Traditional Total Factor Productivity (TFP) metrics often overlook biophysical limits and the depletion of natural capital. This study proposes an alternative paradigm: the Andean-Amazonian Bioeconomy (AAB), which integrates Georgescu-Roegen’s Law of Entropy and ancestral knowledge into an expanded production function. By applying the Malmquist Productivity Index and a Fixed Effects (FE) panel data model, we analyzed a dataset (1995–2024) from six Latin American countries. This approach utilizes the Human Development Index (HDI) as the primary proxy for social welfare. The methodology addresses country heterogeneity and multicollinearity, significantly enhancing the model’s explanatory power to an Adjusted R2 of 0.695. Our findings reveal a ‘Biocultural Paradox’: where conservation, often viewed as a cost by traditional income-based metric, emerges as vital investment. Our model demonstrate that the preservation of the biocultural fund- represented here as Biocultural Savings [S]- is a positive and highly significant predictor of social well-being (β = 0.685, p < 0.01), alongside a positive impact from the indigenous population index (β = 0.015, p < 0.1), suggesting that cultural identity plays a foundational role in regional resilience. We conclude that achieving ‘Vivir Bien’ (Living Well) requires a shift toward indicators that prioritize the biocultural fund -the stock of ancestral knowledge and biodiversity- over mere resource flow. This study provides a scientifically rigorous framework for sustainability policies across the Global South.

Echoes of Georgescu-Roegen's thermodynamic view in Latin American development debates.

ABSTRACT Based on fieldwork with Egyptian workers in the Dubai metropolitan area, I seek to understand the tension between a search for moral and economic stability and processes of growth and mobility that destabilise the foundations and shape of a viable life. In conversation with a welder who articulated to me his idea of proper Islamic economy based on charity, divine blessing and organic growth, I argue that there is a productive tension between the idea of non-destructive thriving expressed in the Islamic concept of baraka (divine blessing) and hydrocarbon-based capitalist growth. Both require the miraculous possibility of an exception from the second law of thermodynamics. This calls for a critical rethinking of whether growth-based economies can have the sustaining and sustainable capacity that a Muslim economic cosmology associates with the baraka based on lawful income. Capitalism may not be divinely blessed, but divine blessing today materialises through capitalism.

Entropy, gravity, and an apparent violation of the second law

The second law of thermodynamics dictates that local decreases in entropy must be offset by increases elsewhere. While this principle is well established in mechanical systems, its role in biological motor control remains underexplored. This study analysed 576 bimanual coordination trials on 16 participants collected across circadian cycles under normal conditions and thermal perturbations to test whether human motor systems strategically regulate functional movement stability. Movement entropy peaked during circadian temperature minima at dawn and declined to its lowest level during temperature maxima in the late afternoon, showing a significant inverse correlation with core body temperature. Thermal perturbations using heat and ice vests amplified these circadian patterns, with cold challenges exerting stronger effects than heat challenges. Despite substantial variations in movement entropy across conditions, task performance in maintaining target phase coordination remained stable. These findings provide preliminary evidence that biological systems can achieve local order through strategic entropy redistribution, increasing movement variability under challenging physiological conditions. The results offer initial empirical support suggesting that human motor control can function as an entropy-management system, revealing how biological systems satisfy thermodynamic laws while preserving functional stability.

Cellular aging is characterized by the progressive accumulation of intracellular damage, declining repair capacity, and altered mechanochemical signaling, ultimately leading to cellular senescence and loss of tissue homeostasis. Despite extensive experimental and theoretical efforts, the fundamental origin of senescence and its irreversible nature remain incompletely understood. In particular, it is unclear whether senescence must be imposed as a predefined cellular state or can instead emerge dynamically from more basic damage-repair mechanisms. In this work, we propose a unified age-damage structured mathematical framework for cellular aging that integrates intracellular damage accumulation, biochemical signaling, mechanical stress, and population renewal within a thermodynamically consistent variational structure. The model combines continuum thermodynamics with age-structured population dynamics, ensuring compliance with the second law of thermodynamics and providing a rigorous basis for irreversible aging processes. A central result of the model is the emergence of a damage-driven loss of homeostasis at a critical threshold of effective load, beyond which no steady intracellular damage state exists. This transition generates irreversibility at the single-cell level and propagates to the population scale through transport in age-damage space, leading naturally to the emergence of cellular senescence without introducing ad hoc senescence rules. Mechanical stress enters the model through a quadratic contribution to the effective damage load, producing a pronounced nonlinear sensitivity and predicting abrupt acceleration of aging beyond a critical stress level. To facilitate analysis and computation, we derive a reduced ODE-PDE system that retains the essential couplings between damage accumulation, biochemical signaling, mechanical stress, and population renewal. Analytical arguments and numerical illustrations demonstrate how transient mechanical or biochemical perturbations can induce persistent senescence at the population level. Overall, the proposed framework provides a mechanistic and thermodynamically grounded explanation of irreversible senescence as an emergent phenomenon in age-structured cell populations.

