood, particularly for components containing internal cavities and cooling channels. This study investigates the thermal response of solid (Alpha), blind-hole (Bravo), and channeled (Charlie) AISI 316L substrates using dual infrared thermography, transient finite element modeling, and Short-Time Fourier Transform (STFT)-frequency-domain analysis. Despite substantial differences in internal heat-dissipation pathways, all substrate configurations exhibited similar peak surface temperatures (~1700–2100 °C), indicating that conventional temperature monitoring alone is insufficient to distinguish geometry-dependent melt-pool behavior. To address this limitation, a Spectral Entropy Index (SEI) derived from STFT analysis was proposed to quantify thermal stability. The channeled substrate exhibited the lowest entropy value (Hs = 0.172), compared with the solid (Hs = 0.181) and blind-hole (Hs = 0.183) configurations, indicating a more ordered and predictable thermal response. Furthermore, distinct variations in the spectral stability shadow revealed geometry-dependent oscillatory behavior that was not observable from thermal histories. Finite element simulations showed good agreement with experimental measurements in conduction-dominated regions (RMSE ≈ 46 °C), whereas deviations were observed within the melt-pool region (~250–310 °C), highlighting the increasing influence of fluid-flow phenomena not captured by the conduction-based model. The results demonstrate that internal substrate architecture primarily influences melt-pool stability through frequency-domain thermodynamics rather than significant changes in peak temperature. The proposed STFT method provides a quantitative approach for monitoring thermal stability and assessing the feasibility of L-DED repair over complex internal geometries. Full article
(This article belongs to the Section High-Energy Beam Surface Engineering and Coatings)
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18 pages, 632 KB  
Article
Coupled Irreversibilities and Asymmetric Dissipation in Liquid-State Thermocells
by Xiongxiong Wu, Zhimin Yang and Yanning Yang
Thermo 2026, 6(2), 41; https://doi.org/10.3390/thermo6020041 - 1 Jun 2026
Viewed by 170
Abstract
Liquid-state thermocells (LTCs) are emerging electrochemical heat engines for harvesting low-grade thermal energy across small temperature differences. Their practical performance is jointly limited by internal dissipation associated with ionic and electrochemical transport, as well as by external irreversibility arising from finite thermal coupling [...] Read more.
Liquid-state thermocells (LTCs) are emerging electrochemical heat engines for harvesting low-grade thermal energy across small temperature differences. Their practical performance is jointly limited by internal dissipation associated with ionic and electrochemical transport, as well as by external irreversibility arising from finite thermal coupling to the heat source and sink. In this work, a finite-rate thermodynamic framework is developed for LTCs subject to coupled internal and external irreversibilities. The model combines effective thermoelectrochemical transport, a phenomenological asymmetric Joule-heat partition parameter motivated by electrode and interfacial heat effects, and non-ideal thermal contacts, thereby enabling analytical optimization of power output in four representative configurations. Closed-form expressions are derived for the maximum power and the efficiency at maximum power (EMP), together with the admissible operating domain and an equivalent-circuit interpretation. The results show that the thermal impedance ratio governs a transition between externally limited and internally limited regimes. In the externally dominated limit, all configurations recover the Curzon–Ahlborn efficiency, whereas in the internally dominated limit, the asymptotic EMP depends on the side receiving irreversible heat release. When both dominant irreversibilities are located on the hot side, the highest EMP is achieved, while the opposite configuration yields the lowest EMP. These findings provide a thermodynamic benchmark for the LTC architecture and clarify how thermal contact asymmetry and internal heat release pathways should be coordinated to enhance performance in low-grade heat recovery. Full article
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28 pages, 3763 KB  
Article
Finite-Dimension Thermodynamics for Optimizing Power Plants Including Heat-Storage Device
by Pierre Neveu, Baptiste Rebouillat and Quentin Falcoz
Energies 2026, 19(11), 2615; https://doi.org/10.3390/en19112615 - 28 May 2026
Viewed by 176
Abstract
This paper deals with the optimal integration of power plants, including a storage device. For such systems, numerous structures are possible, involving different numbers of heat exchangers, and for each of them, optimal operating temperatures need to be found. Moreover, the heat-storage system [...] Read more.
