Entropy Production Rate Research Articles

Energy analysis of Francis turbine for various mass flow rate conditions based on entropy production theory

A methodology of the entropy production theory is employed in hydro turbine flows to analyze the hydraulic loss characteristics quantitatively. The entropy production theory has its distinctive superiority over than traditional pressure drop method because it calculates energy loss through integrating entire computational domain so that it can identify location of energy loss and reflect energy loss characteristics intuitively. This simulated study was implemented by commercial software ANSYS CFX with shear stress turbulence model for a Francis turbine versus various discharge conditions. After comparing with experimental data, the energy loss in different flow components was analyzed and the ability of flow parts to generate energy loss was evaluated versus various conditions quantitatively. Then, the distributions of entropy production rate (EPR) were displayed in stay&guide vanes, runner and draft tube. The conclusions indicate that draft tube is the main part generating the most energy loss compared with other parts. The energy loss fluctuation of runner was obtained and three dominant frequencies were captured with two low frequencies 11.93 [Hz], 15.9 [Hz] and one high frequency 27.83 [Hz]. This study indicates that entropy production theory can provide sufficient theoretical and engineering guidance for the energy loss analysis in hydro turbine flows.

Superradiant Many-Qubit Absorption Refrigerator

We show that the lower levels of a large-spin network with a collective anti-ferromagnetic interaction and collective couplings to three reservoirs may function as a quantum absorption refrigerator. In appropriate regimes, the steady-state cooling current of this refrigerator scales quadratically with the size of the working medium, i.e., the number of spins. The same scaling is observed for the noise and the entropy production rate.

Thermogravitational convection of ferrofluid combined with the second law of thermodynamics for an open chamber with a heat-generating solid block under an influence of uniform magnetic field

The present numerical study scrutinizes the effect of uniform Lorentz force on the thermogravitational energy transport and entropy production of nanosuspension in an open domain with a heat-generating solid element. The left border is kept at low temperature (Tc) whilst the horizontal borders are assumed to be adiabatic. Finite volume method (FVM) is employed to work out the heat and mass transfer equations. For fixed value of Rayleigh number (Ra = 107), numerical analysis was optimized for wide ranges of nanoparticle volume fraction (ϕ = 1%–4%), thermal conductivity ratio of a heat generating body (k⁎ = 0.1–5), Hartmann parameter (Ha = 0–100), angle of inclined magnetic field (γ = 0°–90°) and non-dimensional temperature drop (Ω = 0.001–0.1). The numerical solutions were analyzed employing patterns of temperature and stream function as well as average Nusselt number and entropy lines. The outcomes indicated that, an increasing magnetic parameter Ha leads to reduction of mean Nu and the rate of entropy production. An addition of nano-sized particles enhances the energy transport and average entropy production for the system. It is also revealed that the maximum energy transport strength occurs at high thermal conductivity ratio (k⁎ = 5).

Information Geometry, Fluctuations, Non-Equilibrium Thermodynamics, and Geodesics in Complex Systems.

Information theory provides an interdisciplinary method to understand important phenomena in many research fields ranging from astrophysical and laboratory fluids/plasmas to biological systems. In particular, information geometric theory enables us to envision the evolution of non-equilibrium processes in terms of a (dimensionless) distance by quantifying how information unfolds over time as a probability density function (PDF) evolves in time. Here, we discuss some recent developments in information geometric theory focusing on time-dependent dynamic aspects of non-equilibrium processes (e.g., time-varying mean value, time-varying variance, or temperature, etc.) and their thermodynamic and physical/biological implications. We compare different distances between two given PDFs and highlight the importance of a path-dependent distance for a time-dependent PDF. We then discuss the role of the information rate and relative entropy in non-equilibrium thermodynamic relations (entropy production rate, heat flux, dissipated work, non-equilibrium free energy, etc.), and various inequalities among them. Here, is the information length representing the total number of statistically distinguishable states a PDF evolves through over time. We explore the implications of a geodesic solution in information geometry for self-organization and control.