Multiscale systems are ubiquitous in science and technology, but are notoriously challenging to simulate as short spatiotemporal scales must be appropriately linked to emergent bulk physics. When expensive high-dimensional dynamical systems are coarse-grained into low-dimensional models, the entropic loss of information leads to emergent physics which are dissipative, history-dependent, and stochastic. To machine learn coarse-grained dynamics from time-series observations of particle trajectories, we propose a framework using the metriplectic bracket formalism that preserves these properties by construction; most notably, the framework guarantees discrete notions of the first and second laws of thermodynamics, conservation of momentum, and a discrete fluctuation-dissipation balance crucial for capturing nonequilibrium statistics. We introduce the mathematical framework abstractly before specializing to a particle discretization. As labels are generally unavailable for entropic state variables, we introduce a self-supervised learning strategy to identify emergent structural variables. We validate the method on benchmark systems and demonstrate its utility on two challenging examples: 1) coarse-graining star polymers at challenging levels of coarse-graining while preserving nonequilibrium statistics, and 2) learning models from high-speed video of colloidal suspensions that capture coupling between local rearrangement events and emergent stochastic dynamics. We provide open-source implementations in both PyTorch and LAMMPS, enabling large-scale inference and extensibility to diverse particle-based systems.

The objective of this work is to present sustainability analysis and performance evaluation of six hydropower units through exergy-based indices. The method of exergy analysis, based on the first and second laws of thermodynamics, was utilized to evaluate system irreversibility and environmental impact. The Exergy Efficiency, Sustainability Efficiency Index (SEI), and Exergy Ecological Index (ECEI) were determined and plotted in MATLAB. The efficiency and exergy performance results show that Unit 6 had the highest exergy efficiency at 89.3%, and Unit 1 had the least at 82.1%. The values of SEI and ECEI showed that elevated exergy efficiency contributes to increasing sustainability and ecological performance in parallel. The results demonstrate that exergy analysis can provide a broader and more accurate measure of system performance than energy analysis in hydroelectric power systems. The approach shows that local reference environmental conditions must be incorporated to establish system equilibrium. It also suggests that exergy analysis should be used as a standard tool for the optimization and performance management of hydropower plants. Its integration would help the operators take measures against malfunction, minimize losses and improve the environmental and thermodynamic sustainability of energy systems.

ABSTRACT Aiming at the problem of structural instability caused by creep in deep rocks, by introducing the gradient damage theory, a constitutive model that accurately describes the vermic‐damage evolution of rocks is constructed. Assuming that the rock is an isotropic continuous medium, the internal damage is mainly caused by the initiation and propagation of microcracks, and the total strain includes elastic, viscoelastic, and viscoplastic strains. The damage gradient term is introduced to describe the damage effect of adjacent micro‐units, solving the singularity of strain localization in traditional theories. Meanwhile, based on the first and second laws of thermodynamics, the total free energy and damage driving force are derived, and the bidirectional coupling effect of creep and damage is quantified. A rock creep damage model considering gradient damage is constructed. The creep constitutive model of rock considering gradient damage is in good agreement with the experimental curve, and the correlation coefficient is above 0.95. The core reason is that the model accurately fits the physical properties and creep‐damage evolution law of rock. On the one hand, the gradient damage hypothesis fully considers the nature of natural heterogeneity of rock and can truly describe the gradient expansion process of internal defects from local to global. The material is not simplified as a uniform damage body. On the other hand, the model effectively quantifies the two‐way coupling effect of creep promoting damage and damage accelerating creep. It avoids the limitation of the traditional model to separate the two. Through parameter sensitivity analysis, the physical meanings of the model parameters are made clear.

We examine the differences between the driven turbulence described by the Kuramoto-Sivashinsky (KS) equation and the second law of thermodynamics. A general velocity and entropy density system is analyzed with the unified thermodynamic algorithm of metriplectic dynamics, and we show that the positive spectra of the KS equation due to an external energy source prevent its metriplectic description. A variant of the KS equation is produced that monotonically generates an entropy, but the only equilibria of this variant system are spatially constant. Numerical experiments are performed comparing the evolution of the KS equation and its thermodynamic variant. The entropy of this thermodynamic system is increased further by the driving effects of the KS equation, reconciling the generation of entropy with the energy source of the KS equation. Further numerical experiments restrict the positive spectra in the KS equation to determine the effect on the system time evolution. While rescaling the growth rates of instabilities reproduces similar behavior on a slower time scale, introduction of individual positive spectra reproduces the formation of equilibria, relative equilibria, and a transition to chaos. The unified thermodynamic algorithm's implications for the KS equation and the transition between the KS equation and its metriplectic counterpart present a novel pathway to study deterministic dynamical systems with instability.