This paper deals with the optimal integration of power plants, including a storage device. For such systems, numerous structures are possible, involving different numbers of heat exchangers, and for each of them, optimal operating temperatures need to be found. Moreover, the heat-storage system can be located at different temperature levels, offering another degree of freedom when optimizing the whole system. If process simulators are presently very powerful tools for optimizing complex processes, they need to propose a primary design before any optimization steps. Finite-Dimension Thermodynamics (FDT) could help engineers to propose this primary design, close to the optimal one. To this aim, the FDT method is generalized for power-generation systems including a storage device and any number of heat exchangers. The optimization step consists of maximizing the power generation submitted to the thermodynamics constraints (first and second laws) related to each heat exchanger, power block, and thermal storage system. Two types of heat transfer law are studied and compared: Newton’s law K×T and phenomenological law issued from thermodynamics of irreversible processes L×1/T). Remarkable results have been found: (i) all the studied structures lead to the Curzon–Ahlborn efficiency when optimized with Newton’s law, (ii) for the same driving source (same high temperature and same power), and without any storage system, the output power production varies as N−2, N being the number of the heat exchangers, (iii) Charge and discharge times scenarios have a big impact on the optimal operating temperatures and on the resulting daily energy production. Efficiencies of operational plants, including nuclear or solar plants and ORC, are finally compared with the theoretical efficiency found at the maximum power point. This shows that FDT provides a good assessment of the actual efficiency of existing power plants. Full article
(This article belongs to the Special Issue Advanced Analysis of Thermodynamic and Thermal Energy)
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14 pages, 16451 KB  
Article
Study on Flow Mechanisms in Shale Oil Horizontal Wells Using Fiber-Optic DTS Production Logging
by Hong Zhuo, Si Li, Shaohua Li, Zhangying Han, Xiuling He, Guishan Li and Jianwei Ren
Geosciences 2026, 16(5), 194; https://doi.org/10.3390/geosciences16050194 - 12 May 2026
Viewed by 435
Abstract
In response to the challenges in monitoring the production profile during the development of the Qingcheng shale oil field in the Changqing Oilfield, this study systematically investigates the application mechanism and practical effectiveness of Distributed Temperature Sensing (DTS) technology for dynamic monitoring in [...] Read more.
In response to the challenges in monitoring the production profile during the development of the Qingcheng shale oil field in the Changqing Oilfield, this study systematically investigates the application mechanism and practical effectiveness of Distributed Temperature Sensing (DTS) technology for dynamic monitoring in horizontal wells. By establishing a coupled model of fracture–matrix dual-porosity media flow and wellbore thermodynamics, which integrates mass, momentum, and energy conservation equations solved via the finite difference method, an interpretation method for the production profile based on the Joule–Thomson effect is proposed. The model was calibrated using shut-in temperature data and validated by comparing simulated temperature profiles with DTS measurements under constant-rate production. Field tests conducted in six horizontal wells in the Qingcheng oil field enabled the quantitative analysis of cluster-level production contributions along the horizontal section, with a water-producing zone localization accuracy of ±3.5 m. The results indicate that shale oil wells exhibit a non-uniform production characteristic of “high at the front and low at the rear” during the early production stage, where the production contribution from fully fractured segments can be up to 2.8 times that of adjacent segments. Inversion of the fiber-optic monitoring data reveals that differences in the conductivity of hydraulic fractures are the primary cause of flow heterogeneity. This research provides a theoretical foundation and technical support for the efficient development of shale oil, contributing to the transition of China’s continental shale oil development from “experience-driven” to “data-driven.” Full article
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15 pages, 303 KB  
Article
Thermodynamic Limits of Fault-Tolerant Quantum Computing Beyond the Weak-Coupling, Quasistatic Regime
by Mrittunjoy Guha Majumdar
Entropy 2026, 28(5), 546; https://doi.org/10.3390/e28050546 - 11 May 2026
Viewed by 451
Abstract
The standard Landauer bound WkBTln2 sets the fundamental thermodynamic cost for information erasure under ideal conditions: weak system–bath coupling, quasistatic operation, and equilibrium reservoirs. However, realistic quantum error correction (QEC) operates in a profoundly different regime—finite-time syndrome [...] Read more.
