Specific Entropy Production Research Articles

Decoding Stress: The Universal Language of Entropy Production

The accurate quantification of stress remains a formidable challenge in the realm of physiological research, largely owing to the intricate nature of the stress response and its potential overlap with other physiological processes. In this vein, our research introduces a novel metric: the stress entropic load (SEL), grounded in thermodynamic principles. SEL is mathematically construed as a time-dependent function, articulated through various heat and temperature alterations, as well as changes in respiratory gas exchanges. This measure is posited as a predictive tool for stress and metabolic alterations in homeothermic organisms, including humans. Our empirical exploration involved 12 healthy male volunteers, structured in a dual-phase experimental design. The initial phase focused on achieving a resting metabolic rate (RMR), guided by specific criteria encompassing oxygen uptake, carbon dioxide release, and respiratory quotient. In instances where RMR benchmarks were not met within a 40-minute window, the study progressed, presuming RMR attainment. The collected data from this segment were pivotal in calculating the body's entropy production at rest. The subsequent phase entailed participants engaging in tasks via the WinSCAT software, signifying the onset of the stress phase. Here, entropy production was scrutinized to gauge stress levels. Crucially, SEL was ascertained by contrasting entropy production during the RMR phase (serving as a baseline) against that recorded throughout the experiment's entirety. Our findings indicate that SEL, as an indicator of specific entropy production, emerges as a viable marker of stress induced by prolonged mental effort. Notably, extended interaction with WinSCAT software markedly augmented SEL rates. The progression of SEL over time offered insights into when participants commenced stress-inducing tasks, underscoring its viability as a biological marker for mental exertion. Intriguingly, such stress did not manifest in conventional stress indicators like blood pressure or heart rate, though it did affect oxygen and carbon dioxide production. While these results lend credence to the utility of SEL as a stress marker, they are preliminary in nature, illuminating the prospective significance of SEL in the realms of stress measurement and physiological research. The project was funded by MUNI/G/1249/2021 grant by the Masaryk University. This is the full abstract presented at the American Physiology Summit 2024 meeting and is only available in HTML format. There are no additional versions or additional content available for this abstract. Physiology was not involved in the peer review process.

Entropy Production Using Ecological and Physiological Models of Stand Growth Dynamics as an Example

According to the Prigogine–Glansdorff principle, in a thermodynamic system where non-equilibrium processes occur, the change in entropy production is negative or equal to zero. Forest plantations are an example of such thermodynamic systems. Based on the ecological–physiological models of the forest stand growth dynamics developed by the authors of this work, the specific entropy production in the growth of stands was calculated, which is known to be proportional to the entropy production. It is shown that at the age when the minimum value of the specific entropy production is reached, the biomass of the stand has a maximum value. This conclusion is an important predictive factor for practical forestry, since determining the time of the minimum entropy production allows us to determine the time interval at which the biomass of the stand reaches its maximum value.

Моделирование динамики хода роста древостоев на основе термодинамического подхода

The forest ecosystem is a common example of the functioning of open thermodynamic systems. The work analyzes the change in the entropy of an open thermodynamic system where the following processes can be realized: absorption of short-wave solar radiation – differentiation process; total biomass growth process associated with the consumption of resources for respiration and competition. As a result of these processes, the negative entropy flow enters the system, and the positive entropy is produced in the system. As the stand grows, its biomass reaches a maximum, which corresponds to the steady state in the ecosystem. It is shown that, in accordance with the Prigogine’s theorem, the specific entropy production in an open system takes on a minimum positive value. With a further increase in the age of the stand, the steady state of the open thermodynamic system evolves to an equilibrium state, at which a decrease in the plant biomass is observed, and the entropy tends to a maximum value in accordance with the 2nd law of thermodynamics (ecosystem decay). The analysis of the behavior of an open thermodynamic system forms the basis of a new ecological and physiological model of the stand growth dynamics. The model proposed uses the following parameters: the biomass of an individual tree and the number of trees per hectare. In order to model the biomass growth dynamics of an individual tree, the von Bertalanffy equation is used. It contains a dynamic equation describing growth of an individual due to resource uptake and limitation of growth due to resource consumption. The equation that characterizes the dynamics of stand size derives from the condition of reaching the maximum biomass of the stand during the stand’s growth. In general, the stand’s dynamics model has only three independent parameters. They are the onset time of the steady state, the resource consumption rate and the factor linking the area and biomass of the organism. The model verification is presented by calculating the biomass dynamics for full (normal) pine plantations of the first five quality classes (Ib, Ia, I, II, III). The model’s quality is assessed by the dimensionless Nash-Sutcliffe model efficiency coefficient, the value of which is usually greater than 0.95. This corresponds to a description of the data that is close to ideal.

