Thermodynamic Entropy Production Research Articles

Revisit nonequilibrium thermodynamics based on thermomass theory and its applications in nanosystems

Abstract The development of non-Fourier heat conduction models is encouraged by the invalidity of Fourier’s law to explain heat conduction in ultrafast or ultrasmall systems. The production of negative entropy will result from the combination of traditional nonequlibrium thermodynamics and non-Fourier heat conduction models. To resolve this paradox, extended irreversible thermodynamics (EIT) introduces a new state variable. However, real dynamics variables like force and momentum are still missing from nonequilibrium thermodynamics and EIT’s generalized force and generalized flux. Heat has both mass and energy, according to thermomass theory and Einstein’s mass-energy relation. The generalized heat conduction model containing non-Fourier effects was established by thermomass gas model. The thermomass theory reshapes the concept of the generalized force and flux, temperature, and entropy production in nonequilibrium thermodynamics and revisits the assumption for the linear regression of the fluctuations in Onsager reciprocal relation. The generalized heat conduction model based on thermomass theory has been used to study thermal conductivity, thermoelectric effect, and thermal rectification effect in nanosystems.

Quantum relative entropy uncertainty relation.

For classic systems, the thermodynamic uncertainty relation (TUR) states that the fluctuations of a current have a lower bound in terms of the entropy production. Some TURs are rooted in information theory, particularly derived from relations between observations (mean and variance) and dissimilarities, such as the Kullback-Leibler divergence, which plays the role of entropy production in stochastic thermodynamics. We generalize this idea for quantum systems, where we find a lower bound for the uncertainty of quantum observables given in terms of the quantum relative entropy. We apply the result to obtain a quantum thermodynamic uncertainty relation in terms of the quantum entropy production, valid for arbitrary dynamics and nonthermal environments.

Thermodynamic entropy production in the dynamical Casimir effect

Thermodynamic entropy production in the dynamical Casimir effect

Convective heat transport and entropy generation in butterfly-shaped magneto-nanofluidic systems with bottom heating and top cooling

PurposeThe purpose of this study is to carry out a comprehensive analysis of magneto-hydrodynamics (MHD), nanofluidic flow dynamics and heat transfer as well as thermodynamic irreversibility, within a novel butterfly-shaped cavity. Gaining a thorough understanding of these phenomena will help to facilitate the design and optimization of thermal systems with complex geometries under magnetic fields in diverse applications.Design/methodology/approachTo achieve the objective, the finite element method is used to solve the governing equations of the problem. The effects of various controlling parameters such as butterfly-shaped triangle vertex angle (T), Rayleigh number (Ra), Hartmann number (Ha) and magnetic field inclination angle (γ ) on the hydrothermal performance are analyzed meticulously. By investigating the effects of these parameters, the authors contribute to the existing knowledge by shedding light on their influence on heat and fluid transport within butterfly-shaped cavities.FindingsThe major findings of this study reveal that the geometrical shape significantly alters fluid motion, heat transfer and irreversibility production. Maximum heat transfer, as well as entropy generation, occurs when the Rayleigh number reaches its maximum, the Hartmann number is minimized and the angle of the magnetic field is set to 30° or 150°, while the butterfly wings angle or vertex angle is kept at a maximum of 120°. The intensity of the magnetic field significantly controls the heat flow dynamics, with higher magnetic field strength causing a reduction in the flow strength as well as heat transfer. This configuration optimizes the heat transfer characteristics in the system.Research limitations/implicationsFurther research can be expanded on this study by examining thermal performance under different curvature effects, orientations, boundary conditions and additional factors. This can be accomplished through numerical simulations or experimental investigations under various multiphysical scenarios.Practical implicationsThe geometric configurations explored in this research have practical applications in various engineering fields, including heat exchangers, crystallization processes, microelectronic devices, energy storage systems, mixing processes, food processing, air-conditioning, filtration and more.Originality/valueThis study brings value by exploring a novel geometric configuration comprising the nanofluidic flow, and MHD effect, providing insights and potential innovations in the field of thermal fluid dynamics. The findings contribute a lot toward maximizing thermal performance in diverse fields of applications. The comparison of different hydrothermal behavior and thermodynamic entropy production under the varying geometric configuration adds novelty to this study.

