Terms Of Entropy Production Research Articles

Irreversibility in Active Matter Systems: Fluctuation Theorem and Mutual Information

We consider a Brownian particle which, in addition to being in contact with a thermal bath, is driven by fluctuating forces which stem from active processes in the system, such as self-propulsion or collisions with other active particles. These active fluctuations do not fulfill a fluctuation-dissipation relation and therefore play the role of a non-equilibrium environment, which keeps the system permanently out of thermal equilibrium even in the absence of external forces. We investigate how the out-of-equilibrium character of the active matter system and the associated irreversibility is reflected in the trajectories of the Brownian particle. Specifically, we analyze the log-ratio of path probabilities for observing a certain particle trajectory forward in time versus observing its time-reversed twin trajectory. For passive Brownian motion, it is well-known that this path probability ratio quantifies irreversibility in terms of entropy production. For active Brownian motion, we show that in addition to the usual entropy produced in the thermal environment the path probability ratio contains a contribution to irreversibility from mutual information production between the particle trajectory and the history of the non-equilibrium environment. The resulting irreversibility measure fulfills an integral fluctuation theorem and a second-law like relation. When deriving and discussing these relations, we keep in mind that the active fluctuations can occur either due to a suspension of active particles pushing around a passive colloid or due to active self-propulsion of the particle itself; we point out the similarities and differences between these two situations. We obtain explicit expressions for active fluctuations modeled by an Ornstein-Uhlenbeck process. Finally, we illustrate our general results by analyzing a Brownian particle which is trapped in a static or moving harmonic potential.

Thermodynamic analysis of modified teleparallel gravity involving higher-order torsion derivative terms

The present study is elaborated to investigate the validity of thermodynamical laws in a modified teleparallel gravity based on higher-order derivative terms of torsion scalar. For this purpose, we consider spatially flat FRW model filled with perfect fluid matter contents. Firstly, we explore the possibility of existence of equilibrium as well as non-equilibrium picture of thermodynamics in this extended version of teleparallel gravity. Here, we present the first law and the generalized second law of thermodynamics (GSLT) using Hubble horizon. It is found that non-equilibrium description of thermodynamics exists in this theory with the presence of an extra term called as entropy production term. We also establish GSLT using the logarithmic corrected entropy. Further, by taking the equilibrium picture, we discuss validity of GSLT at Hubble horizon for two different F models. Using Gibbs law and the assumption that temperature of matter within Hubble horizon is similar to itself, We use different choices of scale factor to discuss the GSLT validity graphically in all scenarios. It is found that the GSLT is satisfied for a specified range of free parameters in all cases.

Similarities and differences between non-equilibrium steady states and time-periodic driving in diffusive systems

A system that violates detailed balance evolves asymptotically into a non-equilibrium steady state (NESS) with non-vanishing currents. Analogously, when detailed balance holds at any instant of time but the system is driven through time-periodic variations of external parameters, it evolves toward a time-periodic state, which can also support non-vanishing currents. In both cases the maintenance of currents throughout the system incurs a cost in terms of entropy production. Here we compare these two scenarios for one dimensional diffusive systems with periodic boundary condition, a framework commonly used to model biological and artificial molecular machines. We first show that the entropy production rate in a periodically driven system is necessarily greater than that in a stationary system without detailed balance, when both are described by the same (time-averaged) current and probability distribution. Next, we show how to construct both a NESS and a periodic driving that support a given time averaged probability distribution and current. Lastly, we show that although the entropy production rate of a periodically driven system is higher than that of an equivalent steady state, the difference between the two entropy production rates can be tuned to be arbitrarily small.

Non-isothermal General Ericksen–Leslie System: Derivation, Analysis and Thermodynamic Consistency

We derive a model describing the evolution of a nematic liquid-crystal material under the action of thermal effects. The first and second laws of thermodynamics lead to an extension of the general Ericksen-Leslie system where the Leslie stress tensor and the Oseen-Frank energy density are considered in their general forms. The work postulate proposed by Ericksen-Leslie is traduced in terms of entropy production. We finally analyze the global-in-time well-posedness of the system for small initial data in the framework of Besov spaces.

