Entropy Production Rate Research Articles

Exact Time-Dependent Thermodynamic Relationships for a Brownian Particle Navigating Complex Networks

The thermodynamic characteristics of systems driven out of equilibrium are examined for M Brownian ratchets organized in a complex network. The precise time-dependent solution reveals that the entropy S, entropy production ep(t), and entropy extraction hd(t) of the system in complex networks increase with system size, which is plausible as these thermodynamic quantities display extensive properties. In other words, as the number of lattice sites increases, the entropy S, entropy production ep(t), and entropy extraction hd(t) increase, demonstrating that these complex networks cannot be reduced to the corresponding one-dimensional lattice. Conversely, the rates for thermodynamic quantities such as velocity V, entropy production rate e˙p(t), and entropy extraction rate h˙ d(t) become independent of the network size in the long-term limit. The exact analytic results also indicate that the free energy decreases with system size. The model system is further analyzed by incorporating heat transfer via kinetic energy. Since heat exchange via kinetic energy does affect the energy extraction rate, the heat dumped to the cold reservoirs also contributes to internal entropy production. Consequently, such systems exhibit a higher degree of irreversibility. The thermodynamic features of a system operating between hot and cold baths are also compared and contrasted with a system functioning in a heat bath where temperature varies linearly along the reaction coordinate. Regardless of the network arrangements, the entropy, entropy production, and extraction rates are significantly larger for the linearly varying temperature case than for a system operating between hot and cold baths.

Analysis of flow and energy dissipation in pump turbine with small guide vane opening

In this study, a detailed flow state analysis of a reversible pump turbine (RPT) under small guide vane opening conditions was conducted using both numerical simulation and experimental methods on three analysis planes at 0.5 span. The entropy production rate (EPR) in entropy production theory was utilized to visualize the location and magnitude of energy losses in the flow process. The focus was placed on the coherent vortex structures in the volute, stay vane, guide vane, and runner flow path. The results demonstrate that, throughout the runner’s cycle, the leading edge of the guide vane experiences low-pressure regions with uneven pressure distribution within the runner channel. Velocity streamlines reveal flow separation and vortex generation at the typical guide vane trailing edge, with a maximum velocity reaching 49.7. Analysis of radial force and torque on typical guide vanes and the runner indicates that radial force and torque on the guide vanes do not significantly change, with the radial force coefficient CF r−x varying between 0.254 and 1.3. Major energy losses are concentrated behind the trailing edge of the guide vane, primarily in the form of jet wake. Coherent vortex structures are observed in the volute, stay vane, guide vane, and runner flow path, with slight turbulent wake at the trailing edge of the stay vane, clear shedding vortex streets, and vortex build-up in the bladeless area between the guide vane and the runner.

Spectral bounds on the entropy flow rate and Lyapunov exponents in differentiable dynamical systems

Abstract Some microscopic dynamics are also macroscopically irreversible, dissipating energy and producing entropy. For many-particle systems interacting with deterministic thermostats, the rate of thermodynamic entropy dissipated to the environment is the average rate at which phase space contracts. Here, we use this identity and the properties of a classical density matrix to derive upper and lower bounds on the entropy flow rate with the spectral properties of the local stability matrix. These bounds are an extension of more fundamental bounds on the Lyapunov exponents and phase space contraction rate of continuous-time dynamical systems. They are maximal and minimal rates of entropy production, heat transfer, and transport coefficients set by the underlying dynamics of the system and deterministic thermostat. Because these limits on the macroscopic dissipation derive from the density matrix and the local stability matrix, they are numerically computable from the molecular dynamics. As an illustration, we show that these bounds are on the electrical conductivity for a system of charged particles subject to an electric field.

Investigation of the transient characteristics of the Francis turbine during runaway process

Transient hydraulic phenomena, including flow separation, vortex structure and high amplitude pressure fluctuation, occur in the turbine during runaway process, significantly affecting the safe and stable operation. To clarify the unsteady flow characteristics in the runaway process, this paper focus on a low head model Francis turbine, examining the transient flow dynamics from rated speed to runaway speed. Numerical simulations show good agreement with experimental test results for the runaway speed and discharge. Results identify that two typical cavitation vortex structures within the runner: A cloud cavitation vortex near the hub on the pressure side and a columnar cavitation vortex on the suction side. Further analysis reveals that the pressure fluctuation induced by the former are low-frequency (0.08fn and harmonics), whereas those induced by the latter are high-frequency (1.16fn and harmonics). Entropy production analysis in homogeneous flow indicates that energy dissipation mainly occurs in the runner and draft tube during the runaway process. Turbulent entropy production within the turbine comprises a significant portion of the total entropy production. Additionally, areas around the recirculation zone exhibit considerable high entropy production, indicating that the energy of the fluid is dissipated by cavitation vortex structures generated in these areas. Additionally, the analysis indicates that the entropy production rate correlates with vapor generation, underscoring the cavitation vortex as the primary cause of energy dissipation. This investigation can provide valuable insights into the energy dissipation mechanisms during the runaway process.