A fixed point for black hole distributions

Understanding distributions of black holes is crucial to both astrophysics and quantum gravity. Studying astrophysical population statistics has even been suggested as a channel to constrain black hole formation from the quantum vacuum. Here we propose a Gedankenexperiment to show that the non-linear properties of binary mergers (simulated with accurate surrogate models) generate an attractor in the space of distributions. Our results show that the joint distribution of spin magnitude and fractional mass loss evolves to a fixed point, converging in a few generations. The features of this fixed point distribution do not depend on the choice of the initial distributions in the range of mass ratios that we are able to probe. Since a black hole merger is irreversible it produces entropy—possibly the largest source of entropy in the Universe. The fixed-point distributions are neither isothermal nor isentropic, and initially thermodynamic states evolve away from thermality. We finally evaluate the specific entropy production rate per merger from initially thermal and non-thermal distributions, which converges to a constant.

Entropy production as a tool for characterizing nonequilibrium phase transitions

Nonequilibrium phase transitions can be typified in a similar way to equilibrium systems, for instance, by the use of the order parameter. However, this characterization hides the irreversible character of the dynamics as well as its influence on the phase transition properties. Entropy production has been revealed to be an important concept for filling this gap since it vanishes identically for equilibrium systems and is positive for the nonequilibrium case. Based on distinct and general arguments, the characterization of phase transitions in terms of the entropy production is presented. Analysis for discontinuous and continuous phase transitions has been undertaken by taking regular and complex topologies within the framework of mean-field theory (MFT) and beyond the MFT. A general description of entropy production portraits for Z_{2} ("up-down") symmetry systems under the MFT is presented. Our main result is that a given phase transition, whether continuous or discontinuous has a specific entropy production hallmark. Our predictions are exemplified by an icon system, perhaps the simplest nonequilibrium model presenting an order-disorder phase transition and spontaneous symmetry breaking: the majority vote model. Our work paves the way to a systematic description and classification of nonequilibrium phase transitions through a key indicator of system irreversibility.

Transition from abstract thermodynamic concepts to perceivable ecological indicators

Entropy and exergy are the central concepts in thermodynamics, and many researchers have used them to characterize ecosystem development. However, these concepts are very abstract to outsiders. Direct measurements of the indicators related to entropy and exergy are difficult and involve large errors. Schneider and Kay (1994) bridged thermodynamic concepts, i.e., entropy and exergy, with perceivable ecological indicators, i.e., canopy surface temperature (Tsurf) and net radiation (Rn) in their maximum exergy destruction principle. However, the connection between entropy and exergy with Tsurf and Rn was based on the similarity between the ecosystem and the Bénard cell, and not on thermodynamic reasoning. Considering the coherence of entropy production and exergy destruction, we analyzed the relationship between entropy production and Tsurf and Rn, based on the first and second laws of thermodynamics, and verified it using long-term monitoring data of a tropical seasonal rain forest. We demonstrated that total entropy production (exergy destruction) linearly increased with increasing Rn and decreasing Tsurf theoretically. Empirical data showed that the total entropy production increased, whereas specific entropy production decreased during the growing season. This indicates that plant growth can enhance exergy conversion efficiency. Rn, Tsurf, and related indicators can be used as surrogates for thermodynamic indicators to measure ecosystem status and development. The bridge between thermodynamic concepts and measurable ecological indicators will improve the application of thermodynamics in ecology studies and the understanding of thermodynamic processes in ecosystem.