Entropic bounds on currents in Langevin systems

We derive a bound on generalized currents for Langevin systems in terms of the total entropy production in the system and its environment. For overdamped dynamics, any generalized current is bounded by the total rate of entropy production. We show that this entropic bound on the magnitude of generalized currents imposes power-efficiency tradeoff relations for ratchets in contact with a heat bath: Maximum efficiency-Carnot efficiency for a Smoluchowski-Feynman ratchet and unity for a flashing or rocking ratchet-can only be reached at vanishing power output. For underdamped dynamics, while there may be reversible currents that are not bounded by the entropy production rate, we show that the output power and heat absorption rate are irreversible currents and thus obey the same bound. As a consequence, a power-efficiency tradeoff relation holds not only for underdamped ratchets but also for periodically driven heat engines. For weak driving, the bound results in additional constraints on the Onsager matrix beyond those imposed by the second law. Finally, we discuss the connection between heat and entropy in a nonthermal situation where the friction and noise intensity are state dependent.

Spacetime thermodynamics in the presence of torsion

It was shown by Jacobson in 1995 that the Einstein equation can be derived as a local constitutive equation for an equilibrium spacetime thermodynamics. With the aim to understand if such thermodynamical description is an intrinsic property of gravitation, many attempts have been done so far to generalise this treatment to a broader class of gravitational theories. Here we consider the case of the Einstein-Cartan theory as a prototype of theories with non-propagating torsion. In doing so, we study the properties of Killing horizons in the presence of torsion, establish the notion of local causal horizon in Riemann-Cartan spacetimes, and derive the generalised Raychaudhuri equation for this kind of geometries. Then, starting with the entropy that can be associated to these local causal horizons, we derive the Einstein-Cartan equation by implementing the Clausius equation. We outline two ways of proceeding with the derivation depending on whether we take torsion as a geometric field or as a matter field. In both cases we need to add internal entropy production terms to the Clausius equation as the shear and twist cannot be taken to be zero a priori for our setup. This fact implies the necessity of a non-equilibrium thermodynamics treatment for the local causal horizon. Furthermore, it implies that a non-zero twist at the horizon will in general contribute to the Hartle-Hawking tidal heating for black holes with possible implications for future observations.

Stochastic thermodynamics of periodically driven systems: Fluctuation theorem for currents and unification of two classes.

Periodic driving is used to operate machines that go from standard macroscopic engines to small nonequilibrium microsized systems. Two classes of such systems are small heat engines driven by periodic temperature variations, and molecular pumps driven by external stimuli. Well-known results that are valid for nonequilibrium steady states of systems driven by fixed thermodynamic forces, instead of an external periodic driving, have been generalized to periodically driven heat engines only recently. These results include a general expression for entropy production in terms of currents and affinities, and symmetry relations for the Onsager coefficients from linear-response theory. For nonequilibrium steady states, the Onsager reciprocity relations can be obtained from the more general fluctuation theorem for the currents. We prove a fluctuation theorem for the currents for periodically driven systems. We show that this fluctuation theorem implies a fluctuation dissipation relation, symmetry relations for Onsager coefficients, and further relations for nonlinear response coefficients. The setup in this paper is more general than previous studies, i.e., our results are valid for both heat engines and molecular pumps. The external protocol is assumed to be stochastic in our framework, which leads to a particularly convenient way to treat periodically driven systems.

Effects of heat source and sink on entropy generation and MHD natural convection of Al2O3-Cu/water hybrid nanofluid filled with square porous cavity

The present work is focused on the analysis of the entropy generation and magneto-hydrodynamics natural convection flow and heat transfer in a square porous cavity differentially heated and cooled by heat source and sink, respectively filled with the Cu-Al2O3-Water hybrid nanofluid. The effective segments of the left and right sides of the cavity are kept at cooled temperature and the effective segments of top and bottom sides are kept at hot temperature. The enclosure’s ineffective segments of its sides are kept adiabatic. The thermal conductivity and the dynamic viscosity of the nanofluid are represented by different experimental correlations which are suitable to each nanoparticles. The finite difference methodology is used to solve the dimensionless partial differential equations governing the problem. A comparison with previously published studies and the present results shows very good agreement. Results are presented for entropy production in terms of Hartmann number, nanoparticle volume fraction and geometric parameters of the cavity.

