Irreversible Entropy Production Research Articles

Quantum thermodynamics of boundary time-crystals

Time-translation symmetry breaking is a mechanism for the emergence of non-stationary many-body phases, so-called time-crystals, in Markovian open quantum systems. Dynamical aspects of time-crystals have been extensively explored over the recent years. However, much less is known about their thermodynamic properties, also due to the intrinsic nonequilibrium nature of these phases. Here, we consider the paradigmatic boundary time-crystal system, in a finite-temperature environment, and demonstrate the persistence of the time-crystalline phase at any temperature. Furthermore, we analyze thermodynamic aspects of the model investigating, in particular, heat currents, power exchange and irreversible entropy production. Our work sheds light on the thermodynamic cost of sustaining nonequilibrium time-crystalline phases and provides a framework for characterizing time-crystals as possible resources for, e.g. quantum sensing. Our results may be verified in experiments, for example with trapped ions or superconducting circuits, since we connect thermodynamic quantities with mean value and covariance of collective (magnetization) operators.

Temperature fluctuations in mesoscopic systems.

Temperature is a fundamental concept in thermodynamics. In macroscopic thermodynamics, systems possess their own intrinsic temperature which equals the reservoir temperature when they equilibrate. In stochastic thermodynamics for simple systems at the microscopic level, thermodynamic quantities other than temperature (a deterministic parameter of the reservoir) are stochastic. To bridge the disparity in the perspectives about temperature between the micro- and macroregimes, we assign a generic mesoscopic N-body system an intrinsic fluctuating temperature T in this work. We simplify the complicated dynamics of numerous particles to one stochastic differential equationwith respect to T, where the noise term accounts for finite-size effects arising from random energy transfer between the system and the reservoir. Our analysis reveals that these fluctuations make the extensive quantities (in the thermodynamic limit) deviate from being extensive. Moreover, we derive finite-size corrections, characterized by heat capacity of the system, to the Jarzynski equality. A possible violation of the principle of maximum work that scales with N^{-1} is also discussed. Additionally, we examine the impact of temperature fluctuations in a finite-size Carnot engine. We show that irreversible entropy production resulting from the temperature fluctuations of the working substance diminishes the average efficiency of the cycle as η_{C}-〈η〉∼N^{-1}, highlighting the unattainability of the Carnot efficiency η_{C} for mesoscopic heat engines even under the quasistatic limit. Our general framework paves the way for further exploration of nonequilibrium thermodynamics and the corresponding finite-size effects in a mesoscopic regime.

Investigating the Relationship between Sea Surface Temperature and the Mechanical Efficiency of Tropical Cyclones

Abstract Previous studies have investigated how sea surface temperature (SST) affects the potential intensity of tropical cyclones (TCs). However, this is an upper bound only on the maximum near-surface azimuthal winds and does not fully account for the effects of atmospheric moisture. Potential intensity might not vary in the same way as the total kinetic energy (WKE) of a TC would with changing SST. The term WKE is related, via the conceptualization of the TC as a heat engine, to TC mechanical efficiency. We investigate how TC mechanical efficiency varies with SST in a series of moist, axisymmetric, radiative–convective numerical experiments with constant SSTs ranging from 295 to 307.5 K. We find a −2.1% K−1 decrease in the mechanical efficiency with SST. While the increase in the net heat energy gained by the TC heat engine acts to increase WKE, the mechanical efficiency still decreases with SST due to the effects of moisture on WKE and on the total heat input to the TC. Moist convection in an unsaturated atmosphere is associated with substantial irreversible entropy production, which detracts from the energy that the TC can use to power its winds. The increasing moisture content in a warmer atmosphere predicted by Clausius–Clapeyron scaling leads this irreversibility to increase in an unsaturated atmosphere, presenting a larger penalty on WKE and decreasing the mechanical efficiency. Our results highlight the importance of giving full consideration to the effects of moisture on the TC heat engine in studies of how climate affects TCs. Significance Statement The purpose of this study is to investigate how the “mechanical efficiency” of tropical cyclones varies with sea surface temperature. This matters because the conceptualization of the tropical cyclone as a heat engine implies that the kinetic energy of its wind field is generated at this efficiency. The mechanical efficiency may be affected by changes in climate. Our results demonstrate that the mechanical efficiency decreases at −2.1% K−1 with sea surface temperature, and in particular highlight the important role of moisture in this result.