Effects of enclosure shape on MHD nanofluid flow and irreversibility in different shaped systems under fluid volume constraint

PurposeThe purpose of this study is to investigate the influence of enclosure shape on magnetohydrodynamic (MHD) nanofluidic flow, heat transfer and irreversibility in square, trapezoidal and triangular thermal systems under fluid volume constraints, with the aim of optimizing thermal behavior in diverse applications.Design/methodology/approachThe study uses numerical simulations based on a finite element-based technique to analyze the effects of the Rayleigh number (Ra), Hartmann number (Ha), magnetic field orientation (γ) and nanoparticle concentration (ζ) on heat transfer characteristics and thermodynamic entropy production.FindingsThe key findings reveal that the geometrical design significantly influences fluid velocity, heat transfer and irreversibility. Trapezoidal thermal systems outperform square systems, while triangular systems achieve optimal enhancement. Nanoparticle concentration enhances heat transfer and flow strength at higher Rayleigh numbers. The magnetic field intensity has a significant impact on fluid flow and heat transport in natural convection, with higher Hartmann numbers resulting in reduced flow strength and heat transfer. The study also highlights the influence of various parameters on thermodynamic entropy production.Research limitations/implicationsFurther research can explore additional geometries, parameters and boundary conditions to expand the understanding of enclosure shape effects on MHD nanofluidic flow and heat transfer. Experimental validation can complement the numerical simulations presented in this study.Originality/valueThis study provides valuable insights into the impact of enclosure shape on heat transfer performance in MHD nanofluid flow systems. The findings contribute to the optimization of thermal behavior in applications such as electronics cooling and energy systems. The comparison of different enclosure shapes and the analysis of thermodynamic entropy production add novelty to the study.

Channel capacity: limitation of entropy rate during cell signal transduction

Cellular signal transduction is mediated through chain activation reactions involving signalling molecules. Information thermodynamics may be a promising approach for quantifying signal transduction. A cell signal is transduced through the signal molecule activation as a step of a signal transduction cascade. In each step, two types of entropy can be defined. First, the signal transduction was defined using thermodynamic entropy production during the chemical activation of signal molecules. Second, the chronology was described as a code string, and the logarithm of the number of signal code strings corresponded to the information entropy. Finally, the total entropy during signal transduction was determined by summing the two entropies. When maximising the total entropy, the total entropy rate per signalling molecule concentration was found to be consistent independently of each transduction step (i.e., signal molecule types). Consequently, the speed limit of the entropy rate can be calculated, providing the capacity, which is an essential property of the signal transduction cascade. The theory introduced here is expected to provide a basic framework for understanding new methods of discovering signal cascades and intracellular signal transduction.

Bound for the moment generating function from the detailed fluctuation theorem.

A famous consequence of the detailed fluctuation theorem (FT), p(Σ)/p(-Σ)=exp(Σ), is the integral FT 〈exp(-Σ)〉=1 for a random variable Σ and a distribution p(Σ). When Σ represents the entropy production in thermodynamics, the main outcome of the integral FT is the second law, 〈Σ〉≥0. However, a full description of the fluctuations of Σ might require knowledge of the moment generating function (MGF), G(α):=〈exp(αΣ)〉. In the context of the detailed FT, we show the MGF is lower bounded in the form G(α)≥B(α,〈Σ〉) for a given mean 〈Σ〉. As applications, we verify that the bound is satisfied for the entropy produced in the heat exchange problem between two reservoirs mediated by a weakly coupled bosonic mode and a qubit swap engine.

Optimization of the performance of M-Cycle indirect evaporative cooling via thermodynamic approach

ABSTRACT For the further energy conservation, the study on the optimizing the M-Cycle indirect evaporative cooling (MIEC) performance is meaningful. With the aim of the optimization, a model of a general MIEC system was established, the thermodynamic entropy production optimization method was used to fully reflect the energy quality and irreversibility. The inlet parameters, supply air ratio, dew point temperature efficiency, unit-cooling capacity and Entropy Production Number were used to analyze and improve the cooling and thermodynamic performance of the general MIEC. A total of 6750 air treatment processes have been studied with the self-programmed FORTRA. It is concluded that when the inlet temperature is high, with the increase in inlet relative humidity, the unit-cooling capacity of the system greatly improves while the Entropy Production Number increases relatively small. When the ambient humidity variation range is large, the irreversible loss of the system can be reduced by coordinating the supply air ratio and dew point temperature efficiency of the MIEC system. Ultimately, the results of this study will provide theoretical reference for the design and operation of the practical engineering of the MIEC.

