Average Entropy Production Rate Research Articles

Plasma kinetics: Discrete Boltzmann modeling and Richtmyer–Meshkov instability

In this paper, a discrete Boltzmann method (DBM) for plasma kinetics is proposed and further used to investigate the non-equilibrium characteristics in Orszag–Tang (OT) vortex and Richtmyer–Meshkov instability (RMI) problems. The construction of DBM mainly considers two aspects. The first is to build a physical model with sufficient capability to capture underlying physics. The second is to devise schemes for extracting more valuable information from massive data. For the first aspect, the generated model is equivalent to a magnetohydrodynamic model, and a coarse-grained model for extracting the most relevant thermodynamic non-equilibrium (TNE) behaviors including the entropy production rate. For the second aspect, the DBM uses non-conserved kinetic moments of (f−feq) to describe the non-equilibrium states and behaviors of complex systems. It is found that (i) for OT vortex, the entropy production rate and compression difficulty first increase and then decrease with time. (ii) For RMI with interface inversion and re-shock process, the influence of magnetic field on TNE effects shows stages: before the interface inversion, the TNE strength is enhanced by delaying the interface inversion; while after the interface inversion, the TNE strength is significantly reduced. Both the global average TNE strength and entropy production rate contributed by non-organized energy flux can be used as physical criteria to identify whether or not the magnetic field is sufficient to prevent the interface inversion. In general, this paper proposes a generalized physical modeling and analysis scheme that has the potential for investigating the kinetic physics in plasma.

Statistical features of systems driven by non-Gaussian processes: theory & practice

Nowadays many tools, e.g. fluctuation relations, are available to characterize the statistical properties of non-equilibrium systems. However, most of these tools rely on the assumption that the driving noise is normally distributed. Here we consider a class of Markov processes described by Langevin equations driven by a mixture of Gaussian and Poissonian noises, focusing on their non-equilibrium properties. In particular, we prove that detailed balance does not hold even when correlation functions are symmetric under time reversal. In such cases, a breakdown of the time reversal symmetry can be highlighted by considering higher order correlation functions. Furthermore, the entropy production may be different from zero even for vanishing currents. We provide analytical expressions for the average entropy production rate in several cases. We also introduce a scale dependent estimate for entropy production, suitable for inference from experimental signals. The empirical entropy production allows us to discuss the role of spatial and temporal resolutions in characterizing non-equilibrium features. Finally, we revisit the Brownian gyrator introducing an additional Poissonian noise showing that it behaves as a two dimensional linear ratchet. It has also the property that when Onsager relations are satisfied its entropy production is positive although it is minimal. We conclude discussing estimates of entropy production for partially accessible systems, comparing our results with the lower bound provided by the thermodynamic uncertainty relations.

Extreme value statistics of edge currents in Markov jump processes and their use for entropy production estimation

The infimum of an integrated current is its extreme value against the direction of its average flow. Using martingale theory, we show that the infima of integrated edge currents in time-homogeneous Markov jump processes are geometrically distributed, with a mean value determined by the effective affinity measured by a marginal observer that only sees the integrated edge current. In addition, we show that a marginal observer can estimate a fraction of the average entropy production rate in the underlying nonequilibrium process from the extreme value statistics in the integrated edge current. The estimated average rate of dissipation obtained in this way equals the above mentioned effective affinity times the average edge current. Moreover, we show that estimates of dissipation based on extreme value statistics can be significantly more accurate than those based on thermodynamic uncertainty ratios, as well as those based on a naive estimator obtained by neglecting nonMarkovian correlations in the Kullback-Leibler divergence of the trajectories of the integrated edge current.

Thermodynamics of signal transduction systems and fluctuation theorem in a signal cascade

Biochemical chain reactions are signal transduction cascades that can transmit biological information about the intracellular environment. In this study, we modelled a chain reaction as a code string for applying information theory. Herein, we assumed that cell signal transduction selects a strategy to maximize the transduced signal per signal event duration. To investigate the same, we calculated the information transmission capacity of the reaction chain by maximizing the average entropy production rate per reaction time, indicating the idea of the entropy coding method. Moreover, we defined a signal cascade trajectory. Subsequently, we found that the logarithm of the forward and reverse transition ratio per reaction time is equal to the entropy production rate, which derives the form of the fluctuation theorem in signal transduction. Our findings suggest the application of information entropy theory for analysing signal transduction.

Properties of the dissipation functions for passive and active systems.