The standard Landauer bound WkBTln2 sets the fundamental thermodynamic cost for information erasure under ideal conditions: weak system–bath coupling, quasistatic operation, and equilibrium reservoirs. However, realistic quantum error correction (QEC) operates in a profoundly different regime—finite-time syndrome extraction, strong coupling to cryogenic environments, and non-equilibrium dynamics. Here, we develop a unified thermodynamic framework for fault-tolerant quantum computing that incorporates corrections beyond the ideal Landauer limit. We derive a generalized bound on the heat dissipation per QEC cycle: QminkBTln2+kBTΔISB+τ, and scaling this result to large-scale quantum computers, we find that the total heat load grows polynomially with code distance but remains in the nanowatt range for million-qubit systems—well within the cooling power of modern dilution refrigerators. Applying our model to superconducting qubit architectures, we show that while strong coupling can add up to ∼20% to the ideal cost, finite-time effects contribute approximately 0.55% at 100 ns and 5.5% at 10 ns reset operations. Our results establish that the true thermodynamic cost of fault tolerance, while exceeding the naive Landauer estimate, does not pose a fundamental obstacle to scalability; the dominant engineering challenges lie in the heat load of control electronics and wiring, not in the fundamental dissipation of qubit reset. Full article
37 pages, 3575 KB  
Article
LFNMR-Informed Multi-Phase Moisture Modelling of Wood Biodegradation by Coniophora puteana
by Royson Donate Dsouza, Tiina Belt and Stefania Fortino
Forests 2026, 17(4), 492; https://doi.org/10.3390/f17040492 - 16 Apr 2026
Viewed by 476
Abstract
Fungal decay fundamentally alters moisture transport in wood through complex bio-physical coupling mechanisms that remain poorly understood. Brown-rot fungi such as Coniophora puteana (Schumach.: Fr.) P. Karst. degrade wood through chelator-mediated Fenton (CMF) chemistry, producing hydroxyl radicals that depolymerise cellulose and hemicellulose before [...] Read more.
Fungal decay fundamentally alters moisture transport in wood through complex bio-physical coupling mechanisms that remain poorly understood. Brown-rot fungi such as Coniophora puteana (Schumach.: Fr.) P. Karst. degrade wood through chelator-mediated Fenton (CMF) chemistry, producing hydroxyl radicals that depolymerise cellulose and hemicellulose before significant mass loss. This diffusion-dependent process requires elevated moisture content and leads to structural degradation. However, existing models fail to capture the interaction between boundary-driven fungal colonization, decay-induced property changes, and multi-phase multi-Fickian moisture redistribution, particularly the separate evolution of bound- and free-water phases during decay. Here, we present a transport-response bio-hygrothermal finite element model that couples boundary-driven Monod-type fungal colonization kinetics with multi-phase moisture transport (free water, bound water, vapor) in decaying wood. Although fungal biomass evolution is simulated via a reaction–diffusion equation, decay progression is not derived from biomass–substrate interaction but prescribed independently as an experimentally informed input. The model incorporates decay-modified sorption isotherms, permeability evolution, and boundary-driven biomass influx, along with associated moisture transport, into the governing equations. The model is validated against low-field nuclear magnetic resonance (LF-NMR) measurements of C. puteana decay in Scots pine over 35 days. The model successfully reproduces the experimentally observed moisture evolution: a peak free-water content of 50%–70% during weeks 1–2, followed by a progressive decline, while bound water remains remarkably constant despite advancing decay. Monte Carlo uncertainty quantification demonstrates hierarchical parameter control: bound water is governed solely by thermodynamic factors, while free water responds to interacting biological and physical processes. Time-resolved correlation analysis shows a fundamental transition from colonization-dominated (weeks 1–2) to transport-dominated (weeks 3–5) moisture control, quantitatively explaining the experimentally observed shift from accumulation to depletion. This transport-response framework for analyzing moisture behavior under externally defined decay progression establishes quantitative parameter hierarchies that may inform the development of future substrate-coupled bio-hygrothermal models. Full article
(This article belongs to the Special Issue Advanced Numerical and Experimental Methods for Timber Structures)
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18 pages, 333 KB  
Article
A Small Patch Hypothesis in Cosmology
by Meir Shimon
Astronomy 2026, 5(1), 4; https://doi.org/10.3390/astronomy5010004 - 9 Feb 2026
Viewed by 931
Abstract
If our observable Universe is only a tiny region of a vastly larger and conformally older spacetime, then the usual formulations of the classical flatness and horizon problems of the Hot Big Bang can be reinterpreted as artifacts manifesting an observational selection effect; [...] Read more.