Weather pattern dynamics over western Europe under climate change: predictability, information entropy and production

Abstract. The impact of climate change on weather pattern dynamics over the North Atlantic is explored through the lens of the information theory of forced dissipative dynamical systems. The predictability problem is first tackled by investigating the evolution of block entropies on observational time series of weather patterns produced by the Met Office, which reveals that predictability is increasing as a function of time in the observations during the 19th century and beginning of the 20th century, while the trend is reversed at the end of the 20th century and beginning of the 21st century. This feature is also investigated in the 15-member ensemble of the UK Met Office CMIP5 model for the 20th and 21st centuries under two climate change scenarios, revealing a wide range of possible evolutions depending on the realization considered, with an overall decrease in predictability in the 21st century for both scenarios. Lower bounds of the information entropy production are also extracted, providing information on the degree of time asymmetry and irreversibility of the dynamics. The analysis of the UK Met Office model runs suggests that the information entropy production will increase by the end of the 21st century, by a factor of 10 % in the Representative Carbon Pathway RCP2.6 scenario and a factor of 30 %–40 % in the RCP8.5 one, as compared to the beginning of the 20th century. This allows one to make the conjecture that the degree of irreversibility is increasing, and hence heat production and dissipation will also increase under climate change, corroborating earlier findings based on the analysis of the thermodynamic entropy production.

Towards a Social-Ecological-Entropy Perspective of Sustainable Exploitation of Natural Resources

An innovative and integrative modeling strategy for assessing the sustainability and resilience of social-ecological systems (SES) is presented by introducing a social-ecological entropy production (SEEP) method. In analogy to the thermodynamic entropy production of irreversible processes, we discuss a theoretical model that relates energy and information flow with the cultural and epistemological peculiarities of different communities that exploit the same natural resource. One of the innovative aspects of our approach comes from the fact that sustainability is assessed by a single parameter (SEEP) incorporating the simulation outcomes of all the populations participating in the dynamics, and not only on the fate of the resource. This is significant as far as the non-linearities introduced by the coupling of the different dynamics considered may lead to high sensitivity to small perturbations. Specifically, by assuming two possible types of technical and environmental knowledge-transfer methods [direct (D) and phase-in (P)] within each one of the two communities that exploit and restore a resource, we generate four mathematical models to explore the long-term sustainability scenario due to the intervention, by a new epistemological community, of an initially sustainable resource-community SES. By exploring the space of four key parameters characterizing the degree of technical and environmental knowledge, as well as the rates of social inclusion and knowledge transfer, our simulations show that, from 400 scenarios studied in each case, the P-P model predicts 100% sustainable cases in the use of the resource after the intervention by the second community. The mixed scenarios P-D and D-P predict about 29%, and the D-D scenario only predicts 23% of sustainable cases. Catastrophic outcomes are predicted at about 71% in P-D and D-P scenarios, and about 77% of extinction of the system by exhaustion of the resource and community populations in the D-D scenario. In this form, our theoretical strategy and the knowledge-transfer scenarios studied may help policymakers to find a priori science-based criteria to solve possible controversies arising from social-ecological interventions.

Covariant nonequilibrium thermodynamics from Ito-Langevin dynamics

Using the recently developed covariant Ito-Langevin dynamics, we develop a nonequilibrium thermodynamic theory for small systems coupled to multiplicative noises. The theory is based on Ito calculus, and is fully covariant under time-independent nonlinear transformation of variables. Assuming instantaneous detailed balance, we derive expressions for various thermodynamic functions, including work, heat, entropy production, and free energy, both at ensemble level and at trajectory level, and prove the second law of thermodynamics for arbitrary nonequilibrium processes. We relate time-reversal asymmetry of path probability to entropy production, and derive its consequences such as fluctuation theorem and nonequilibrium work relation. For Langevin systems with additive noises, our theory is equivalent to the common theories of stochastic energetics and stochastic thermodynamics. Using concrete examples, we demonstrate that whenever kinetic coefficients or metric tensor depend on system variables, the common theories of stochastic thermodynamics and stochastic energetics should be replaced by our theory.

Exactly solvable model of a passive Brownian heat engine and its comparison with active engines

We perform an extensive analysis of passive as well as active micro-heat engines with different single-particle stochastic models. Using stochastic thermodynamics we calculate the thermodynamic work, heat, entropy production and efficiency of passive and active Brownian heat engines analytically, as well as numerically, and compare them. We run the heat engines with a protocol for which the average thermodynamic quantities are calculated exactly for an arbitrary cycle time. We also discuss the group of protocols for which exact non-quasistatic calculations can be done, completely in the passive engine case and partially in the active engines. We obtain detailed thermodynamics of non-quasistatic (i.e. powerful) single-particle micro heat engines. The quasistatic (i.e. zero power) limit of the results is obtained by taking a long (infinite) cycle time. We also study the distributions of position of the confined particle in both passive and active engines. We compare their characteristics in terms of the parameter that measures the competition between the active persistence in the particle position (due to active noises) and the harmonic confinement. We also calculate excess kurtosis that measures the non-Gaussianity of these distributions. Our analysis shows that the efficiency of such thermal machines can be enhanced or reduced depending on the activity present in the model.