A graphic approach to include dissipative-like effects in reversible thermal cycles

Since the decade of 1980’s, a connection between a family of maximum-work reversible thermal cycles and maximum-power finite-time endoreversible cycles has been established. The endoreversible cycles produce entropy at their couplings with the external heat baths. Thus, this kind of cycles can be optimized under criteria of merit that involve entropy production terms. Meanwhile the relation between the concept of work and power is quite direct, apparently, the finite-time objective functions involving entropy production have not reversible counterparts. In the present paper we show that it is also possible to establish a connection between irreversible cycle models and reversible ones by means of the concept of “geometric dissipation”, which has to do with the equivalent role of a deficit of areas between some reversible cycles and the Carnot cycle and actual dissipative terms in a Curzon-Ahlborn engine.

Entropy Production in Field Theories without Time-Reversal Symmetry: Quantifying the Non-Equilibrium Character of Active Matter

Active matter systems operate far from equilibrium due to the continuous energy injection at the scale of constituent particles. At larger scales, described by coarse-grained models, the global entropy production rate S quantifies the probability ratio of forward and reversed dynamics and hence the importance of irreversibility at such scales: it vanishes whenever the coarse-grained dynamics of the active system reduces to that of an effective equilibrium model. We evaluate S for a class of scalar stochastic field theories describing the coarse-grained density of self-propelled particles without alignment interactions, capturing such key phenomena as motility-induced phase separation. We show how the entropy production can be decomposed locally (in real space) or spectrally (in Fourier space), allowing detailed examination of the spatial structure and correlations that underly departures from equilibrium. For phase-separated systems, the local entropy production is concentrated mainly on interfaces with a bulk contribution that tends to zero in the weak-noise limit. In homogeneous states, we find a generalized Harada-Sasa relation that directly expresses the entropy production in terms of the wavevector-dependent deviation from the fluctuation-dissipation relation between response functions and correlators. We discuss extensions to the case where the particle density is coupled to a momentum-conserving solvent, and to situations where the particle current, rather than the density, should be chosen as the dynamical field. We expect the new conceptual tools developed here to be broadly useful in the context of active matter, allowing one to distinguish when and where activity plays an essential role in the dynamics.

Numerical assessment of the reduction of the entropy production rate caused by fin segmentation in heat exchangers

A numerical comparison of the entropy production rates caused by plain and segmented fins is presented. These fins evolve as helical surfaces around their respective tubes, which are themselves arranged according to a standard layout in heat exchanger applications. A finite volume, two-layered, Reynolds Averaged Navier-Stokes (RANS) model was implemented to calculate the properties of a turbulent stream of hot air flowing through the array of tubes. This approach enabled an appropriate evaluation of the mean and the fluctuating contributions to the thermal and viscous entropy production terms. It was found that fin segmentation reduced the production of entropy nearly 16% with respect to the plain fin design. For this particular setup it was also shown that the thermal contribution to the global production of entropy is one-order-of-magnitude larger than its viscous counterpart. The numerical results agree with the experimental observations previously reported by other researchers. Some design recommendations are given at the end of the conclusions section.

Theoretical Analysis for Heat Transfer Optimization in Subcritical Electrothermal Energy Storage Systems

Electrothermal energy storage (ETES) provides bulk electricity storage based on heat pump and heat engine technologies. A subcritical ETES is described in this paper. Based on the extremum principle of entransy dissipation, a geometry model is developed for heat transfer optimization for subcritical ETES. The exergy during the heat transfer process is deduced in terms of entropy production. The geometry model is validated by the extremum principle of entropy production. The theoretical analysis results show that the extremum principle of entransy dissipation is an effective criterion for the optimization, and the optimum heat transfer for different cases with the same mass flux or pressure has been discussed. The optimum heat transfer can be achieved by adjusting the mass flux and pressure of the working fluid. It also reveals that with the increase of mass flux, there is a minimum exergy in the range under consideration, and the exergy decreases with the increase of the pressure.