If our observable Universe is only a tiny region of a vastly larger and conformally older spacetime, then the usual formulations of the classical flatness and horizon problems of the Hot Big Bang can be reinterpreted as artifacts manifesting an observational selection effect; we occupy a small causal domain of a much larger causally-connected and possibly non-flat spacetime. A sufficiently large positive cosmological constant, Λ, sets the future asymptotic horizon scale of the observable Universe, ∼Λ1/2, thereby implying that the observable Universe may simply be a minute patch of a far larger pre-existing one, hereafter a Small Patch Hypothesis. Importantly, this observational bound is purely geometric; regardless of when the Universe is observed, the maximum accessible scale is finite and fixed by Λ, independent of inflationary dynamics, anthropic arguments, or assumptions about the global hosting spacetime. The externally possibly frozen past-eternal state implied by a pre-existing, causally connected spacetime motivates, but does not strictly require, viewing the perturbation field as being in (or arbitrarily close to) a coarse-grained maximum-entropy—equilibrium—configuration. Conditionalizing only on fixed mean and variance, a Gaussian distribution uniquely emerges, while the absence of entropy gradients corresponds to adiabaticity. In this work these features are therefore treated as plausible maximum-ignorance priors for super-horizon perturbations, rather than as rigorously derived consequences of a fully developed microscopic notion of gravitational entropy. In this sense, inflation becomes one viable realization of the proposed Small Patch Hypothesis. Here, one particular non-inflationary alternative is considered for illustrative purposes in which a primordial spectrum Pζ(k) of the gauge-invariant perturbation ζ that pre-dates the Big Bang grows logarithmically toward large scales, k0, and in fact diverges at some finite kc. If kcΛ1/2, then our local cosmic patch probes only the regime where ζ1 and appears exceptionally smooth. Over the comparatively narrow observable window, this Pζ(k) mimics a slightly red-tilted, inflation-like spectrum. Rather than introducing high-energy new fields, this perspective frames large-scale homogeneity, isotropy, Gaussianity, adiabaticity, and the observed thermodynamic Arrow of Time as possible consequences of restricted observational access to a much larger Universe in equilibrium, rather than signatures of a unique early-Universe mechanism. Current observations cannot distinguish this logarithmically running spectrum from the standard power-law one, but future probes—for example high-resolution 21-cm measurements of the Dark Ages—may be able to falsify it. Full article
20 pages, 1826 KB  
Article
Entropy, Information, and the Curvature of Spacetime in the Informational Second Law
by Florian Neukart, Eike Marx and Valerii Vinokur
Information 2026, 17(2), 169; https://doi.org/10.3390/info17020169 - 6 Feb 2026
Viewed by 1285
Abstract
We develop an informational extension of spacetime thermodynamics in which local entropy production is coupled to spacetime curvature within an effective covariant framework. Spacetime is modeled as a continuum limit of finite-capacity information registers, giving rise to a coarse-grained entropy field whose gradients [...] Read more.