Entropy Production of Stars

The entropy production (inside the volume bounded by a photosphere) of main-sequence stars, subgiants, giants, and supergiants is calculated based on B–V photometry data. A non-linear inverse relationship of thermodynamic fluxes and forces as well as an almost constant specific (per volume) entropy production of main-sequence stars (for 95% of stars, this quantity lies within 0.5 to 2.2 of the corresponding solar magnitude) is found. The obtained results are discussed from the perspective of known extreme principles related to entropy production.

Entropy Production of Main-Sequence Stars

The entropy production (inside the volume bounded by a photosphere) of main-sequence stars is calculated based on B–V photometry data. The entropy-production distribution function and the dependences of entropy production on temperature and luminosity are obtained for these stars for the first time. A very small range of variation of specific (per volume) entropy production discovered for main-sequence stars (only 0.5 to 1.8 solar magnitudes) is an interesting result that can be crucial for understanding thermodynamic processes of stars.

Nonequilibrium thermodynamics of kinetic metamorphism in snow

Entropy production rates derived from nonequilibrium thermodynamics are used to show that depth hoar develops from the natural progression of snow toward thermal equilibrium. Laboratory experiments were undertaken to examine the evolution of snow microstructure under nonequilibrium thermal conditions. Snow samples with similar initial microstructure were subjected to either a fixed temperature gradient or fixed heat input. The metamorphism for both sets of boundary conditions produced similar depth hoar chains with comparable increases in effective thermal conductivity. Examination of the entropy production rates showed that the microstructural changes resulted from the snow or the surroundings moving toward a stationary state under the given non-equilibrium constraints imposed by the boundary conditions. This behavior is dictated by the second law of thermodynamics.A numerical model applied nonequilibrium thermodynamics to depth hoar formation at the grain scale. Entropy production rate relations were developed for an open system of ice and water vapor subjected to heat and mass flow. Heat conduction in the bonds had the highest specific entropy production rate, indicating it was the most inefficient part of the snow system at transferring heat. As the metamorphism advanced, the bond sizes grew to enhance the conduction pathways through the snow and increase the heat transfer. This spontaneous microstructural evolution moved the system and the surroundings toward equilibrium by reducing the local temperature gradients across the bonds and increasing the entropy production rate density.

Effectiveness of entropy-based functions in the analysis of ecosystem state and development

Following the advances in the field of the thermodynamics of far-from-equilibrium systems, several ecological orientors (indicators able to describe the stage and orientation of ecosystem development) incorporating entropy terms have been proposed. Although most of the proposed functions have a good theoretical basis and have proved to perform adequately as ecological indicators, their suitability as ecological orientors has yet to receive a full confirmation in real case studies. The aim of the present contribution is to examine how several entropy-based indicators (exergy, structural information, entropy production, specific entropy production and the Eco-exergy index) perform as orientors when applied to a special case of ecological succession, i.e. eutrophication, in a homogeneous set of shallow lakes lying along a trophic gradient, from oligotrophy to hyper-eutrophy. The results show that a coherent pattern of response emerge, which is also consistent with the classical ecological theory. In particular, the maximisation of storage and the minimisation of specific entropy production are confirmed as the most reliable principles of ecosystem development, whereas the maximisation of dissipation (as entropy production) appears as a debatable criterion of development.