Emergence of extended Newtonian gravity from thermodynamics

Discovery of a novel thermodynamic aspect of nonrelativistic gravity is reported. Here, initially, an unspecified scalar field potential is considered and treated not as an externally applied field but as a thermodynamic variable on an equal footing with the fluid variables. It is shown that the second law of thermodynamics imposes a stringent constraint on the field, and, quite remarkably, the allowable field turns out to be only of gravity. The resulting field equation for the gravitational potential derived from the analysis of the entropy production rate contains a dissipative term due to irreversibility. It is found that the system relaxes to the conventional theory of Newtonian gravity up to a certain spatial scale, whereas on the larger scale there emerges non-Newtonian gravity described by a nonlinear field equation containing a single coefficient. A comment is made on an estimation of the coefficient that has its origin in the thermodynamic property of the system.

Thermodynamic Uncertainty Relation and Thermodynamic Speed Limit in Deterministic Chemical Reaction Networks.

We generalize the thermodynamic uncertainty relation (TUR) and thermodynamic speed limit (TSL) for deterministic chemical reaction networks (CRNs). The scaled diffusion coefficient derived by considering the connection between macro- and mesoscopic CRNs plays an essential role in our results. The TUR shows that the product of the entropy production rate and the ratio of the scaled diffusion coefficient to the square of the rate of concentration change is bounded below by two. The TSL states a trade-off relation between speed and thermodynamic quantities, the entropy production, and the time-averaged scaled diffusion coefficient. The results are proved under the general setting of open and nonideal CRNs.

Thermodynamics and the quantum speed limit in the non-Markovian regime

Quantum speed limit (QSL) for open quantum systems in the non-Markovian regime is analyzed. We provide a the lower bound for the time required to transform an initial state to a final state in terms of thermodynamic quantities such as the energy fluctuation, entropy production rate and dynamical activity. Such bound was already analyzed for Markovian evolution satisfying detailed balance condition. Here we generalize this approach to deal with arbitrary evolution governed by time-local generator. Our analysis is illustrated by three paradigmatic examples of qubit evolution: amplitude damping, pure dephasing, and the eternally non-Markovian evolution.

Mechanism for the Generation of Robust Circadian Oscillations through Ultransensitivity and Differential Binding Affinity.

Biochemical circadian rhythm oscillations play an important role in many signaling mechanisms. In this work, we explore some of the biophysical mechanisms responsible for sustaining robust oscillations by constructing a minimal but analytically tractable model of the circadian oscillations in the KaiABC protein system found in the cyanobacteria S. elongatus. In particular, our minimal model explicitly accounts for two experimentally characterized biophysical features of the KaiABC protein system, namely, a differential binding affinity and an ultrasensitive response. Our analytical work shows how these mechanisms might be crucial for promoting robust oscillations even in suboptimal nutrient conditions. Our analytical and numerical work also identifies mechanisms by which biological clocks can stably maintain a constant time period under a variety of nutrient conditions. Finally, our work also explores the thermodynamic costs associated with the generation of robust sustained oscillations and shows that the net rate of entropy production alone might not be a good figure of merit to asses the quality of oscillations.

Non-extensive thermodynamic entropy to predict the dynamics behavior of COVID-19

The current world observations in COVID-19 are hardly tractable as a whole, making situations of information to be incompleteness. In pandemic era, mathematical modeling helps epidemiological scientists to take informing decisions about pandemic planning and predict the disease behavior in the future. In this work, we proposed a non-extensive entropy-based model on the thermodynamic approach for predicting the dynamics of COVID-19 disease. To do so, the epidemic details were considered into a single and time-dependent coefficients model. Their four constraints, including the existence of a maximum point were determined analytically. The model was worked out to give a log-normal distribution for the spread rate using the Tsallis entropy. The width of the distribution function was characterized by maximizing the rate of entropy production. The model predicted the number of daily cases and daily deaths with a fairly good agreement with the World Health Organization (WHO) reported data for world-wide, Iran and China over 2019-2020-time span. The proposed model in this work can be further calibrated to fit on different complex distribution COVID-19 data over different range of times.

Fluctuation theorem convergence in a viscoelastic medium demonstrated experimentally using a dusty plasma.

The convergence of the steady-state fluctuation theorem (SSFT) is investigated in a shear-flow experiment performed in a dusty plasma. This medium has a viscoelastic property characterized by the Maxwell relaxation time τ_{M}. Using measurements of the time series of the entropy production rate, for subsystems of various sizes, it is discovered that the SSFT convergence time decreases with the increasing system size until it eventually reaches a minimum value of τ_{M}, no matter the size of the subsystem. This result indicates that the convergence of the SSFT is limited by the energy-storage property of the viscoelastic medium.