Influence of staggered vane shunt plate on performance characteristics of reactor coolant pump

In order to explore the influence of the axial position of the shunt plate of staggered guide vane on reactor coolant pump(RCP), a mixed-flow RCP was taken as the model for numerical simulation. Based on the entropy production theory, the energy loss in the flow component under different flow conditions was analyzed, and the vortex core distribution in volute and the pressure pulsation at the hydrodynamic interface were studied. The results show the staggered guide vane reduces the head and efficiency slightly, the optimal scheme decreases by 0.9% and 0.6%. Placement of the shunt plate significantly influences entropy production within the guide vane and volute, especially when positioned near the front and back plates. When shunt plate is set centrally, the energy loss due to staggered guide vane is relatively smaller and closer to the original structure. The entropy production rate of guide vane inlet and shunt plate leading edge is higher, but with the increase of flow rate, the shunt plate leading edge is no longer the main location of energy dissipation. Middle placement of staggered guide vanes effectively reduces the outflow vortex band by Omega vortex analysis, and the amplitude of pressure pulsation at the interface decreases obviously.

Generalized Itô’s lemma and the stochastic thermodynamics of diffusion with resetting

Abstract Methods from the theory of stochastic processes are increasingly being used to extend classical thermodynamics to mesoscopic non-equilibrium systems. One characteristic feature of these systems is that averaging the stochastic entropy with respect to an ensemble of stochastic trajectories leads to a second law of thermodynamics that quantifies the degree of departure from thermodynamic equilibrium. A well known mechanism for maintaining a diffusing particle out of thermodynamic equilibrium is stochastic resetting. In its simplest form, the position of the particle instantaneously resets to a fixed position x 0 at a sequence of times generated from a Poisson process of constant rate r. Within the context of stochastic thermodynamics, instantaneous resetting to a single point is a unidirectional process that has no time-reversed equivalent. Hence, the average rate of entropy production calculated using the Gibbs–Shannon entropy cannot be related to the degree of time-reversal symmetry breaking. The problem of unidirectionality can be avoided by considering resetting to a random position or diffusion in an intermittent confining potential. In this paper we show how stochastic entropy production along sample paths of diffusion processes with resetting can be analyzed in terms of extensions of Itô’s formula for stochastic differential equations (SDEs) that include both continuous and discrete processes. First, we use the stochastic calculus of jump-diffusion processes to calculate the rate of stochastic entropy production for instantaneous resetting, and show how previous results are recovered upon averaging over sample trajectories. Second, we formulate single-particle diffusion in a switching potential as a hybrid SDE and develop a hybrid extension of Itô’s stochastic calculus to derive a general expression for the rate of stochastic entropy production. We illustrate the theory by considering overdamped Brownian motion in an intermittent harmonic potential. Finally, we calculate the average rate of entropy production for a population of non-interacting Brownian particles moving in a common switching potential. In particular, we show that the latter induces statistical correlations between the particles, which means that the total entropy is not given by the sum of the 1-particle entropies.

Minimum-dissipation principle for synchronized stochastic oscillators far from equilibrium

We prove a linear stability-dissipation relation (SDR) for q-state Potts models driven far from equilibrium by a nonconservative force. At a critical coupling strength, these models exhibit a synchronization transition from a decoherent into a synchronized state. In the vicinity of this transition, the SDR connects the entropy production rate per oscillator to the phase-space contraction rate, a measure of stability, in a simple way. For large but finite systems, we argue that the SDR implies a minimum-dissipation principle for driven Potts models as the dynamics selects stable nonequilibrium states with least dissipation. This principle holds arbitrarily far from equilibrium, for any stochastic dynamics, and for all q. Published by the American Physical Society 2024

Energy Aware Technology Mapping of Genetic Logic Circuits.