Numerical Investigation of the Unsteady Interaction Within a Close-Coupled Centrifugal Compressor Used in an Aero Engine

Abstract The present work forms part of a research project of the Institute of Jet Propulsion and Turbomachinery at the RWTH Aachen University in collaboration with GE Aviation. The subject is the detailed numerical analysis of the unsteady flow field, focusing on the interaction between the impeller and the passage diffuser of a close-coupled transonic centrifugal compressor used in an aero engine. The centrifugal compressor investigated is characterized by a close-coupled impeller and passage diffuser with a radial gap of only 3.6%. The close coupling tends to provide a high aerodynamic efficiency but simultaneously cause a high unsteady interaction between the impeller and the diffuser. These unsteady effects can have a significant impact on the performance of both components and present a challenge to state-of-the-art numerical methods. With increasing compressor efficiency, the more important it is to have an understanding of the detailed unsteady flow physics. Experimental data was obtained from a state-of-the art centrifugal compressor test rig located at the Institute of Jet Propulsion. Steady and unsteady pressure measurements within the impeller and diffuser are used to gain detailed information on the temporal, time-averaged, and spectral pressure distributions within the stage to validate the CFD. The work presented here shows the unsteady phenomena caused by the interaction and the location and propagation of these phenomena within the centrifugal stage. Within the impeller, the exducer is in first order excited by the blade passing frequency (BPF) of the diffuser, whereas in the diffuser both the BPF and the passage passing frequency (PPF), are present up until the end of the pipe-diffuser. Significant effects on the integral component performance could only be identified for the impeller. Special focus is paid to evaluate the diffuser upstream pressure field, since this is the major source of unsteadiness within the impeller. The performance of the rotor decreases due to the unsteady interaction. This effect is traced back to the unsteady tip-clearance flow, in which the time-averaged mass transport decreases, whereas the specific entropy production increases in a nonlinear way. Within the diffuser, local effects counteracting with respect to the integral performance are found. In front of the throat, there is less decay in the total pressure as a result of tangentially expanding pressure waves. Within the passage a decrease in flow uniformity in the unsteady flow is identified as the reason for the lower diffusion up until the throat and higher losses within the downstream diffuser passage.

Optimal ecological performance of a four-temperature-level absorption heat pump

The new thermo-ecological performance optimization that combines first and second law of thermodynamics has been carried out for an irreversible absorption heat pump operating between four-temperature-levels. Multi-irreversibilities considered in the system include finite-rate transfer, heat leakage and internal dissipations. The ecological coefficient of performance ECOP defined as the ratio of the heating load to the loss rate of availability (or entropy generation rate) is considered as the objective function. The goal of the new thermo-ecological performance optimization is to maximize this objection function with respect to the working fluid temperatures in the main components of the system. The maximum ECOP and the corresponding optimal coefficient of performance, specific heating load, specific entropy production rate and heat-transfer areas have been determined analytically. The effects of the internal irreversibility, the heat leakage coefficient, the source temperature ratios, the overall heat-transfer coefficients of the heat-exchangers and the distribution ratio rate of the total heat-reject quantity between the absorber and the condenser on the global and optimal performances have been analyzed and discussed.

Macroecology: The Organizing Forces

The fundamental problem in ecology is the relationship between organisms and the physical world. This question is approached through the study of ecosystems as wholes. Pristine, autonomous Arctic lakes provide an invaluable starting point for such investigations. Studies on these lakes, initiated in 1958, indicate that the dominant fish populations assume a recognizable and repeatable structure, which if not disturbed by external forces, is maintained indefinitely. The observable characteristics are high biomass, large individual size, great age, uniformity of individuals despite great variation in age, and relatively few juveniles. This configuration expresses a state of least specific energy dissipation or least specific entropy production and may be regarded as a standing wave in the energy flow. Similar characteristics were found in the dominant species in a wide range of ecosystems worldwide. A state of least dissipation develops when two energy transport processes interfere with each other in the vicinity of thermodynamic equilibrium. Thus it is postulated that living organisms originated through the agonistic interaction between two energy transport processes within materials, initially occurring in an environment close to thermodynamic equilibrium. These two processes, fundamental to energy transfer, are recognized as the principle of least action and its diametrical opposite, the principle of most action. Each force dominates system behavior in a different time frame: most action in the short-term (ecological time) and least action over the long-term (evolutionary time). Interaction between the countervailing forces provides an understanding of a wide range of emergent ecological generalities such as succession, r- and K-selection, the stability and diversity of ecosystems, and the directionality of evolutionary change.