Quality of the thermodynamic uncertainty relation for fast and slow driving

The thermodynamic uncertainty relation originally proven for systems driven into a non-equilibrium steady state (NESS) allows one to infer the total entropy production rate by observing any current in the system. This kind of inference scheme is especially useful when the system contains hidden degrees of freedom or hidden discrete states, which are not accessible to the experimentalist. A recent generalization of the thermodynamic uncertainty relation to arbitrary time-dependent driving allows one to infer entropy production not only by measuring current-observables but also by observing state variables. A crucial question then is to understand which observable yields the best estimate for the total entropy production. In this paper we address this question by analyzing the quality of the thermodynamic uncertainty relation for various types of observables for the generic limiting cases of fast driving and slow driving. We show that in both cases observables can be found that yield an estimate of order one for the total entropy production. We further show that the uncertainty relation can even be saturated in the limit of fast driving.

Thermodynamics of fluctuations based on time-and-space averages.

We develop nonequilibrium theory by using averages in time and space as a generalized way to upscale thermodynamics in nonergodic systems. The approach offers a classical perspective on the energy dynamics in fluctuating systems. The rate of entropy production is shown to be explicitly scale dependent when considered in this context. We show that while any stationary process can be represented as having zero entropy production, second law constraints due to the Clausius theorem are preserved due to the fact that heat and work are related based on conservation of energy. As a demonstration, we consider the energy dynamics for the Carnot cycle and for Maxwell's demon. We then consider nonstationary processes, applying time-and-space averages to characterize nonergodic effects in heterogeneous systems where energy barriers such as compositional gradients are present. We show that the derived theory can be used to understand the origins of anomalous diffusion phenomena in systems where Fick's law applies at small length scales, but not at large length scales. We further characterize fluctuations in capillary-dominated systems, which are nonstationary due to the irreversibility of cooperative events.

Dynamics of Marangoni convection in radiative flow of power-law fluid with entropy optimization

The flow of non-Newtonian liquids and their heat transfer characteristic gained more importance due to their technological, industrial and in many engineering applications. Inspired by these applications, the magnetohydrodynamic (MHD) flow of non-Newtonian liquid characterized by a power-law model is scrutinized. Further, viscous dissipation, Marangoni convection and thermal radiation are taken into the account. In addition, the production of entropy is investigated as a function of temperature, velocity and concentration. For different flow parameters, the total entropy production (EP) rate is examined. The appropriate similarity transformations are used to reduce the modeled equations reduced into ordinary differential equations (ODEs). The Runge–Kutta–Fehlberg 45-order procedure is then used to solve these reduced equations numerically using the shooting technique. Results reveal that the escalating values of radiation parameter escalate the heat transference, but the contrary trend is portrayed for escalating values of power-law index. The augmented values of thermal Marangoni number decline the heat transference. The gain in values of radiation parameter progresses the entropy generation.

Numerical study for entropy generation and melting heat in flow of modified hybrid nanomaterial (Ag + MWCNTs + SWCNTs + Water)

The main theme behind this work is to model and analyze melting heat in the squeezed flow of a modified hybrid nanomaterial (Ag + MWCNTs + SWCNTs + Water). Entropy generation in the presence of viscous dissipation is investigated. Modeling is performed for basefluid (Water), nanofluid (SWCNTs + Water), hybrid nanofluid (MWCNTs + SWCNTs + Water), and modified hybrid nanomaterial (Ag + MWCNTs + SWCNTs + Water). Entropy production rate, velocity, Bejan number, skin friction coefficient, temperature, and Nusselt number are evaluated graphically under sundry variables. Non-linear coupled equations (ODEs) are constructed from the expressions (PDEs (continuity, momentum, and energy)) by adopting suitable transformations. The obtained coupled systems are then solved numerically by the bvp4c technique (shooting method with RK-4 algorithm). To execute this methodology, first we have converted our governed non-linear ODEs into a system of first-order ODEs. It is due to the fact that bvp4c works on the basis of the Runge–Kutta method, which is applicable to first-order ODEs. The velocity of the fluid increases with an increment in squeezing and melting parameters while it is reduced via nanoparticle concentration for silver. Fluid temperature reduces with melting while it boosts with squeezing number. Both melting and squeezing number boost skin friction. Nusselt number increases with both melting and squeezing number. Entropy is minimized via the squeezing number. The Bejan number is higher for both melting and squeezing number. It is concluded that performance of modified hybrid nanomaterial is best when compared with nanomaterial and hybrid nanomaterial.