The dissipation function for a system is defined as the natural logarithm of the ratio between probabilities of a trajectory and its time-reversed trajectory, and its probability distribution follows a well-known relation called the fluctuation theorem. Using the generic Langevin equations, we derive the expressions of the dissipation function for passive and active systems. For passive systems, the dissipation function depends only on the initial and the final values of the dynamical variables of the system, not on the trajectory of the system. Furthermore, it does not depend explicitly on the reactive or dissipative coupling coefficients of the generic Langevin equations. In addition, we study a one-dimensional case numerically to verify the fluctuation theorem with the form of the dissipation function we obtained. For active systems, we define the work done by active forces along a trajectory. If the probability distribution of the dynamical variables is symmetric under time reversal, in both cases, the average rate of change of the dissipation function with trajectory duration is nothing but the average entropy production rate of the system and reservoir.

Entropy production analysis of a radial inflow turbine with variable inlet guide vane for ORC application

The fluctuation of heat source conditions leads to the off-design operation and efficiency reduction of the radial inflow turbine (RIT). The adjustment of the outlet angle of inlet guide vane (IGV) is an important way to improve the turbine performance under off-design conditions. Since the energy dissipation caused by friction and flow separation is the main reason for the reduction of RIT efficiency, the entropy production analysis method is used to diagnose the location with high local energy loss in the RIT and evaluate its total energy loss under different working conditions in this paper. Firstly, an appropriate outlet angle of the IGV is determined according to the inlet pressure and outlet pressure of the RIT in organic Rankine cycle (ORC). Then, the effects of inlet pressure and outlet pressure on its energy loss are studied. The results indicate that the average entropy production rate (EPR) of the rotor in the RIT is the highest, which is mainly from the tip clearance and the inlet region. More than 70% of total entropy production of the turbine comes from the rotor, followed by the diffuser. The turbine can achieve lower total entropy production at higher outlet pressure or lower inlet pressure. Compared with a fixed IGV, the turbine with variable IGV can achieve higher turbine efficiency and output power under off-design conditions. The maximum increase in the efficiency and output power of the turbine with variable IGV under different inlet pressures is 3.8% and 12.9%, respectively.

Analysis of Energy Loss Characteristics of Vertical Axial Flow Pump Based on Entropy Production Method under Partial Conditions.

The energy loss of the vertical axial flow pump device increases due to the unstable internal flow, which reduces the efficiency of the pump device and increases its energy consumption of the pump device. The research results of the flow loss characteristics of the total internal conduit are still unclear. Therefore, to show the internal energy loss mechanism of the axial flow pump, this paper used the entropy production method to calculate the energy loss of the total conduit of the pump device to clarify the internal energy loss mechanism of the pump device. The results show that the energy loss of the impeller is the largest under various flow conditions, accounting for more than 40% of the total energy loss of the pump device. The variation trend of the volume average entropy production and the energy loss is similar under various flow coefficients (KQ). The volume average entropy production rate (EPR) and the energy loss decrease first and then increase with the increase of flow, the minimum volume average entropy production is 378,000 W/m3 at KQ = 0.52, and the area average EPR of the impeller increases gradually with the increase of flow. Under various flow coefficient KQ, the energy loss of campaniform inlet conduit is the smallest, accounting for less than 1% of the total energy loss. Its maximum value is 63.58 W. The energy loss of the guide vane and elbow increases with the increase of flow coefficient KQ, and the maximum ratio of energy loss to the total energy loss of the pump device is 29% and 21%, respectively, at small flow condition KQ = 0.38. The energy loss of straight outlet conduit reduces first and then increases with the increase of flow coefficient KQ. When flow coefficient KQ = 0.62, it accounts for 27% of the total energy loss of the pump device, but its area average entropy production rate (EPR) and volume average entropy production rate (EPR) are small. The main entropy production loss in the pump device is dominated by entropy production by turbulent dissipation (EPTD), and the proportion of entropy production by direct dissipation (EPDD) is the smallest.