Characteristics of cavitating flows in cryogenic pump units in a combined cycle power system based on liquefied natural gas and solar energy

The cavitation of cryogenic pump units is an important cause for the low cold energy recovery efficiency and low utilization efficiency of solar energy in combined cycle power systems based on liquefied natural gas (LNG) and solar energy. Through numerical simulation of cavitation in cryogenic pump units, the research established the correlation mechanism between cavitation evolution and energy characteristics. By using the transport-based cavitation model considering the thermomechanical effect of cryogenic media, a novel numerical simulation model for two-phase flows during cryogenic cavitation was developed. In addition, the numerical model of cavitation was verified to be reliable. The cavitation performance of the two-stage LNG submerged pump in cryogenic pump units was studied under multiple conditions. In addition, the evolution of cavitating flow regimes under conditions of different flow rates and its influences on flow patterns of various flow passage components were investigated by combining analysis on temperature changes and flow fields. The entropy production diagnostic model (EPDM) was also adopted to discuss the distribution of the irreversible entropy production rate (EPR) in the evolution process of cavitation. Results show that the interfacial EPR that characterizes the phase-transition intensity after inception of cavitation exerts significant influences. Analysis of influencing mechanisms of changes in temperature, changes in flow fields, and distribution characteristics of energy consumption can provide a theoretical basis for further optimization.

Modeling Kelvin Helmholtz Instability Tube and Knot Dynamics and Their Impact on Mixing in the Lower Thermosphere

AbstractWe present modeling results of tube and knot (T&K) dynamics accompanying thermospheric Kelvin Helmholtz Instabilities (KHI) in an event captured by the 2018 Super Soaker campaign (R. L. Mesquita et al., 2020, https://doi.org/10.1029/2020JA027972). Chemical tracers released by a rocketsonde on 26 January 2018 showed coherent KHI in the lower thermosphere that rapidly deteriorated within 45–90 s. Using wind and temperature data from the event, we conducted high resolution direct numerical simulations (DNS) employing both wide and narrow spanwise domains to facilitate (wide domain case) and prohibit (narrow domain case) the axial deformation of KH billows that allows tubes and knots to form. KHI T&K dynamics are shown to produce accelerated instability evolution consistent with the observations, achieving peak dissipation rates nearly two times larger and 1.8 buoyancy periods faster than axially uniform KHI generated by the same initial conditions. Rapidly evolving twist waves are revealed to drive the transition to turbulence; their evolution precludes the formation of secondary convective instabilities and secondary KHI seen to dominate the turbulence evolution in artificially constrained laboratory and simulation environments. T&K dynamics extract more kinetic energy from the background environment and yield greater irreversible energy exchange and entropy production, yet they do so with weaker mixing efficiency due to greater energy dissipation. The results suggest that enhanced mixing from thermospheric KHI T&K events could account for the discrepancy between modeled and observed mixing in the lower thermosphere (Garcia et al., 2014, https://doi.org/10.1002/2013JD021208; Liu, 2021, https://doi.org/10.1029/2020GL091474) and merits further study.

Geometric Modeling for Control of Thermodynamic Systems

This paper discusses the way that energy and entropy can be regarded as storage functions with respect to supply rates corresponding to the power and thermal ports of the thermodynamic system. Then, this research demonstrates how the factorization of the irreversible entropy production leads to quasi-Hamiltonian formulations, and how this can be used for stability analysis. The Liouville geometry approach to contact geometry is summarized, and how this leads to the definition of port-thermodynamic systems is discussed. This notion is utilized for control by interconnection of thermodynamic systems.