We develop an informational extension of spacetime thermodynamics in which local entropy production is coupled to spacetime curvature within an effective covariant framework. Spacetime is modeled as a continuum limit of finite-capacity information registers, giving rise to a coarse-grained entropy field whose gradients define an informational flux. Within a nonminimally coupled scalar–tensor formulation, the resulting field equations imply that the local divergence of this flux is sourced by the Ricci scalar, establishing a direct relation between curvature and entropy production. The corresponding integral form links cumulative entropy generation to the integrated spacetime curvature over a causal region. In stationary limits, the framework reproduces the Bekenstein–Hawking entropy of horizons, while in homogeneous expanding cosmologies it yields monotonic entropy growth consistent with the observed arrow of time. The construction remains compatible with unitarity at the microscopic level and with holographic entropy bounds in the stationary limit. Numerical solutions in flat FLRW backgrounds are used as consistency checks of the coupled evolution equations and confirm the expected curvature–entropy behavior across cosmological epochs. Overall, the results provide a thermodynamically consistent interpretation of curvature as a geometric source of irreversible information flow, without modifying the underlying gravitational field equations. Full article
(This article belongs to the Section Information Theory and Methodology)
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24 pages, 875 KB  
Article
Energy Dissipation Analysis of Contact/Impact of Deformable Bodies Using Numerical Modelling
by Ondřej Holiš, Tomáš Dvořák, Matej Koiš, Ivan Němec, Miroslav Trcala and Jiří Vala
Buildings 2026, 16(3), 592; https://doi.org/10.3390/buildings16030592 - 31 Jan 2026
Viewed by 528
Abstract
The numerical analysis of dissipative energy in dynamic problems involving impact and contact phenomena relies on the physical principles of classical thermodynamics and on the constitutive equations of the material, supplemented by some additional considerations of potential contact interfaces. From the mathematical perspective, [...] Read more.
The numerical analysis of dissipative energy in dynamic problems involving impact and contact phenomena relies on the physical principles of classical thermodynamics and on the constitutive equations of the material, supplemented by some additional considerations of potential contact interfaces. From the mathematical perspective, we come to a weak form of partial differential equation(s) of evolution with initial, boundary, and interface conditions, whose numerical analysis is required using the method of discretisation in time and typically the finite element technique. Dissipative energy is an important metric for quantifying the portion of mechanical work that is permanently converted to plastic work and thermal energy, among other applications. Crucially, the localised accumulation of this energy, often expressed as the plastic work density, is the primary physical parameter driving microstructural changes, damage initiation, and crack propagation under intense loading. This paper demonstrates how the dissipative energy resulting from material nonlinearities can be evaluated in dynamic problems involving the impact of one body on another and provides a quantitative comparison of numerically calculated dissipated energy using three types of nonlinear constitutive material models, namely the plastic material model with Rankine–Hill criterion, the Mazars damage model, and the Kelvin–Voigt viscoelastic model. Full article
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50 pages, 3177 KB  
Review
Computational Entropy Modeling for Sustainable Energy Systems: A Review of Numerical Techniques, Optimization Methods, and Emerging Applications
by Łukasz Łach
Energies 2026, 19(3), 728; https://doi.org/10.3390/en19030728 - 29 Jan 2026
Cited by 1 | Viewed by 1226
Abstract
Thermodynamic entropy generation quantifies irreversibility in energy conversion processes, providing rigorous thermodynamic foundations for optimizing efficiency and sustainability in thermal and energy systems. This critical review synthesizes advances in computational entropy modeling across numerical methods, optimization strategies, and sustainable energy applications. Computational fluid [...] Read more.