General thermodynamic efficiency loss, aging and Gompertz mortality law

A simple and general thermodynamic theory is applied to describe the irreversible aspects of the continuous process of functional efficiency loss, which occurs in dissipative biological structures after they reach maturity [1]. This theory, among other things, follows Prigogine [2] by considering that these dissipative structures perform their functions and carry out cyclical processes per se since they are self-organizing away from equilibrium. By using the irreversible thermodynamic theory of aging by Montemayor-Aldrete et al [1], we have obtained results such as the following: The accumulated damage that occurs in dissipative biological structures after they reach maturity, which is the product of linear loss of functional efficiency with time, leads to the law of exponential mortality rate by Gompertz. The average solar power volumetric density of frequency ν dissipated by circular molecules of radius , which reside on the inner surface of some lipid vesicles that float in the Archean oceans and that contain water and other chemical components are obtained. Such expression resembles the Stefan–Boltzmann law which describes the power radiated from a black body in terms of its temperature. Also, an expression for the volumetric density of the average entropy production rate by molecules of radius is obtained. Finally, the coupling processes that occur between the matter and heat fluxes between the interior and the exterior of lentil-shaped lipid vesicles pumped by the solar radiation action are analyzed qualitatively as well as their possible consequences in relation to the prebiotic chemical evolution of dissipative systems that can give rise to life.

Irreversibility and entropy production of a thermally driven micromachine

We discuss the non-equilibrium properties of a thermally driven micromachine consisting of three spheres which are in equilibrium with independent heat baths characterized by different temperatures. Within the framework of a linear stochastic Langevin description, we calculate the time-dependent average irreversibility that takes a maximum value for a finite time. This time scale is roughly set by the spring relaxation time. The steady-state average entropy production rate is obtained in terms of the temperatures and the friction coefficients of the spheres. The average entropy production rate depends on thermal and/or mechanical asymmetry of a three-sphere micromachine. We also obtain the center of mass diffusion coefficient of a thermally driven three-sphere micromachine as a function of different temperatures and friction coefficients. With the results of the total entropy production rate and the diffusion coefficient, we finally discuss the efficiency of a thermally driven micromachine.

Stationary Markov jump processes in terms of average transition times: setup and some inequalities of kinetic and thermodynamic kind

The parametrization of continuous-time stationary Markov jump processes is worked out in terms of average times at which the site-to-site transitions take place again (recurrence) or occur starting from a given initial localization of the system (occurrence). The foremost result is the solution of the inverse problem of achieving the rate constants from an essential set of average occurrence/recurrence times. Then we provide the expression of the average entropy production rate at the stationary state in terms of average recurrence times only, elaborate the randomness parameter (squared coefficient of variation) which quantifies the relative precision of the timing of a given transition of interest, and derive some inequalities in which only a partial amount information about the network does enter. In particular, we get lower bounds on the randomness parameter and derive inequalities of both kinetic and thermodynamic kind.

Entropy in Cell Biology: Information Thermodynamics of a Binary Code and Szilard Engine Chain Model of Signal Transduction.

A model of signal transduction from the perspective of informational thermodynamics has been reported in recent studies, and several important achievements have been obtained. The first achievement is that signal transduction can be modelled as a binary code system, in which two forms of signalling molecules are utilised in individual steps. The second is that the average entropy production rate is consistent during the signal transduction cascade when the signal event number is maximised in the model. The third is that a Szilard engine can be a single-step model in the signal transduction. This article reviews these achievements and further introduces a new chain of Szilard engines as a biological reaction cascade (BRC) model. In conclusion, the presented model provides a way of computing the channel capacity of a BRC.

The Conservation of Average Entropy Production Rate in a Model of Signal Transduction: Information Thermodynamics Based on the Fluctuation Theorem.

Cell signal transduction is a non-equilibrium process characterized by the reaction cascade. This study aims to quantify and compare signal transduction cascades using a model of signal transduction. The signal duration was found to be linked to step-by-step transition probability, which was determined using information theory. By applying the fluctuation theorem for reversible signal steps, the transition probability was described using the average entropy production rate. Specifically, when the signal event number during the cascade was maximized, the average entropy production rate was found to be conserved during the entire cascade. This approach provides a quantitative means of analyzing signal transduction and identifies an effective cascade for a signaling network.

Excess Entropy Production in Quantum System: Quantum Master Equation Approach

For open systems described by the quantum master equation (QME), we investigate the excess entropy production under quasistatic operations between nonequilibrium steady states. The average entropy production is composed of the time integral of the instantaneous steady entropy production rate and the excess entropy production. We propose to define average entropy production rate using the average energy and particle currents, which are calculated by using the full counting statistics with QME. The excess entropy production is given by a line integral in the control parameter space and its integrand is called the Berry-Sinitsyn-Nemenman (BSN) vector. In the weakly nonequilibrium regime, we show that BSN vector is described by $\ln \breve{\rho}_0$ and $\rho_0$ where $\rho_0$ is the instantaneous steady state of the QME and $\breve{\rho}_0$ is that of the QME which is given by reversing the sign of the Lamb shift term. If the system Hamiltonian is non-degenerate or the Lamb shift term is negligible, the excess entropy production approximately reduces to the difference between the von Neumann entropies of the system. Additionally, we point out that the expression of the entropy production obtained in the classical Markov jump process is different from our result and show that these are approximately equivalent only in the weakly nonequilibrium regime.