Thermodynamic Unification of Optimal Transport: Thermodynamic Uncertainty Relation, Minimum Dissipation, and Thermodynamic Speed Limits

Thermodynamics serves as a universal means for studying physical systems from an energy perspective. In recent years, with the establishment of the field of stochastic and quantum thermodynamics, the ideas of thermodynamics have been generalized to small fluctuating systems. Independently developed in mathematics and statistics, the optimal transport theory concerns the means by which one can optimally transport a source distribution to a target distribution, deriving a useful metric between probability distributions, called the Wasserstein distance. Despite their seemingly unrelated nature, an intimate connection between these fields has been unveiled in the context of continuous-state Langevin dynamics, providing several important implications for nonequilibrium systems. In this study, we elucidate an analogous connection for discrete cases by developing a thermodynamic framework for discrete optimal transport. We first introduce a novel quantity called dynamical state mobility, which significantly improves the thermodynamic uncertainty relation and provides insights into the precision of currents in nonequilibrium Markov jump processes. We then derive variational formulas that connect the discrete Wasserstein distances to stochastic and quantum thermodynamics of discrete Markovian dynamics described by master equations. Specifically, we rigorously prove that the Wasserstein distance equals the minimum product of irreversible entropy production and dynamical state mobility over all admissible Markovian dynamics. These formulas not only unify the relationship between thermodynamics and the optimal transport theory for discrete and continuous cases, but also generalize it to the quantum case. In addition, we demonstrate that the obtained variational formulas lead to remarkable applications in stochastic and quantum thermodynamics, such as stringent thermodynamic speed limits and the finite-time Landauer principle. These bounds are tight and can be saturated for arbitrary temperatures, even in the zero-temperature limit. Notably, the finite-time Landauer principle can explain finite dissipation even at extremely low temperatures, which cannot be explained by the conventional Landauer principle.1 MoreReceived 26 July 2022Revised 1 December 2022Accepted 13 December 2022DOI:https://doi.org/10.1103/PhysRevX.13.011013Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasEntropy productionNonequilibrium & irreversible thermodynamicsNonequilibrium statistical mechanicsQuantum thermodynamicsStochastic processesStochastic thermodynamicsThermodynamics of computationTechniquesGraph theoryStatistical PhysicsInterdisciplinary PhysicsGeneral Physics

Numerical Calculation of the Irreversible Entropy Production of Additively Manufacturable Off-Set Strip Fin Heat-Transferring Structures

In this manuscript, off-set strip fin structures are presented which are adapted to the possibilities of additive manufacturing. For this purpose, the geometric parameters, including fin height, fin spacing, fin length, and fin longitudinal displacement, are varied, and the Colburn j-factor and the Fanning friction factor are numerically calculated in the Reynolds number range of 80-920. The structures are classified with respect to their entropy production number according to Bejan. This method is compared with the results from partial differential equations for the calculation of the irreversible entropy production rate due to shear stresses and heat conduction. This study reveals that the chosen temperature difference leads to deviation in terms of entropy production due to heat conduction, whereas the dissipation by shear stresses shows only small deviations of less than 2%. It is further shown that the variation in fin height and fin spacing has only a small influence on heat transfer and pressure drop, while a variation in fin length and fin longitudinal displacement shows a larger influence. With respect to the entropy production number, short and long fins, as well as large fin spacing and fin longitudinal displacement, are shown to be beneficial. A detailed examination of a single structure shows that the entropy production rate due to heat conduction is dominated by the entropy production rate in the wall, while the fluid has only a minor influence.