Pro-Inflammatory Cytokines are Dysregulated in Depression and Correlated With Measures of Psychopathology

This paper presents a kinematic assumption free and thermodynamically consistent non-linear formulation incorporating finite strain and finite deformation for thermoviscoelastic plates/shells based on the conservation and balance laws of the classical continuum mechanics (CCM) in R3 (see Surana and Mathi, (2020) for linear theory). The conservation and balance laws in Lagrangian description with finite strain measure and the conjugate stress measure in R3 are considered. The conjugate pairs in the second law of thermodynamics (SLT), the consideration of additional physics and the principle of equipresence are utilized to determine the constitutive variables and their argument tensors. The constitutive theory for the contravariant second Piola–Kirchhoff stress tensor is derived using Green’s strain tensor and its convected time derivatives of up to order n as its argument tensors using representation theorem with complete basis (i.e. using integrity). The convected time derivatives of the Green’s strain tensor up to order n provide ordered rate constitutive theory for the dissipation mechanism that is naturally non-linear due to Green’s strain measure. The constitutive theory for heat vector derived using representation theorem and integrity is also a non-linear constitutive theory. Simplified linear forms of these constitutive theories are also presented. The solution methods for the mathematical model for the BVPs as well as the IVPs using p-version hierarchical higher degree and higher order finite element method are presented. Due to dissipation, the energy equation is integral part of the mathematical model that accounts for rate of mechanical work resulting in rate of entropy production, hence heat.The plate/shell geometry (flat or curved) is described by its middle surface containing the nodal vectors (at each of the nine nodes), the ends of which define bottom and top surfaces of the plate/shell (Surana and Mathi, 2020). The geometry is mapped into ξηζ natural coordinate space in a two unit cube. The p-version hierarchical local approximations in ξηζ are constructed to describe the deformation of the plate/shell middle surface as well as its faces that is controlled by p-levels in ξ,η and ζ directions (element local approximation). The formulation presented here is accurate for very thin as well as very thick plate/shells and for small as well as finite deformation and finite strains. Non-linear constitutive theories based on integrity allow more complex constitutive behavior in term of strains as well as strain rates, hence dissipation mechanism. Dissipation mechanism is described by an ordered rate theory based on SLT and additional physics. The formulation presented here always ensures thermodynamic equilibrium during the evolution as it is derived using the conservation and balance laws of CCM in R3. The formulation always preserves three dimensional nature of the deformation physics regardless of the plate/shell thickness and is free of locking problems and shear correction factors that plague most of the currently used plate/shell formulations.

Information geometry and non-equilibrium thermodynamic relations in the over-damped stochastic processes

An advantageous method for understanding complexity is information geometry theory. In particular, a dimensionless distance, called information length , permits us to describe time-varying, non-equilibrium processes by measuring the total change in the information along the evolution path of a stochastic variable or the total number of statistically different states the variable passes through in time. Here, we elucidate the meaning of information length and information rate in light of thermodynamics (entropy production rate , non-equilibrium free energy , microscopic chemical potential μ, etc). In particular, the average ⟨∂ t μ⟩ gives the average rate of work (power) while the second moment is proportional to Γ2. Here, the angular brackets denote average and V is the potential. The upper bound on the entropy production rate is set by the product of Γ and the RMS value of the fluctuating part δμ = μ − ⟨μ⟩. Specifically, in the case of the non-autonomous Ornstein–Uhlenbeck process for a stochastic variable x, we show that is bounded above by Γ2 up to the fluctuation normalization σ 2 = ⟨(δx)2⟩ where σ is the standard deviation and δx = x − ⟨x⟩ is the fluctuating component of x. The equality holds in the (isothermal) case where σ and the temperature D are constant. We discuss the implications of as a proxy for the entropy production along an evolution path and understanding self-organization.

Self-Organization, Entropy Generation Rate, and Boundary Defects: A Control Volume Approach.