Min-Max principle of entropy production with time in aquatic communities

The study of entropy is important for understanding essential nature of complex and functional systems from thermodynamic viewpoint. However, entropy content of living systems cannot be estimated both by experiment and by calculation. On the contrary, entropy production has been evaluated for plants, animals, human bodies and lake-ecosystems. The present paper provides entropy production for aquatic communities using data of respiration in aquatic food webs. Oxygen-uptake by respiration in organisms decomposes macromolecules such as carbohydrate, protein and lipid and liberates chemical energy, which is then used to chemical reactions and motions of matter in organisms to support lively order in structure and function in organisms. Finally, this chemical energy becomes heat energy and discarded to the outside (dissipation function). Accompanying this heat energy, entropy production which inevitably occurs by irreversibility also discarded to the outside. Here, dissipation function and entropy production are estimated from data of respiration. Both specific dissipation function and specific entropy production in aquatic communities become two-phase character with respect to trophic diversity: early increase and later decrease with the increase of trophic diversity. The trophic diversity in these aquatic ecosystems is shown to be positively correlated with the degree of eutrophication, and the degree of eutrophication is “arrow of time” in the hierarchy of aquatic ecosystems. Hence, specific dissipation function and specific entropy production have the two-phase: early increase and later decrease with “time”. This two-directional tendency with time may be characterized as “Biological Principle” in contrast to “Physical Principle” (variation principle) that is always one-directional.

Use of thermodynamic indices as ecological indicators of the development state of lake ecosystems: Specific dissipation

Abstract This paper proposes the ratio between the entropy produced and the exergy stored by the biological component of an ecosystem (which may be called the specific entropy production or the specific dissipation of a community) as a tool for understanding the evolution of ecological systems. Specific dissipation, which may be taken as representing a renewed version of Odum's Schrodinger ratio, is here proposed as an indicator of ecosystems maturity as well as an ecological orientor whose minimisation is expected throughout ecosystem development. After having presented an empirical method for estimating the specific dissipation in lake ecosystems, it has been applied to the characterization of the development state of the communities of a set of shallow lakes which lye from oligotrophic to hyper-eutrophic conditions. The adequacy of the proposed indicator has been tested and discussed along two different ecological series: the seasonal progression of phytoplankton and the trophic gradient. The results confirm that the ratio is an appropriate indicator of ecosystem maturity and support the hypothesis that its minimisation is one of the primary “goals” of ecosystem development.

The strategy of ecosystem development: specific dissipation as an indicator of ecosystem maturity

The ratio of entropy generation rate to entropy embodied in structures relatively to the surroundings can be considered as an indicator of the ability of a self-organizing dissipative system to maintain itself far from equilibrium by pumping out entropy. The higher the ratio (which may be called the specific entropy production or the specific dissipation of a system), the lower the capacity of a system to convert the incoming low-entropy energy into internal organization. It appears that the ratio attains special significance for interpreting the evolution of biological systems, as the maximum expression of self-organizing systems, from the sub-cellular to the ecosystem scale. This paper proposes specific dissipation, written as the ratio of biological entropy production to exergy stored in the living biomass, as a thermodynamic orientor as well as an indicator of the development state of ecological systems. After having presented a method for estimating the specific dissipation in lakes, the adequacy of the proposed indicator is discussed and also tested by comparing its response to those of some classical ecological attributes (successional sequences of species, biodiversity, individual body size, structural organization and generation time of organisms) throughout the seasonal progression of the plankton community in Lake Trasimeno (Umbria, Italy). The results support the hypothesis that the minimization of specific dissipation is a primary criterion of evolution of ecological systems and also sustain the use of specific dissipation as an indicator of ecological maturity.