Eddy Viscosity and Reynolds Stress Models of Entropy Generation in Turbulent Channel Flows

This paper presents new models of entropy production for incompressible turbulent channel flows. A turbulence model is formulated and analyzed with direct numerical simulation (DNS) data. A Reynolds-averaged Navier–Stokes (RANS) approach is used and applied to the turbulence closure of mean and fluctuating variables and entropy production. The expression of the mean entropy production in terms of other mean flow quantities is developed. This paper presents new models of entropy production by incorporating the eddy viscosity into the total shear stress. Also, the Reynolds shear stress is used as an alternative formulation. Solutions of the entropy transport equations are presented and discussed for both laminar and turbulent channel flows.

A numerically research on energy loss evaluation in a centrifugal pump system based on local entropy production method

Inspired by wide application of the second law of thermodynamics to flow and heat transfer devices, local entropy production analysis method was creatively introduced into energy assessment system of centrifugal water pump. Based on Reynolds stress turbulent model and energy equation model, the steady numerical simulation of the whole flow passage of one IS centrifugal pump was carried out. The local entropy production terms were calculated by user defined functions, mainly including wall entropy production, turbulent entropy production, and viscous entropy production. The numerical results indicated that the irreversible energy loss calculated by the local entropy production method agreed well with that calculated by the traditional method but with some deviations which were probably caused by high rotatability and high curvature of impeller and volute. The wall entropy production and turbulent entropy production took up large part of the whole entropy production about 48.61% and 47.91%, respectively, which indicated that wall friction and turbulent fluctuation were the major factors in affecting irreversible energy loss. Meanwhile, the entropy production rate distribution was discussed and compared with turbulent kinetic energy dissipation rate distribution, it showed that turbulent entropy production rate increased sharply at the near wall regions and both distributed more uniformly. The blade region in leading edge near suction side, trailing edge and volute tongue were the main regions to generate irreversible exergy loss. This research broadens a completely new view in evaluating energy loss and further optimizes pump using entropy production minimization.

Entropy production, hydrodynamics, and resurgence in the primordial quark-gluon plasma from holography

Microseconds after the Big Bang quarks and gluons formed a strongly-coupled non-conformal liquid driven out-of-equilibrium by the expansion of the Universe. We use holography to determine the non-equilibrium behavior of this liquid in a Friedmann-Lemaitre-Robertson-Walker Universe and develop an expansion for the corresponding entropy production in terms of the derivatives of the cosmological scale factor. We show that the resulting series has zero radius of convergence and we discuss its resurgent properties. Finally, we compute the resummed entropy production rate in de Sitter Universe at late times and show that the leading order approximation given by bulk viscosity effects can strongly overestimate/underestimate the rate depending on the microscopic parameters.

Theory of entropy production in quantum many-body systems

We define the entropy operator as the negative of the logarithm of the density matrix, give a prescription for extracting its thermodynamically measurable part, and discuss its dynamics. For an isolated system we derive the first, second and third laws of thermodynamics. For weakly-coupled subsystems of an isolated system, an expression for the long time limit of the expectation value of the rate of change of the thermodynamically measurable part of the entropy operator is derived and interpreted in terms of entropy production and entropy transport terms. The interpretation is justified by comparison to the known expression for the entropy production in an aged classical Markovian system with Gaussian fluctuations and by a calculation of the current-induced entropy production in a conductor with electron-phonon scattering.

Entropy generation in Gaussian quantum transformations: applying the replica method to continuous-variable quantum information theory

AbstractIn spite of their simple description in terms of rotations or symplectic transformations in phase space, quadratic Hamiltonians such as those modelling the most common Gaussian operations on bosonic modes remain poorly understood in terms of entropy production. For instance, determining the quantum entropy generated by a Bogoliubov transformation is notably a hard problem, with generally no known analytical solution, while it is vital to the characterisation of quantum communication via bosonic channels. Here we overcome this difficulty by adapting the replica method, a tool borrowed from statistical physics and quantum field theory. We exhibit a first application of this method to continuous-variable quantum information theory, where it enables accessing entropies in an optical parametric amplifier. As an illustration, we determine the entropy generated by amplifying a binary superposition of the vacuum and a Fock state, which yields a surprisingly simple, yet unknown analytical expression.