Thermodynamic entropy generation quantifies irreversibility in energy conversion processes, providing rigorous thermodynamic foundations for optimizing efficiency and sustainability in thermal and energy systems. This critical review synthesizes advances in computational entropy modeling across numerical methods, optimization strategies, and sustainable energy applications. Computational fluid dynamics, finite element methods, and lattice Boltzmann methods enable spatially resolved entropy analysis in convective, conjugate, and microscale systems, but exhibit varying maturity levels and accuracy–cost trade-offs. The minimization of entropy generation and the integration of artificial intelligence demonstrate quantifiable performance improvements in heat exchangers, renewable energy systems, and smart grids, with reported efficiency gains of 15 to 39% in specific applications under controlled conditions. While overall performance depends critically on system scale, operating regime, and baseline configuration, persistent limitations still constrain practical deployment. Systematic conflation between thermodynamic entropy (quantifying physical irreversibility) and information entropy (measuring statistical uncertainty) leads to inappropriate method selection; validation challenges arise from entropy’s status as a non-directly-measurable state function; high-order maximum entropy models achieve superior uncertainty quantification but require prohibitive computational resources; and standardized benchmarking protocols remain absent. Research fragmentation across thermodynamics, information theory, and machine learning communities limits integrated frameworks capable of addressing multi-scale, transient, multiphysics systems. This review provides structured, cross-method, application-aware synthesis identifying where computational entropy modeling achieves industrial readiness versus research-stage development, offering forward-looking insights on physics-informed machine learning, unified theoretical frameworks, and real-time entropy-aware control as critical directions for advancing sustainable energy system design. Full article
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24 pages, 9410 KB  
Article
Performance Analysis and Optimization of Fuel Cell Vehicle Stack Based on Second-Generation Mirai Vehicle Data
by Liangyu Tao, Yan Zhu, Hongchun Zhao and Zheshu Ma
Sustainability 2026, 18(3), 1172; https://doi.org/10.3390/su18031172 - 23 Jan 2026
Viewed by 876
Abstract
To accurately investigate the loss characteristics of fuel cell vehicles (FCVs) under actual operating conditions and enhance their power performance and economic efficiency, this study establishes a numerical model of the proton exchange membrane fuel cell (PEMFC) stack based on real-world data from [...] Read more.
To accurately investigate the loss characteristics of fuel cell vehicles (FCVs) under actual operating conditions and enhance their power performance and economic efficiency, this study establishes a numerical model of the proton exchange membrane fuel cell (PEMFC) stack based on real-world data from the second-generation Mirai. The stack model incorporates leakage current losses and imposes a limit on maximum current density. Besides, this study analyzes the effects of operating parameters (PEM water content, hydrogen partial pressure, current density, oxygen partial pressure, and operating temperature) on stack power output, efficiency, and eco-performance coefficient (ECOP). Furthermore, Non-Dominated Sequential Genetic Algorithm (NSGA-II) is employed to optimize the PEMFC stack performance, yielding the optimal operating parameter set for FCV operation. Further simulations are conducted on dynamic performance characteristics of the second-generation Mirai under two typical driving cycles, evaluating the power performance and economy of the FCV before and after optimization. Results demonstrate that the established PEMFC stack model accurately analyzes the output performance of an actual FCV when compared with real-world performance test data from the second-generation Mirai. Through optimization, output power increases by 7.4%, efficiency improves by 1.95%, and ECOP rises by 3.84%, providing guidance for enhancing vehicle power performance and improving overall vehicle economy. This study provides a practical framework for enhancing the power performance and overall energy sustainability of fuel cell vehicles, contributing to the advancement of sustainable transportation. Full article
(This article belongs to the Section Sustainable Engineering and Science)
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38 pages, 3177 KB  
Review
Unveiling Scale-Dependent Statistical Physics: Connecting Finite-Size and Non-Equilibrium Systems for New Insights
by Agustín Pérez-Madrid and Iván Santamaría-Holek
Entropy 2026, 28(1), 99; https://doi.org/10.3390/e28010099 - 14 Jan 2026
Viewed by 1064
Abstract
A scale-dependent effective temperature emerges as a unifying principle in the statistical physics of apparently different phenomena, namely quantum confinement in finite-size systems and non-equilibrium effects in thermodynamic systems. This concept effectively maps these inherently complex systems onto equilibrium states, thereby enabling the [...] Read more.