Ecosystem growth and development

One of the most important features of biosystems is how they are able to maintain local order (low entropy) within their system boundaries. At the ecosystem scale, this organization can be observed in the thermodynamic parameters that describe it, such that these parameters can be used to track ecosystem growth and development during succession. Thermodynamically, ecosystem growth is the increase of energy throughflow and stored biomass, and ecosystem development is the internal reorganization of these energy mass stores, which affect transfers, transformations, and time lags within the system. Several proposed hypotheses describe thermodynamically the orientation or natural tendency that ecosystems follow during succession, and here, we consider five: minimize specific entropy production, maximize dissipation, maximize exergy storage (includes biomass and information), maximize energy throughflow, and maximize retention time. These thermodynamic orientors were previously all shown to occur to some degree during succession, and here we present a refinement by observing them during different stages of succession. We view ecosystem succession as a series of four growth and development stages: boundary, structural, network, and informational. We demonstrate how each of these ecological thermodynamic orientors behaves during the different growth and development stages, and show that while all apply during some stages only maximizing energy throughflow and maximizing exergy storage are applicable during all four stages. Therefore, we conclude that the movement away from thermodynamic equilibrium, and the subsequent increase in organization during ecosystem growth and development, is a result of system components and configurations that maximize the flux of useful energy and the amount of stored exergy. Empirical data and theoretical models support these conclusions.

Calorimetry and thermodynamics of living systems

Calorimetry of living systems and classical thermodynamics developed in parallel, from Lavoisier’s early ice calorimeter experiments on guinea pigs, followed by Dubrunfaut’s macrocalorimetric research of fermentation processes and Atwater-Rosa’s whole-body calorimetry on humans and domestic animals, to the introduction of the famous Tian-Calvet instrument that found entrance into so many different fields of biology. In this work, six examples of living-system calorimetry and thermodynamics are presented. These are: (i) glycolytic oscillations far off the thermodynamic equilibrium; (ii) growth and energy balances in fermenting and respiring yeast cultures; (iii) direct and indirect calorimetric monitoring of electrically stimulated reptile metabolism; (iv) biologic and climatic factors influencing the temperature constancy and distribution in the mound of a wood ant colony as an example of a complex ecological system; (v) energetic considerations on the clustering of European honeybees in winter as a means to save energy and stored food as well as for their Japanese counterparts in defending against hornet predators; and (vi) energetic and evolutionary aspects of the mass specific entropy production rate, the so-called bound dissipation or psiu-function. The examples presented here are just a very personal selection of living systems from a broad spectrum at all levels of complexity. Common for all of them is that they were investigated calorimetrically on the background of classical and irreversible thermodynamics.

Approach of evolutionary theories of ageing, stress, senescence-like phenotypes, calorie restriction and hormesis from the view point of far-from-equilibrium thermodynamics

B. L. Strehler wrote that “Any system that is not in thermodynamic equilibrium will approach that state at a rate that is a function of absolute temperature and the energy barriers to the rearrangements of components”. Far-from-equilibrium thermodynamics allows a global systemic description of the cellular behaviour. This approach transcends the genetic and stochastic considerations on ageing as well as some evolutionary questions about ageing. The fundamental difference between the processes of development and ageing could reflect the intrinsic differences existing between biological systems where an increase in specific entropy production (SEP) is, respectively, still possible or not. The increase of the potential of SEP which probably occurred with evolution might explain in part why life span could increase. However, this SEP-driven increase in life span was possible only in those species which did not take advantage of their increased potential of SEP to ameliorate their reproductive capacity at the expense of possible increases in repair capacity. The criteria of stability of far-from-equilibrium open systems and the theory of attractors also help to sort the possible types of cellular stress responses: normal ageing, hormesis, stress-induced premature senescence, apoptosis or necrosis.

Modelling the nonlinear viscoelastic behavior of amorphous glassy polymers

Constitutive equations are derived for the nonlinear viscoelastic response of glassy polymers at isothermal loading with small strains. The model is based on the concept of temporary networks, where the rates of breakage and reformation for active chains depend on the specific entropy production. It is demonstrated that the stress-strain relations with a dissipation-driven internal clock adequately predict an apparent aging of polycarbonate observed in dynamic tests on stretched specimens.