Geometrical Bounds on Irreversibility in Squeezed Thermal Bath

Irreversible entropy production (IEP) plays an important role in quantum thermodynamic processes. Here, we investigate the geometrical bounds of IEP in nonequilibrium thermodynamics by exemplifying a system coupled to a squeezed thermal bath subject to dissipation and dephasing, respectively. We find that the geometrical bounds of the IEP always shift in a contrary way under dissipation and dephasing, where the lower and upper bounds turning to be tighter occur in the situation of dephasing and dissipation, respectively. However, either under dissipation or under dephasing, we may reduce both the critical time of the IEP itself and the critical time of the bounds for reaching an equilibrium by harvesting the benefits of squeezing effects in which the values of the IEP, quantifying the degree of thermodynamic irreversibility, also become smaller. Therefore, due to the nonequilibrium nature of the squeezed thermal bath, the system-bath interaction energy has a prominent impact on the IEP, leading to tightness of its bounds. Our results are not contradictory with the second law of thermodynamics by involving squeezing of the bath as an available resource, which can improve the performance of quantum thermodynamic devices.

Probabilities for informational free lunches in stochastic thermodynamics

By considering an explicit nonequilibrium model, we analyze the statistics of the irreversible work, w irr, and the irreversible entropy production, Δ i s, within the stochastic energetics framework. Restating the second law of thermodynamics as a function of w irr, we introduce the explicit probability of violating the canonical form of that second law for a different set of parameters and initial conditions of the model. Moreover, we study the irreversible entropy production along the same lines, since it can be cast as a generalization of the irreversible work. From an informational perspective, our result allows one to quantify the probability of deleting information without performing work, contrarily to the Landauer’s principle, which we classify as an informational free lunch. We chose for the initial conditions cases of low information content (equilibrium) and high information content (delta distributed).

Entropy Production in Non-Markovian Collision Models: Information Backflow vs. System-Environment Correlations.

We investigate the irreversible entropy production of a qubit in contact with an environment modelled by a microscopic collision model in both Markovian and non-Markovian regimes. Our main goal is to contribute to the discussions on the relationship between non-Markovian dynamics and negative entropy production rates. We employ two different types of collision models that do or do not keep the correlations established between the system and the incoming environmental particle, while both of them pertain to their non-Markovian nature through information backflow from the environment to the system. We observe that as the former model, where the correlations between the system and environment are preserved, gives rise to negative entropy production rates in the transient dynamics, the latter one always maintains positive rates, even though the convergence to the steady-state value is slower as compared to the corresponding Markovian dynamics. Our results suggest that the mechanism underpinning the negative entropy production rates is not solely non-Markovianity through information backflow, but rather the contribution to it through established system-environment correlations.

Irreversible entropy production rate in a parametrically driven-dissipative system: The role of self-correlation between noncommuting observables

In this paper, we explore the emergence of the Wigner entropy production rate in the stationary state of a two-mode Gaussian system. The interacting modes dissipate into different local thermal baths. Also, one of the bosonic modes evolves into the squeezed-thermal state because of the parametric amplification process. Using the Heisenberg-Langevin approach, combined with quantum phase space formulation, we get an analytical expression for the steady-state Wigner entropy production rate. It contains two key terms. The first one is an Onsager-like expression that describes heat flow within the system. The second term resulted from vacuum fluctuations of the baths. Analyses show that self-correlation between the quadratures of the parametrically amplified mode pushes the mode towards the thermal squeezed state. It increases vacuum entropy production of the total system and reduces the heat current between the modes. The results imply that, unlike other previous proposals, squeezing can constrain the efficiency of actual non-equilibrium heat engines by irreversible flows.

Quantum Thermodynamics of Holographic Quenches and Bounds on the Growth of Entanglement from the Quantum Null Energy Condition