Energy and its dissipation are fundamental to all living systems, including cells. Insufficient abundance of energy carriers─as caused by the additional burden of artificial genetic circuits─shifts a cell's priority to survival, also impairing the functionality of the genetic circuit. Moreover, recent works have shown the importance of energy expenditure in information transmission. Despite living organisms being non-equilibrium systems, non-equilibrium models capable of accounting for energy dissipation and non-equilibrium response curves are not yet employed in genetic design automation (GDA) software. To this end, we introduce Energy Aware Technology Mapping, the automated design of genetic logic circuits with respect to energy efficiency and functionality. The basis for this is an energy aware non-equilibrium steady state model of gene expression, capturing characteristics like energy dissipation─which we link to the entropy production rate─and transcriptional bursting, relevant to eukaryotes as well as prokaryotes. Our evaluation shows that a genetic logic circuit's functional performance and energy efficiency are disjoint optimization goals. For our benchmark, energy efficiency improves by 37.2% on average when comparing to functionally optimized variants. We discover a linear increase in energy expenditure and overall protein expression with the circuit size, where Energy Aware Technology Mapping allows for designing genetic logic circuits with the energetic costs of circuits that are one to two gates smaller. Structural variants improve this further, while results show the Pareto dominance among structures of a single Boolean function. By incorporating energy demand into the design, Energy Aware Technology Mapping enables energy efficiency by design. This extends current GDA tools and complements approaches coping with burden in vivo.

Power dissipation and entropy production rate of high-dimensional optical matter systems

Power dissipation and entropy production rate of high-dimensional optical matter systems

Decomposing Thermodynamic Dissipation of Linear Langevin Systems via Oscillatory Modes and Its Application to Neural Dynamics

Recent developments in stochastic thermodynamics have elucidated various relations between the entropy production rate (thermodynamic dissipation) and the physical limits of information processing in nonequilibrium dynamical systems. These findings have been actively utilized and have opened new perspectives in the analysis of real biological systems. In neuroscience also, the importance of quantifying entropy production has attracted increasing attention as a means to understand the properties of information processing in the brain. However, the relationship between entropy production rate and oscillations, which is prevalent in many biological systems, is unclear. For example, neural oscillations, such as delta, theta, and alpha waves, play crucial roles in brain information processing. Here, we derive a novel decomposition of the entropy production rate of linear Langevin systems. We show that one of the components of the entropy production rate, called the housekeeping entropy production rate, can be decomposed into independent positive contributions from oscillatory modes. Our decomposition enables us to calculate the contribution of oscillatory modes to the housekeeping entropy production rate. In addition, when the noise matrix of the Langevin equation is diagonal, the contribution of each oscillatory mode is further decomposed into the contribution of each element of the system. To demonstrate the utility of our decomposition, we apply our decomposition to an electrocorticography dataset recorded during awake and anesthetized conditions in monkeys, wherein the properties of oscillations change drastically. We show the consistent trends across different monkeys; i.e., the contribution of oscillatory modes from the delta band are larger in the anesthetized condition than in the awake condition, while those from the higher-frequency bands, such as the theta band, are smaller. These results allow us to interpret the change in neural oscillation in terms of stochastic thermodynamics and the physical limit of information processing. Published by the American Physical Society 2024

Loss characteristics and optimization method of a compressed air energy storage radial turbine with nozzle governing

During the operation of the compressed air energy storage (CAES) system, a discrepancy exists between the air storage pressure and the turbine inlet pressure. At the same time, to ensure that the turbine operates efficiently when the system load varies, the turbine needs to be regulated reasonably. In this paper, the influence of three nozzle governing (NG) parameters on turbine performance during the NG process is investigated: the inlet pressure of the NG region, the area of the NG region, and the base pressure. The flow characteristics and loss mechanisms under partial admission conditions and NG conditions are also analyzed. Furthermore, the NG process is optimized by using a transition section. The results show that the loss under the NG condition with low inlet pressure at the NG region is similar to the partial admission loss, both of which are mainly affected by the area of the NG region. In both working conditions, vortex structures appear at the stator outlet of the NG region. At the same time, the mixing of different airflows and the flow separation phenomenon within the rotor leads to a significant increase in entropy production rate. The transition section can attenuate the leakage and reduce the entropy production rate in the radial gap between the stator and rotor, increasing turbine efficiency by up to 1.1 % at maximum when using the transition section.

Numerical analysis of flow and heat transfer characteristics in Taylor-Couette-Poiseuille flow utilizing Large Eddy Simulation method