Invariance Properties of the Entropy Production, and the Entropic Pairing of Inertial Frames of Reference by Shear-Flow Systems.

This study examines the invariance properties of the thermodynamic entropy production in its global (integral), local (differential), bilinear, and macroscopic formulations, including dimensional scaling, invariance to fixed displacements, rotations or reflections of the coordinates, time antisymmetry, Galilean invariance, and Lie point symmetry. The Lie invariance is shown to be the most general, encompassing the other invariances. In a shear-flow system involving fluid flow relative to a solid boundary at steady state, the Galilean invariance property is then shown to preference a unique pair of inertial frames of reference—here termed an entropic pair—respectively moving with the solid or the mean fluid flow. This challenges the Newtonian viewpoint that all inertial frames of reference are equivalent. Furthermore, the existence of a shear flow subsystem with an entropic pair different to that of the surrounding system, or a subsystem with one or more changing entropic pair(s), requires a source of negentropy—a power source scaled by an absolute temperature—to drive the subsystem. Through the analysis of different shear flow subsystems, we present a series of governing principles to describe their entropic pairing properties and sources of negentropy. These are unaffected by Galilean transformations, and so can be understood to “lie above” the Galilean inertial framework of Newtonian mechanics. The analyses provide a new perspective into the field of entropic mechanics, the study of the relative motions of objects with friction.

Irreversibility and Biased Ensembles in Active Matter: Insights from Stochastic Thermodynamics

Active systems evade the rules of equilibrium thermodynamics by constantly dissipating energy at the level of their microscopic components. This energy flux stems from the conversion of a fuel, present in the environment, into sustained individual motion. It can lead to collective effects without any equilibrium equivalent, some of which can be rationalized by using equilibrium tools to recapitulate nonequilibrium transitions. An important challenge is then to delineate systematically to what extent the character of these active transitions is genuinely distinct from equilibrium analogs. We review recent works that use stochastic thermodynamics tools to identify, for active systems, a measure of irreversibility comprising a coarse-grained or informatic entropy production. We describe how this relates to the underlying energy dissipation or thermodynamic entropy production, and how it is influenced by collective behavior. Then, we review the possibility of constructing thermodynamic ensembles out of equilibrium, where trajectories are biased toward atypical values of nonequilibrium observables. We show that this is a generic route to discovering unexpected phase transitions in active matter systems, which can also inform their design.

Geometrical aspects of entropy production in stochastic thermodynamics based on Wasserstein distance

We study a relationship between optimal transport theory and stochastic thermodynamics for the Fokker-Planck equation. We show that the lower bound on the entropy production is the action measured by the path length of the $L^2$-Wasserstein distance. Because the $L^2$-Wasserstein distance is a geometric measure of optimal transport theory, our result implies a geometric interpretation of the entropy production. Based on this interpretation, we obtain a thermodynamic trade-off relation between transition time and the entropy production. This thermodynamic trade-off relation is regarded as a thermodynamic speed limit which gives a tighter bound of the entropy production. We also discuss stochastic thermodynamics for the subsystem and derive a lower bound on the partial entropy production as a generalization of the second law of information thermodynamics. Our formalism also provides a geometric picture of the optimal protocol to minimize the entropy production. We illustrate these results by the optimal stochastic heat engine and show a geometrical bound of the efficiency.

Entropy production study of an IRS device having diathermic conical funnels with surface radiation

The present study involves the thermodynamic performance and entropy production analysis of an infrared suppression (IRS) system. The IRS device is usually used in ocean liners, warships, and cargo ships to reduce the turbine exhaust temperature. First, the governing differential equations (Navier-Stokes, energy, turbulence, radiation equations) are solved using ANSYS Fluent 19.0 to elucidate the thermodynamic performance of the IRS device. Then entropy production and irreversibilities are calculated in post-processing. The pertinent parameters, viz. Reynolds number at nozzle inlet (6.12 × 105 to 3.11 × 106), the nozzle outlet fluid temperature (400 to 600 K), nozzle overlap, funnel overlap, and the types of guide vanes are varied to analyze the impact of these parameters on entropy generation. The effect of different boundary conditions for funnel walls (i.e., adiabatic, diathermic with or without radiation) on entropy generation is discussed. A comparison of various types of guide vanes is also performed. It is found that entropy production (or irreversibility) is less when mass entrainment is more, i.e., device outlet temperature is less. Moreover, entropy production caused by heat transfer has the main contribution in total entropy production than that caused due to fluid friction. The entropy generation is found to be minimum for zero nozzle overlapping, zero funnel overlapping, diathermic funnel wall with radiation, and QCGV (quarter circular guide vane) type. The mass entertainment is maximum, and device outlet temperature is minimum with the mentioned conditions.