Insights and hindsights into the molecular mechanism of ATP hydrolysis by muscle myosin, kinesin/unconventional myosins, and axonemal dynein motors.

• A moving-bed thermochemical energy storage system is experimentally investigated. • Pumice-based salt-in-matrix composite sorbents are developed and implemented. • The system achieves an energy storage density of 189.7 kWh/m 3 . • Maximum effective energy and exergy efficiencies are 52.7% and 6.8%, respectively. • A correlation between air humidity difference and temperature lift is established. In the last decade, low-grade thermochemical energy storage systems have been gaining interest due to their long-term heat storage potential and high energy storage density. Despite the advantageous aspects of this heat storage method, previously investigated fixed-bed reactors suffer from low heat and mass transfer performance and offer limited process control. In order to overcome these challenges, a new multi-layer moving bed reactor was designed, manufactured, and tested in this study. The proposed reactor consists of reaction and storage sections where eight independent sorption beds have freedom of movement between the two sections. Such a design enables a modular concept, where each sorption bed could be charged or discharged individually, while the remaining sorption beds are stored inside their own hermetically insulated chambers. In the system, two different sizes of pumice stones, namely PM1 and PM2, were used as the host matrix, and three different thermochemical materials were synthesized by impregnation of the LiCl-CaCl 2 mixture and CaCl 2 as salts into pumice. During the experiments, comparative analyses of different materials, short-cycle full-system analyses, long-cycle energy density analyses, and multi-bed performance analyses have been performed. Additionally, the impact of air velocity was investigated. The evaluations were performed based on the First and Second Laws of Thermodynamics. Study results demonstrated that each sorption bed provides an average heat output between 0.58 and 1.07 kW depending on the inlet air conditions and the composition of thermochemical material. According to the study results, the energy storage density of the system was obtained as 189.7 kWh/m 3 with the use of PM2-CaCl 2 . On the other hand, 4.2 m/s was found as the most optimal air velocity, proving the highest average heat output during the discharging process and the highest moisture desorption rate per unit of heat consumed during the charging process. A linear correlation between the air absolute humidity difference and the air temperature lift for the discharging process was also obtained, which could provide useful insights for the performance prediction of thermochemical energy storage systems.

Newtons laws of motion (NLM) and Einsteins Special Theory of Relativity (STR) form the conceptual backbone of classical and modern physics, respectively. Despite their extensive empirical success, both frameworks are typically formulated without explicit consideration of thermodynamic constraints such as temperature evolution, system openness, and energy dissipation. This work investigates the thermodynamic consistency of NLM and STR by analytically examining their foundational equations under closed, open, and adiabatic system conditions using established principles from classical mechanics, kinetic theory of gases, and thermodynamics. The analysis demonstrates that Newtons equations of motion implicitly assume constant acceleration and unbounded time evolution, which, when applied to open systems, violate energy conservation and imply behaviour akin to perpetual motion. By explicitly incorporating temperature as a dynamical variable and recognising its intrinsic coupling to time, modified equations of motion are derived for closed thermodynamic systems. These equations retain the functional form of Newtonian relations but introduce a bounded temperature increment, deltaT, thereby ensuring compliance with the first and second laws of thermodynamics and preventing divergence in velocity, displacement, or work. A similar thermodynamic examination of STR is conducted, focusing on relativistic length contraction, time dilation, and the mass–energy relation E = mc2. When interpreted in terms of macroscopic or open systems, these relations imply the simultaneous divergence of mass and energy at high velocities, thereby contradicting conservation principles. However, when reformulated for isolated or adiabatic ideal-gas systems, analogous relativistic relationships emerge naturally from mechanical compression and temperature variation, without requiring inertial-frame abstractions or unphysical infinities. The study further demonstrates that the traditional interpretation of E = mc2 as unrestricted mass–energy interconvertibility is thermodynamically inconsistent. Instead, the equation is shown to represent the mechanical work required to accelerate a mass toward relativistic speeds within a finite time, thereby highlighting the physical impossibility of reaching the speed of light for finite-energy systems. Overall, this work establishes that both NLM and STR remain conditionally valid only within restricted thermodynamic domains. By explicitly incorporating temperature, system boundaries, and energy conservation, the analysis clarifies the physical limits of these foundational theories and provides a thermodynamically consistent reinterpretation of classical and relativistic dynamics.