The flow and heat transfer characteristics within the Taylor-Couette-Poiseuille configuration induced by supercritical carbon dioxide flowing through the gap between the turbine shaft and the stationary casing were studied using Large Eddy Simulation. Wavelet analysis was used to calculate pressure fluctuations across various frequencies. Computational assessments were carried out to evaluate changes in the field synergy angle and inertial perturbations within the annular gap. A new theory was introduced to seamlessly integrate temperature, pressure, and velocity fields. Additionally, entropy generation in the Taylor-Couette-Poiseuille flow regime was thoroughly examined. The study revealed the emergence of vortices at the rotating wall, indicating a dynamic process in which large-scale vortices dissolve and more minor ones form. As frequency increases, pressure fluctuations grow. Increasing the mass flow rate can reduce the twisting vortex at the rotating wall and delay the onset of temperature fluctuations. Additionally, increasing the mass flow rate enhances the cooling effect on the rotating shaft. In the radial direction, as r increases, the field synergy angle and the inertial disturbance both show a trend of first decreasing and then increasing. The heat transfer performance is best when r = 0.6 and decreases significantly when r = 0.95. The synergy between the temperature gradient field, pressure gradient field, and velocity field shows a trend opposite to the field synergy angle and the inertial disturbance. As one moves from the rotating wall toward the stationary wall, temperature and velocity entropy production rates decrease, with noticeable fluctuations near the rotating wall.

Energy Aware Technology Mapping of Genetic Logic Circuits.

Energy and its dissipation are fundamental to all living systems, including cells. Insufficient abundance of energy carriers -as caused by the additional burden of artificial genetic circuits- shifts a cell's priority to survival, also impairing the functionality of the genetic circuit. Moreover, recent works have shown the importance of energy expenditure in information transmission. Despite living organisms being non-equilibrium systems, non-equilibrium models capable of accounting for energy dissipation and non-equilibrium response curves are not yet employed in genetic design automation (GDA) software. To this end, we introduce Energy Aware Technology Mapping, the automated design of genetic logic circuits with respect to energy efficiency and functionality. The basis for this is an energy aware non-equilibrium steady state (NESS) model of gene expression, capturing characteristics like energy dissipation -which we link to the entropy production rate- and transcriptional bursting, relevant to eukaryotes as well as prokaryotes. Our evaluation shows that a genetic logic circuit's functional performance and energy efficiency are disjoint optimization goals. For our benchmark, energy efficiency improves by 37.2% on average when comparing to functionally optimized variants. We discover a linear increase in energy expenditure and overall protein expression with the circuit size, where Energy Aware Technology Mapping allows for designing genetic logic circuits with the energy efficiency of circuits that are one to two gates smaller. Structural variants improve this further, while results show the Pareto dominance among structures of a single Boolean function. By incorporating energy demand into the design, Energy Aware Technology Mapping enables energy efficiency by design. This extends current GDA tools and complements approaches coping with burden in vivo.

Classical and quantum thermodynamics in a non-equilibrium regime: Application to thermostatic Stirling engine

We have developed a thermodynamic theory in the non-equilibrium regime, which we describe as a thermodynamic system–bath model [Koyanagi and Tanimura, J. Chem. Phys. 160, 234112 (2024)]. Based on the dimensionless (DL) minimum work principle, non-equilibrium thermodynamic potentials are expressed in terms of non-equilibrium extensive and intensive variables in time derivative form. This is made possible by incorporating the entropy production rate into the definition of non-equilibrium thermodynamic potentials. These potentials can be evaluated from the DL non-equilibrium-to-equilibrium minimum work principle, which is derived from the principle of DL minimum work and is equivalent to the second law of thermodynamics. We thus obtain the non-equilibrium Massieu–Planck potentials as entropic potentials and the non-equilibrium Helmholtz–Gibbs potentials as free energies. Unlike the fluctuation theorem and stochastic thermodynamics theory, this theory does not require the assumption of a factorized initial condition and is valid in the full quantum regime, where the system and bath are quantum mechanically entangled. Our results are numerically verified by simulating a thermostatic Stirling engine consisting of two isothermal processes and two thermostatic processes using the quantum hierarchical Fokker–Planck equations and the classical Kramers equation derived from the thermodynamic system–bath model. We then show that, from weak to strong system–bath interactions, the thermodynamic process can be analyzed using a non-equilibrium work diagram analogous to the equilibrium one for given time-dependent intensive variables. The results can be used to develop efficient heat machines in non-equilibrium regimes.

Noise-Induced Phase Separation and Time Reversal Symmetry Breaking in Active Field Theories Driven by Persistent Noise.

Within the Landau-Ginzburg picture of phase transitions, scalar field theories develop phase separation because of a spontaneous symmetry-breaking mechanism. This picture works in thermodynamics but also in the dynamics of phase separation. Here we show that scalar nonequilibrium field theories undergo phase separation just because of nonequilibrium fluctuations driven by a persistent noise. The mechanism is similar to what happens in motility-induced phase separation where persistent motion introduces an effective attractive force. We observe that noise-induced phase separation occurs in a region of the phase diagram where disordered field configurations would otherwise be stable at equilibrium. Measuring the local entropy production rate to quantify the time-reversal symmetry breaking, we find that such breaking is concentrated on the boundary between the two phases.