Self-organization that leads to the discontinuous emergence of optimized new patterns is related to entropy generation and the export of entropy. Compared to the original pattern that the new, self-organized pattern replaces, the new features could involve an abrupt change in the pattern-volume. There is no clear principle of pathway selection for self-organization that is known for triggering a particular new self-organization pattern. The new pattern displays different types of boundary-defects necessary for stabilizing the new order. Boundary-defects can contain high entropy regions of concentrated chemical species. On the other hand, the reorganization (or refinement) of an established pattern is a more kinetically tractable process, where the entropy generation rate varies continuously with the imposed variables that enable and sustain the pattern features. The maximum entropy production rate (MEPR) principle is one possibility that may have predictive capability for self-organization. The scale of shapes that form or evolve during self-organization and reorganization are influenced by the export of specific defects from the control volume of study. The control volume (CV) approach must include the texture patterns to be located inside the CV for the MEPR analysis to be applicable. These hypotheses were examined for patterns that are well-characterized for solidification and wear processes. We tested the governing equations for bifurcations (the onset of new patterns) and for reorganization (the fine tuning of existing patterns) with published experimental data, across the range of solidification morphologies and nonequilibrium phases, for metallic glass and featureless crystalline solids. The self-assembling features of surface-texture patterns for friction and wear conditions were also modeled with the entropy generation (MEPR) principle, including defect production (wear debris). We found that surface texture and entropy generation in the control volume could be predictive for self-organization. The main results of this study provide support to the hypothesis that self-organized patterns are a consequence of the maximum entropy production rate per volume principle. Patterns at any scale optimize a certain outcome and have utility. We discuss some similarities between the self-organization behavior of both inanimate and living systems, with ideas regarding the optimizing features of self-organized pattern features that impact functionality, beauty, and consciousness.

A second law analysis on flow of a nanofluid in a shell-and-tube heat exchanger equipped with new unilateral ladder type helical baffles

The irreversibility characteristics of a shell and tube heat exchanger (STHE) fitted with the unilateral ladder type helical baffle are investigated. A boehmite nanofluid having different nanoparticle shapes is used as the hot fluid in the tube-side with a constant Reynolds number. The pure water is applied for the cold fluid, which passes inside the shell with various Reynolds numbers. The thermal and frictional entropy productions of both fluids intensify by the Reynolds number amplification. Thereby, the plural entropy production rates of the hot fluid and cold fluid, in the condition of utilizing the platelet nanoparticles, respectively demonstrate 8.4% and 20.9% increases by the Reynolds number variation from 5000 to 20,000. The nanofluid containing the platelet nanoparticles causes the maximum thermal entropy production. All in all, the minimum irreversibility for the whole STHE occurs for the nanofluid containing the oblate spheroid particles, which is recommended for use in this STHE.

Non-equilibrium quadratic measurement-feedback squeezing in a micromechanical resonator

Measurement and feedback control of thermomechanical motion in a micromechanical resonator has been actively studied to achieve extremely high sensing performance by controlling the stochastic thermal noise. Although linear measurement-feedback control in the phase space results in the feedback cooling, extending them to the nonlinear regime, i.e., utilizing quadratic of higher-order dynamic variables in both measurement and control, can further functionalize its operations. Here, we demonstrate fully quadratic measurement-feedback protocol in a micromechanical resonator by driving the second-order nonlinearity and directly measuring quadratic variables referred as Schwinger angular momentum. Our measurement-feedback protocol enables us to achieve a noise reduction at the level of $\ensuremath{-}5.1\ifmmode\pm\else\textpm\fi{}0.2$ dB over the --3-dB limitation in the continuous parametric driving. We unveil that this strong noise reduction originates in the effective cooling effect by investigating entropy production rates. These results would be further extended to investigating general performance of nonlinear information thermodynamic machines, in which the higher-order moments (e.g., variance and correlations) can be controlled with avoiding the nonlinear instability, thanks to the existence of information flows.

The Coordinate Reaction Model: An Obstacle to Interpreting the Emergence of Chemical Complexity.

The way chemical transformations are described by models based on microscopic reversibility does not take into account the irreversibility of natural processes, and therefore, in complex chemical networks working in open systems, misunderstandings may arise about the origin and causes of the stability of non‐equilibrium stationary states, and general constraints on evolution in systems that are far from equilibrium. In order to be correctly simulated and understood, the chemical behavior of complex systems requires time‐dependent models, otherwise the irreversibility of natural phenomena is overlooked. Micro reversible models based on the reaction‐coordinate model are time invariant and are therefore unable to explain the evolution of open dissipative systems. The important points necessary for improving the modeling and simulations of complex chemical systems are: a) understanding the physical potential related to the entropy production rate, which is in general an inexact differential of a state function, and b) the interpretation and application of the so‐called general evolution criterion (GEC), which is the general thermodynamic constraint for the evolution of dissipative chemical systems.