On Description of Acceleration of Spinless Electrons in Law of Heat Conduction a capite ad calcem in Temperature

Acceleration effects of heat flow are included in the law of heat conduction by eliminating the acceleration term between the equation of motion for a spinless electron and the Boltzmann equipartition energy theorem differentiated with respect to time. The resulting law of heat conduction is a capite ad calcem in temperature as given in Equations (17), (19) and (20). (qz/k)z = -(δT/δz) - 1/vh(δT/δt). Evaluation of use of this equation using the entropy production term reveals that as long as the flux, q, and the temperature accumulation both have the same signs, the law does not violate the second law of thermodynamics. For systems that obey the first law of thermodynamics, this is the case. σ == q/T2(q/k + 1/vh • q(δT/δt)). In the chemical potential Stokes-Einstein formulation, when acceleration of the molecule is accounted for, a law of diffusion a capite ad calcem concentration results. In cartesian one-dimensional heat conduction in semi-infinite coordinates, the governing equation for temperature or concentration was solved for by the method of Laplace transforms. The results are in terms of the modified Bessel composite function in space and time of the first order and first kind. This is when τ > X. X > τ the solution is in terms of the Bessel composite function in space and time of the first order and first kind. The wave temperature is a decaying exponential in time when X = τ. An approximate expression for dimensionless temperature was obtained by expanding the binomial series in the exponent in the Laplace domain and after neglecting fourth- and higher-order terms before inversion from the Laplace domain. The Fourier model, the damped wave model and the a capite ad calcem in temperature/concentration model solutions are compared side by side in the form of a graph. The a capite ad calcem model solution is seen to undergo the convex to concave transition sooner than the damped wave model. The results of the a capite ad calcem temperature model for distances further from the surface are closer to the Fourier model solution.

Cosmological evolution of generalized ghost pilgrim dark energy in f ( T ) $f(T)$ gravity

We explore the phenomenon that phantom-like dark energy prevents the formation of black holes by assuming the generalized ghost version of pilgrim dark energy in the background of generalized teleparallel gravity. In this scenario, we construct \(f(T)\) model for explaining the evolutionary behavior of equation of state parameter, \(\omega_{\varLambda}-\omega'_{\varLambda}\) and \(r-s\) planes. We discuss these cosmological parameters graphically by taking different values of redshift parameter and pilgrim dark energy parameter. It is found that the equation of state parameter shows phantom like behavior while \(\omega_{\varLambda}-\omega'_{\varLambda}\) plane possesses thawing region for some particular values of pilgrim dark energy parameter. The statefinder parameters in \(r-s\) plane indicate the behavior of quintessence and phantom models. Finally, we discuss the first and second laws of thermodynamics and investigate the behavior of entropy production term.

Stochastic entropy production arising from nonstationary thermal transport.

We compute statistical properties of the stochastic entropy production associated with the nonstationary transport of heat through a system coupled to a time dependent nonisothermal heat bath. We study the one-dimensional stochastic evolution of a bound particle in such an environment by solving the appropriate Langevin equation numerically, and by using an approximate analytic solution to the Kramers equation to determine the behavior of an ensemble of systems. We express the total stochastic entropy production in terms of a relaxational or nonadiabatic part together with two components of housekeeping entropy production and determine the distributions for each, demonstrating the importance of all three contributions for this system. We compare the results with an approximate analytic model of the mean behavior and we further demonstrate that the total entropy production and the relaxational component approximately satisfy detailed fluctuation relations for certain time intervals. Finally, we comment on the resemblance between the procedure for solving the Kramers equation and a constrained extremization, with respect to the probability density function, of the spatial density of the mean rate of production of stochastic entropy.