Stochastic thermodynamics of a tagged particle within a harmonic chain.

We study the stochastic thermodynamics of an overdamped harmonic chain, which can be viewed equivalently as a one-dimensional Rouse chain or as an approximate model of single file diffusion. We discuss mainly two levels of description of this system: the Markovian level for which the trajectories of all the particles of the chain are known and the non-Markovian level in which only the motion of a tagged particle is available. For each case, we analyze the energy dissipation and its dependence on initial conditions. Surprisingly, we find that the average coarse-grained entropy production rate can become transiently negative when an oscillating force is applied to the tagged particle. This occurs due to memory effects as shown in a framework based on path integrals or on a generalized Langevin equation.

Current fluctuations in a particle-nonconserving reaction-diffusion process

We have considered a one-dimensional coagulation-decoagulation system of classical particles on a finite lattice with reflecting boundaries. It is known that the system undergoes a phase transition from a high-density to a low-density phase. Using a matrix product approach we have obtained an exact expression for the average entropy production rate of the system in the thermodynamic limit. We have also performed a large-deviation analysis for fluctuations of entropy production rate and particle current. It turns out that the characteristics of the kink in the large deviation function can be used to spot the phase transition point. We have found that for very weak driving field (when the system approaches its equilibrium) and also for very strong driving field (when the system is in the low-density phase) the large deviation function for fluctuations of entropy production rate is almost parabolic, while in the high-density phase it prominently deviates from Gaussian behavior. The validity of the Gallavotti-Cohen fluctuation relation for the large deviation function for particle current is also verified.

Finite time thermodynamic optimization for heat-driven binary separation processes

The performance of heat-driven binary separation processes with linear phenomenological heat transfer law (q ∞ Δ(T −1) is optimized by using finite time thermodynamics. Two performance indexes, the dimensionless minimum average entropy production rate and dimensionless minimum average heat consumption of the heat-driven binary separation processes, are taken as optimization objectives, respectively. The separation processes are viewed as heat engines which work between high- and low-temperature reservoirs and produce enthalpy and energy flows out of the system. The temperatures of the heat reservoirs are assumed to be time- and space-variables. The convex optimization problem is solved using numerical method, and the average optimal control problem is solved using Lagrangian function. The major influence factors on the performance of the separation process, such as the properties of different materials and various separation requirements for the separation process, are represented by dimensionless entropy production rate coefficient and dimensionless enthalpy flow rate coefficient. The dimensionless minimum average entropy production rate and dimensionless minimum average heat consumption of the heat-driven binary separation processes are obtained, respectively.

The minimum heat consumption for heat-driven binary separation processes with linear phenomenological heat transfer law

The optimal performance of heat-driven binary separation processes with linear phenomenological heat transfer law (q∝Δ(T −1)) is analyzed by taking the processes as heat engines which work between high- and low-temperature reservoirs and produce enthalpy and energy flows out of the system, and the temperatures of the heat reservoirs are assumed to be time- and space-variables. A numerical method is employed to solve convex optimization problem and Lagrangian function is employed to solve the average optimal control problem. The dimensionless entropy production rate coefficient and dimensionless enthalpy flow rate coefficient are adopted to indicate the major influence factors on the performance of the separation process, such as the properties of different materials and various separation requirements for the separation process. The dimensionless minimum average entropy production rate and dimensionless minimum average heat consumption of the heat-driven binary separation processes are obtained. The obtained results are compared with those obtained with the Newtonian heat transfer law (q∝Δ(T)).

Entropy Production in Oscillating Chemical Systems

Abstract The entropy production in oscillating homogenous chemical systems is investigated by analyzing the difference between the average entropy production rate in a stable periodic oscillatory mode and in the corresponding unstable stationary state. A general analytical expression for this difference in the neighborhood of a Hopf bifurcation is derived. The entropy production in two typical models of chemical systems with unstable stationary states and stable periodic oscillations is investigated, using fixed concentrations as control parameters. The models exemplify both positive and negative entropy production rate differences. One of the investigated models has four free concentrations, the other three. The rate expressions are given by second order mass action kinetics with reverse reactions taken into account. The flows of reactants and products are controlled so that only the free concentrations vary, and the entropy of mixing associated with these flows is discussed.