A scale-dependent effective temperature emerges as a unifying principle in the statistical physics of apparently different phenomena, namely quantum confinement in finite-size systems and non-equilibrium effects in thermodynamic systems. This concept effectively maps these inherently complex systems onto equilibrium states, thereby enabling the direct application of standard statistical physics methods. By offering a framework to analyze these systems as effectively at equilibrium, our approach provides powerful new tools that significantly expand the scope of the field. Just as the constant speed of light in Einstein’s theory of special relativity necessitates a relative understanding of space and time, our fixed ratio of energy to temperature suggests a fundamental rescaling of both quantities that allows us to recognize shared patterns across diverse materials and situations. Full article
(This article belongs to the Section Statistical Physics)
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5 pages, 152 KB  
Editorial
The First Fifty Years of Finite-Time Thermodynamics
by Bjarne Andresen and Peter Salamon
Entropy 2026, 28(1), 49; https://doi.org/10.3390/e28010049 - 30 Dec 2025
Viewed by 581
Abstract
The year 1975 marked the beginning of an entirely new direction for thermodynamics with the publication of Curzon and Ahlborn’s innocent-looking short paper “Efficiency of a Carnot engine at maximum power output” [...] Full article
(This article belongs to the Special Issue The First Half Century of Finite-Time Thermodynamics)
24 pages, 12479 KB  
Article
A Physics-Informed Neural Network (PINN) Approach to Over-Equilibrium Dynamics in Conservatively Perturbed Linear Equilibrium Systems
by Abhishek Dutta, Bitan Mukherjee, Sk Aftab Hosen, Meltem Turan, Denis Constales and Gregory Yablonsky
Entropy 2026, 28(1), 9; https://doi.org/10.3390/e28010009 - 20 Dec 2025
Cited by 1 | Viewed by 1396
Abstract
Conservatively perturbed equilibrium (CPE) experiments yield transient concentration extrema that surpass steady-state equilibrium values. A physics-informed neural network (PINN) framework is introduced to simulate these over-equilibrium dynamics in linear chemical reaction networks without reliance on extensive time-series data. The PINN incorporates the reaction [...] Read more.
Conservatively perturbed equilibrium (CPE) experiments yield transient concentration extrema that surpass steady-state equilibrium values. A physics-informed neural network (PINN) framework is introduced to simulate these over-equilibrium dynamics in linear chemical reaction networks without reliance on extensive time-series data. The PINN incorporates the reaction kinetics, stoichiometric invariants, and equilibrium constraints directly into its loss function, ensuring that the learned solution strictly satisfies physical conservation laws. Applied to three- and four-species reversible mechanisms (both acyclic and cyclic), the PINN surrogate matches conventional ODE integration results, reproducing the characteristic early concentration extrema (maxima or minima) in unperturbed species and the subsequent relaxation to equilibrium. It captures the timing and magnitude of these extrema with high accuracy while inherently preserving total mass. Through the physics-informed approach, the model achieves accurate results with minimal data and a compact network architecture, highlighting its parameter efficiency. Full article
(This article belongs to the Special Issue The First Half Century of Finite-Time Thermodynamics)
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10 pages, 778 KB  
Article
Modeling Carbonation Depth in Hardened Alkali-Activated Slag Under Accelerated Curing: A Multi-Physics Finite Element Approach
by Lei Zhang, Kai Wang, Yang Liu, Xiaoxiong Zha and Yu Lei
Buildings 2026, 16(1), 8; https://doi.org/10.3390/buildings16010008 - 19 Dec 2025
Cited by 1 | Viewed by 615
Abstract
This study develops a numerical model based on a multi-physics coupled finite element method to predict the carbonation depth of hardened alkali-activated slag under accelerated carbonation curing conditions. Drawing on existing literature data, the chemical composition and porosity of alkali-activated slag at different [...] Read more.
This study develops a numerical model based on a multi-physics coupled finite element method to predict the carbonation depth of hardened alkali-activated slag under accelerated carbonation curing conditions. Drawing on existing literature data, the chemical composition and porosity of alkali-activated slag at different ages were determined under non-carbonation conditions, supported by thermodynamic and kinetic analyses of alkali activation reactions. A differential equation governing CO2 diffusion—incorporating diffusion rate, diffusion coefficient, carbonation reaction rate, and related parameters—was established using Fick’s second law. The influence of humidity and carbonation degree on the reaction rate was quantified, and a correlation between carbonation degree and porosity was derived through thermodynamic analysis. These equations were solved numerically in a two-dimensional domain to predict carbonation depth over time. The results demonstrate that the proposed model, using only raw material composition and curing conditions, achieves reasonable accuracy in predicting carbonation depth. Full article
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