Gyrokinetic entropy balances and dynamics in toroidal flux-driven ITG turbulence

Overall entropy balances and radial dynamics for thermodynamic entropy and conventional fluctuation entropy are investigated by means of newly derived coupled equations and the full-f gyrokinetic simulations for toroidal flux-driven ion-temperature-gradient turbulence. When the equations are integrated over the radial direction, in the quasi-steady state, fluctuation entropy production due to collisional dissipation in velocity space and thermodynamic entropy reduction due to energy input/output in real space are found to be balanced through the generation of a heat flux and associated phase mixing. The cross-correlation analysis indicates that collisional dissipation occurs after the formation of fine-scale structures by phase mixing, while there exists an in-phase relationship between thermodynamic entropy production due to profile relaxation and heat flux. However, when the radial dynamics are retained in the equations, this relationship is found to be violated in regions exhibiting heat avalanches. This is because the thermodynamic entropy is dominated by advection, leading to a time lag between heat flux and temperature variation.

Possibility of the total thermodynamic entropy production rate of a finite-sized isolated quantum system to be negative for the Gorini-Kossakowski-Sudarshan-Lindblad-type Markovian dynamics of its subsystem

We investigate a total thermodynamic entropy production rate of an isolated quantum system. In particular, we consider a quantum model of coupled harmonic oscillators in a star configuration, where a central harmonic oscillator (system) is coupled to a finite number of surrounding harmonic oscillators (bath). In this model, when the initial state of the total system is given by the tensor product of the Gibbs states of the system and the bath, every harmonic oscillator is always in a Gibbs state with a time-dependent temperature. This enables us to define time-dependent thermodynamic entropy for each harmonic oscillator and total nonequilibrium thermodynamic entropy as the summation of them. We analytically confirm that the total thermodynamic entropy satisfies the third law of thermodynamics. Our numerical solutions show that, even when the dynamics of the system is well approximated by the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL)-type Markovian master equation, the total thermodynamic entropy production rate can be negative, while the total thermodynamic entropy satisfies the second law of thermodynamics. This result is a counterexample to the common belief that the total entropy production rate is non-negative when the system is under the GKSL-type Markovian dynamics.

Thermodynamic vs statistical entropy production in thermostatted Hamiltonian dynamics

Sufficient conditions were recently established for the rates of thermodynamic entropy production and phase space volume contraction to be identically equal in thermostatted Hamiltonian systems in non-equilibrium steady states (Ramshaw 2017 Phys. Rev. E 96 052122). This equality has previously been interpreted as a statistical analogue of the second law of thermodynamics (SLT). However, that interpretation is unjustified because the volume contraction rate represents the production rate of the statistical entropy of the system and thermostat together, which differs in general from that of the Hamiltonian system itself. This logical lacuna is remedied by identifying two further conditions which combine with the previous conditions to imply a proper statistical analogue of the SLT. The first of these new conditions can simply be imposed a priori, whereas the second, like ergodicity and mixing, involves the asymptotic statistical properties of the dynamics as t → ∞. The latter condition seems likely to be analytically intractable in general, and therefore to require numerical investigation and confirmation in systems of practical interest.

Quantum correlation entropy

We study quantum coarse-grained entropy and demonstrate that the gap in entropy between local and global coarse-grainings is a natural generalization of entanglement entropy to mixed states and multipartite systems. This "quantum correlation entropy" $S^{\rm QC}$ is additive over independent systems, is invariant under local unitary operations, measures total nonclassical correlations (vanishing on states with strictly classical correlation), and reduces to the entanglement entropy for bipartite pure states. It quantifies how well a quantum system can be understood via local measurements, and ties directly to non-equilibrium thermodynamics, including representing a lower bound on the quantum part of thermodynamic entropy production. We discuss two other measures of nonclassical correlation to which this entropy is equivalent, and argue that together they provide a unique thermodynamically distinguished measure.