Entropy production of the contact model

Abstract We propose an expression for the production of entropy for a system described by a stochastic dynamics which is appropriate for the case where the reverse transition rate vanishes but the forward transition is nonzero. The expression is positive definite and based on the inequality x ln ⁡ x − ( x − 1 ) ⩾ 0 . The corresponding entropy flux is linear in the probability distribution allowing its calculation as an average. The expression is applied to the one-dimensional contact process at the stationary state. We found that the rate of entropy production per site is finite with a singularity at the critical point with diverging slope.

TRNG Entropy Model in the Presence of Flicker FM Noise

Flicker Frequency Modulated (FM) noise, which influences free-running Ring Oscillators (ROs), can make a substantial contribution to the entropy generated by RO-based True Random Number Generators (TRNGs). While current TRNG stochastic models predominantly concentrate on white FM noise, the addition of flicker FM noise could remarkably enrich the analysis of the TRNG entropy production rate. This paper introduces an entropy model for TRNGs, employing Gaussian processes, to estimate entropy generation from both white FM and flicker FM noise. We analytically derive the flicker FM noise Auto-Correlation Function (ACF), enabling assessment of entropy contributions conditioned on partial knowledge of the TRNG’s internal state. Utilizing the developed model with commonly reported noise magnitudes found in literature, it is determined that flicker FM noise holds the potential to substantially enhance the TRNG’s entropy rate. However, due to considerable variation in reported magnitudes across limited available research on flicker FM noise, it cannot yet be universally accepted as a dependable source of TRNG entropy.

Investigation of irreversible losses in subsonic compressor cascade flow field: A study on viscous dissipation and temperature gradient term in entropy production rate

The entropy generation rate is a widely employed loss characterization approach in the design and optimization of fluid machinery. This approach is utilized to quantitatively determine various types of losses in the flow field, and it is considered that the temperature gradient term in the entropy generation rate can characterize irreversible losses. This research paper aims to address the question of whether the temperature gradient term in entropy production rate can represent the irreversible losses in a flow field. By employing the Reynolds-Averaged Navier-Stokes (RANS) numerical simulation method, the flow field of a subsonic compressor cascade, both with and without wall heating, was investigated. Statistical analysis was conducted to examine the contributions of viscous dissipation, the temperature gradient term in entropy production rate, wall shear stress work, and global power loss. The study reveals the distribution differences of viscous dissipation and the temperature gradient term in entropy production rate within the separated flow region. The research results demonstrate that, under wall heating conditions, viscous dissipation increased by approximately 45%, and the ratio of the temperature gradient term to global power loss increased from 4% to 125%, exceeding the mechanical energy loss in the flow field. The distribution of the temperature gradient term within the separated flow region cannot be explained by irreversible losses, and it exhibits significant discrepancies with the distribution of viscous dissipation losses. Therefore, the temperature gradient term in entropy production rate cannot represent the local irreversible losses, whereas viscous dissipation serves as an accurate measure of local irreversible losses. The research results provide theoretical support for accurately determining the irreversible losses in the flow field.

Efficiency bounds for bipartite information-thermodynamic systems.

In this paper, we introduce an approach to derive a lower bound for the entropy production rate of a subsystem by utilizing the Cauchy-Schwarz inequality. It extends to establishing comprehensive upper and lower bounds for the efficiency of two subsystems. These bounds are applicable to a wide range of Markovian stochastic processes, which enhances the accuracy in depicting the range of energy conversion efficiency between subsystems. Empirical validation is conducted using a two-quantum-dot system model, which serves to confirm the effectiveness of our inequality in refining the boundaries of efficiency.

Broken detailed balance and entropy production in directed networks.

The structure of a complex network plays a crucial role in determining its dynamical properties. In this paper, we show that the the degree to which a network is directed and hierarchically organized is closely associated with the degree to which its dynamics break detailed balance and produce entropy. We consider a range of dynamical processes and show how different directed network features affect their entropy production rate. We begin with an analytical treatment of a two-node network followed by numerical simulations of synthetic networks using the preferential attachment and Erdös-Renyi algorithms. Next, we analyze a collection of 97 empirical networks to determine the effect of complex real-world topologies. Finally, we present a simple method for inferring broken detailed balance and directed network structure from multivariate timeseries and apply our method to identify non-equilibrium dynamics and hierarchical organisation in both human neuroimaging and financial timeseries. Overall, our results shed light on the consequences of directed network structure on non-equilibrium dynamics and highlight the importance and ubiquity of hierarchical organisation and non-equilibrium dynamics in real-world systems.