The quantum null energy condition (QNEC) is a lower bound on the energy-momentum tensor in terms of the variation of the entanglement entropy of a subregion along a null direction. To gain insights into quantum thermodynamics of many-body systems, we study if the QNEC restricts irreversible entropy production in quenches driven by energy-momentum inflow from an infinite memoryless bath in two-dimensional holographic theories. We find that an increase in both entropy and temperature, as implied by the Clausius inequality of classical thermodynamics, is necessary but not sufficient to not violate QNEC in quenches leading to transitions between thermal states with momentums that are dual to Banados-Teitelboim-Zanelli geometries. For an arbitrary initial state, we can determine the lower and upper bounds on the increase of entropy (temperature) for a fixed increase in temperature (entropy). Our results provide explicit instances of quantum lower and upper bounds on irreversible entropy production whose existence has been established in literature. We also find monotonic behavior of the nonsaturation of the QNEC with time after a quench, and analytically determine their asymptotic values. Our study shows that the entanglement entropy of an interval of length l always thermalizes in time l/2 with an exponent 3/2. Furthermore, we determine the coefficient of initial quadratic growth of entanglement analytically for any l, and show that the slope of the asymptotic ballistic growth of entanglement for a semi-infinite interval is twice the difference of the entropy densities of the final and initial states. We determine explicit upper and lower bounds on these rates of growth of entanglement.

Beating Carnot efficiency with periodically driven chiral conductors.

Classically, the power generated by an ideal thermal machine cannot be larger than the Carnot limit. This profound result is rooted in the second law of thermodynamics. A hot question is whether this bound is still valid for microengines operating far from equilibrium. Here, we demonstrate that a quantum chiral conductor driven by AC voltage can indeed work with efficiencies much larger than the Carnot bound. The system also extracts work from common temperature baths, violating Kelvin-Planck statement. Nonetheless, with the proper definition, entropy production is always positive and the second law is preserved. The crucial ingredients to obtain efficiencies beyond the Carnot limit are: i) irreversible entropy production by the photoassisted excitation processes due to the AC field and ii) absence of power injection thanks to chirality. Our results are relevant in view of recent developments that use small conductors to test the fundamental limits of thermodynamic engines.

Entropy-based formulation of thermodynamics in arbitrary quantum evolution

Given the evolution of an arbitrary open quantum system, we formulate a general and unambiguous method to separate the internal energy change of the system into an entropy-related contribution and a part causing no entropy change, identified as heat and work, respectively. We also demonstrate that heat and work admit geometric and dynamical descriptions by developing a universal dynamical equation for the given trajectory of the system. The dissipative and coherent parts of this equation contribute exclusively to heat and work, where the specific role of a work contribution from a counterdiabatic drive is underlined. Next we define an expression for the irreversible entropy production of the system which does not have explicit dependence on the properties of the ambient environment; rather, it depends on a set of the system's observables excluding its Hamiltonian and is independent of internal energy change. We illustrate our results with three examples.

Singlet Dioxygen ¹O₂, its Generation, Physico-Chemical Properties and its Possible Hormetic Behavior in Cancer Therapy

Singlet dioxygen 1O2 is one excited state among the three other possible spectroscopic states of molecular oxygen. Here, we first describe the use of published spectroscopic data and thermodynamic modeling based on irreversible entropy production. Such concepts are further applied to the synthesis of singlet dioxygen and its reactions with crucial biological molecules. In a last section, we suggest that singlet dioxygen and ozone may be responsible for the success of radiation therapy, that has been used to treat cancer successfully for over 120 years. Its precise mechanism of action remains controversial. We thus aim to clarify the role of singlet oxygen in radiotherapy and chemotherapy. A partial conversion of ionizing radiation in the body into thermal photons could be assumed. The antitumor effect may involve these thermal photons, such as the one delivered by red/infrared sources. Thermal photons (wavelengths of 635 nm and 1270 nm) convert triplet dioxygen into singlet dioxygen by changing the spin of its outer electrons. Despite its short half-life, Singlet dioxygen is responsible for the activation of multiple free radicals (such as hydrogen peroxide), which may target proteins and DNA, induce either apoptosis or oxidative phosphorylation. At moderate concentrations, thermodynamic data suggests that singlet dioxygen may readily react with water to form a potent pro-apoptotic molecule (ozone), thus decreasing cancer growth. However, at high concentration cytotoxic effects against all kind of cells occurs. This strongly suggests a non-linear hormetic behavior of singlet dioxygen. It is also proposed that cytotoxic chemotherapy induces the same free radicals that singlet dioxygen does. There are also other ways to enhance the production of singlet dioxygen, such as phototherapy using Methylene Blue for instance. As a source of reactive oxygen species (ROS), singlet oxygen could thus be a common agent active both in radiotherapy and chemotherapy. It is probable that the activity of radiation therapy and chemotherapy may be mediated by the conversion of triplet to singlet oxygen. This may explain the oxygen effect such as described in radiotherapy and chemotherapy.