The paper addresses the second law of thermodynamics through the Clausius–Duhem inequality in its general form, with entropy flux and entropy production given by suitable constitutive functions. For definiteness the paper investigates possible models of elastic solids where, to account for non-local properties, the stress depends on strain gradients up to second order. While previous approaches are developed through variational formulations or by applying the virtual power method, here it is shown that no change in the energy balance or the form of kinetic energy is necessary; it is sufficient that the entropy flux be given by a suitable constitutive function. The paper also emphasizes that non-local constitutive properties arise from the Clausius–Duhem thermodynamic inequality, while variational formulations and the virtual power method are in fact limited to the purely mechanical context, as they involve only the equation of motion.

This work considers optimal mechanical–electrical power conversion across rigid linkages equipped with current-controlled actuators. A novel cost function derived from a generalization of the Second Law of Thermodynamics is adopted from our previous work, where cycle-averaged energies are interpreted as generalized temperatures. A cost function based on generalized entropy generation is used to formulate an optimal control problem yielding a decoupled velocity feedback controller. Suboptimal gains are found, which are independent of both the excitation characteristics and the mechanical subsystem dynamics, and yield closed-loop stability. The effectiveness and simplicity of the resulting controller is demonstrated by a Monte Carlo simulation study, where random episodes of unknown, periodic forcing are applied under the proposed controller and compared with a maximum-efficiency controller. Results show that the proposed controller offers a higher statistical expectation for the average harvested power.

ABSTRACT This study aims to establish a connection between natural laws and business procedures by developing a quantifiable metric for assessing a firm's efficacy in translating market demand into operational throughput. The research introduces an entropy metric, drawing parallels from the second law of thermodynamics, thereby refashioning the entropy formula for a business context. This metric undergoes rigorous testing against established financial yardsticks, scrutinizing the firm's efficiency and performance. The introduced entropy metric showed significant congruity when juxtaposed with validated performance indicators used in finance and accounting. This comparison fortifies the applicability of the entropy metric in evaluating financial efficiency. Although the concept of entropy has been featured in prior research, the unique metric established in this study is the first of its kind to measure a firm's or a process's performance vis‐à‐vis demand. In a business or process scenario, entropy signifies the deterioration of order or predictability, representing a slow descent into disorder. The presented entropy formula aligns impressively with current financial performance metrics, thus proving to be a practical instrument for gauging a firm's financial and operational health over time.

Progress in the design and development of thermoelectric generator heat recovery systems: A comprehensive review

Mathematical principle underlying the law of entropy increase is vital for actively stable lowering of biosystem entropy.

Ammonia has emerged as a promising hydrogen carrier and carbon-free fuel. This study designs a novel gas turbine-solid oxide fuel cell (GT-SOFC) hybrid energy system, distinct from traditional SOFC-GT configurations, utilising ammonia as the primary fuel. In this hybrid system, ammonia is combusted with oxygen under fuel-rich conditions in the GT, generating both electricity and hydrogen. Hydrogen is then fed into the SOFC for electricity generation. The GT-SOFC hybrid system was designed and modelled using Aspen Plus. The first and second laws of thermodynamics were applied to perform energy and exergy analyses of the proposed system. A parametric study was conducted to study the effect of key parameters on the performance of the hybrid system, including equivalence ratio, combustor pressure, current density in the SOFC, and fuel utilisation ratio. The fuel utilisation ratio in SOFC was found to have a significant impact on the performance of the GT-SOFC hybrid system. The NO x emissions from this hybrid system were found to be negligible. An energy and exergy efficiencies of 75.5% and 72.1%, respectively, were achieved, which were higher compared with the conventional SOFC-GT system with a similar power output. • A novel ammonia-fuelled GT-SOFC hybrid system was designed and modelled. • Parametric study was conducted to evaluate the performance of the hybrid system. • The fuel utilisation ratio in SOFC is the key determining the energy efficiency • Energy and exergy efficiencies of 75.5% and 72.1%, respectively, were achieved.

ABSTRACT Erich Auerbach’s 1952 world literature essay has become canonical for the contemporary disciplinary field organised under this name. But the context in which Auerbach wrote his essay was different to those in which it has been received and demands reconstruction on its own terms. In the immediate postwar period, Goethe’s concept had been recommended as a tool of international cooperation. Yet this vision presupposed the continued existence of a cultural and historical variety that could no longer be taken for granted. Adapting a culturally pessimistic template derived from the second law of thermodynamics, Auerbach predicted the impending loss of the world’s literary languages. For him, world literature marked the end of the humanistic paradigm founded on the individuality of languages and cultures. Rather than oppose this tendency via an appeal to the actuality of national traditions, Auerbach instead sought to recover an alternative paradigm better suited to meet the demands of the new dispensation. Giambattista Vico’s idea of philology, which emphasised the ‘common sense’ spontaneously adopted by individual nations independently of one another, offered a model.