Exergy Criteria of Performance of Waste Heat Recovery Applied for Marine Auxiliary Boiler

Auxiliary boilers onboard motor ships are the subject of ongoing research. Steam is produced by an auxiliary boiler for fuel heating and cargo oil pumping turbines. This marine boiler is a pressure jet burner water tube auxiliary boiler with a 70-80% efficiency rating. The goal of determining the process and components of irreversibility loss in a system is to identify the process and components of exergy losses. The second law of thermodynamics and the concept of irreversible entropy production are the foundations of this study's exergy technique of analysis. This concept of considering entropy at a given steady-state condition rather than as a change in a process is also one of the features of this exergy analysis of the marine oil-fired boiler. The exergy loss in the combustion chamber was calculated and determined to be 35024 kJ, which is the maximum irreversibility in this maritime auxiliary boiler. A numerical analysis of the current nozzle jet burner is undertaken to evaluate the enhancement of the combustion process. The temperature and velocity contour of the fuel stream passing through the nozzle of this auxiliary boiler's burner depicts atomization.

The Connection between Carnot and CAPE Formulations of TC Potential Intensity

Abstract Tropical cyclone (TC) potential intensity (PI) theory has a well-known form, consistent with a Carnot cycle interpretation of TC energetics, which relates PI to mean environmental conditions: the difference between surface and TC outflow temperatures and the air–sea enthalpy disequilibrium. PI has also been defined as a difference in convective available potential energy (CAPE) between two parcels, and quantitative assessments of future changes make use of a numerical algorithm based on this definition. Here, an analysis shows the conditions under which these Carnot and CAPE-based PI definitions are equivalent. There are multiple conditions, not previously enumerated, which in particular reveal a role for irreversible entropy production from surface evaporation. This mathematical analysis is verified by numerical calculations of PI’s sensitivity to large changes in surface-air relative humidity. To gain physical insight into the connection between the CAPE and Carnot formulations of PI, we use a recently developed analytic theory for CAPE to derive, starting from the CAPE-based definition, a new approximate formula for PI that nearly recovers the previous Carnot PI formula. The derivation shows that the difference in undilute buoyancies of saturated and environmental parcels that determines CAPE PI can in fact be expressed as a difference in the parcels’ surface moist static energy, providing a physical link between the Carnot and CAPE formulations of PI. This combination of analysis and physical interpretation builds confidence in previous numerical CAPE-based PI calculations that use climate model projections of the future tropical environment.

Fluctuation theorem for irreversible entropy production in electrical conduction.

Linear irreversible thermodynamics predicts that the entropy production rate can become negative. We demonstrate this prediction for metals under AC driving whose conductivity is well described by the Drude-Sommerfeld model. We then show that these negative rates are fully compatible with stochastic thermodynamics, namely, that the entropy production does fulfill a fluctuation theorem. The analysis is concluded with the observation that the stochastic entropy production as defined by the surprisal or ignorance of the Shannon information does not agree with the phenomenological approach.

Structural approach to the control of a reaction system using thermodynamics-based extent model

This work proposes a novel control strategy to stabilize the decoupled dynamics of a homogeneous reaction system, described by vessel extents, using irreversible thermodynamics. Specifically, the non-negative property of the irreversible entropy production due to reaction allows expressing the reaction rate in terms of a thermodynamic quantity, called chemical affinity, that can then be defined in the space of vessel extents using a linear time-invariant transformation. This structural link in turn allows constructing a Lypunov function candidate to synthesize a nonlinear controller for the stabilization of the reaction rate, and thus of the vessel extents. Numerical simulations are carried out for a reversible reaction to illustrate the proposed approach.