On the Validity of Entropy Production Principles for Linear Electrical Circuits

We explain the (non-)validity of close-to-equilibrium entropy production principles in the context of linear electrical circuits. Both the minimum and the maximum entropy production principles are understood within dynamical fluctuation theory. The starting point are Langevin equations obtained by combining Kirchoff’s laws with a Johnson-Nyquist noise at each dissipative element in the circuit. The main observation is that the fluctuation functional for time averages, that can be read off from the path-space action, is in first order around equilibrium given by an entropy production rate. That allows to understand beyond the schemes of irreversible thermodynamics (1) the validity of the least dissipation, the minimum entropy production, and the maximum entropy production principles close to equilibrium; (2) the role of the observables’ parity under time-reversal and, in particular, the origin of Landauer’s counterexample (1975) from the fact that the fluctuating observable there is odd under time-reversal; (3) the critical remark of Jaynes (1980) concerning the apparent inappropriateness of entropy production principles in temperature-inhomogeneous circuits.     

Irreversibility and entropy production in transport phenomena,III—Principle of minimum integrated entropy production including nonlinear responses

A new variational principle of steady states is found by introducing an integrated type of energy dissipation (or entropy production) instead of instantaneous energy dissipation. This new principle is valid both in linear and nonlinear transport phenomena. Prigogine’s dream has now been realized by this new general principle of minimum “integrated” entropy production (or energy dissipation). This new principle does not contradict with the Onsager–Prigogine principle of minimum instantaneous entropy production in the linear regime, but it is conceptually different from the latter which does not hold in the nonlinear regime. Applications of this theory to electric conduction, heat conduction, particle diffusion and chemical reactions are presented.     

Entropy generation (irreversibility) associated with flow and heat transport mechanism in Sisko nanomaterial

Here a novel applications of entropy generation optimization is presented for nonlinear Sisko nanomaterial flow by rotating stretchable disk. Flow is examined in the absence of magnetohydrodynamics and Joule heating. Total irreversibility rate (entropy generation rate) is investigated for different flow parameters. Heat source/sink and viscous dissipation effects are considered. Impacts of Brownian motion and thermophoresis on irreversibility have been analyzed. Governing flow equations comprise momentum, energy and nanoparticle concentration. Von Karman's similarity variables are implemented for reduction of PDEs into ODEs. Homotopy analysis technique for series solutions is implemented. Attention is given to the irreversibility. The impacts of different flow parameters on velocity, nanoparticle concentration, temperature and irreversibility rate are graphically presented. From obtained results it is examined that irreversibility rate enhances for larger estimation of Brinkman number and diffusion. Furthermore it is also examined that temperature and nanoparticle concentration show contrast behavior through Prandtl number and Brownian motion.     

Exergy flows as bases of constructal law

How do macroscopic systems react when imposed to external forces? A recent analysis of Carnot’s theorem has pointed out that the systems do not convert all the inflow energy to work and dissipation, but that some energy will be incorporated to internal processes. These exergy flows appear as the heat exchanged with a second thermal reservoir of a thermodynamic general engine. Flows of energy from surroundings are driven by internal forces to the systemic process. Also, when the system has evolved to reach a stationary state, internal flows manifest themselves as internal processes. Here, the entropy generation extrema theorem is used to prove how the macroscopic system will react upon forces that are imposed by the external surroundings. This provides the link between the entropy generation extrema approach and the constructal law.     

Deviations from minimum entropy production at steady states of reacting chemical systems arbitrarily close to equilibrium

Our analysis of reacting systems displaced from equilibrium by a matter flux across the boundaries has shown that the state of minimum entropy production differs from the steady state, even in the near equilibrium regime. When the displacement δ from equilibrium is small, the derivative of the dissipation at the steady state and the dissipation itself are both of order δ². The state of least dissipation is displaced from the steady state by terms of order δ² in the species concentrations. The theorem of minimum entropy production may be derived by first truncating the series expansions for the reaction rates, affinities and dissipation assuming that δ is small, and then differentiating to locate the minimum of the dissipation within the resulting idealized model. For chemical systems with an arbitrarily small but macroscopic displacement from equilibrium, this truncation procedure establishes that the dissipation is comparatively small in a neighborhood of the steady state; but it causes large relative errors in the values of the concentration derivatives and time derivatives of the dissipation within that neighborhood, because the operations of series truncation and differentiation do not commute near the steady state, when δ is small but nonzero. Near the steady state, the concentration derivative of the term of order δ³ in the dissipation is comparable to or larger than the derivative of the δ² term.     

Use and validity of principles of extremum of entropy production in the study of complex systems

It is shown how both the principles of extremum of entropy production, which are often used in the study of complex systems, follow from the maximization of overall system conductivities, under appropriate constraints. In this way, the maximum rate of entropy production (MEP) occurs when all the forces in the system are kept constant. On the other hand, the minimum rate of entropy production (mEP) occurs when all the currents that cross the system are kept constant. A brief discussion on the validity of the application of the mEP and MEP principles in several cases, and in particular to the Earth’s climate is also presented.     

On entropy production

We investigate the case of a dynamical system when irreversible time evolution is generated by a nonHermitian superoperator on the states of the system. We introduce a generalized scalar product which can be used to construct a monotonically changing functional of the state, a generalized entropy. This will depend on the level of system dynamics described by the evolution equation. In this paper we consider the special case when the irreversibility derives from imbedding the system of interest into a thermal reservoir. The ensuing time evolution is shown to be compatible both with equilibrium thermodynamics and the entropy production near the final steady state. In particular, Prigogine’s principle of minimum entropy production is discussed. Also the limit of zero temperature is considered. We present comments on earlier treatments.     

The Steady State Fluctuation Relation for the Dissipation Function

We give a proof of transient fluctuation relations for the entropy production (dissipation function) in nonequilibrium systems, which is valid for most time reversible dynamics. We then consider the conditions under which a transient fluctuation relation yields a steady state fluctuation relation for driven nonequilibrium systems whose transients relax, producing a unique nonequilibrium steady state. Although the necessary and sufficient conditions for the production of a unique nonequilibrium steady state are unknown, if such a steady state exists, the generation of the steady state fluctuation relation from the transient relation is shown to be very general. It is essentially a consequence of time reversibility and of a form of decay of correlations in the dissipation, which is needed also for, e.g., the existence of transport coefficients. Because of this generality the resulting steady state fluctuation relation has the same degree of robustness as do equilibrium thermodynamic equalities. The steady state fluctuation relation for the dissipation stands in contrast with the one for the phase space compression factor, whose convergence is problematic, for systems close to equilibrium. We examine some model dynamics that have been considered previously, and show how they are described in the context of this work.     

Entropy production and viscosity of a dilute gas

It is known that the viscosity of a dilute gas can be derived by using kinetic theory. We present here a new derivation by using two entropy production principles: the steepest entropy ascent (SEA) principle and the maximum entropy production (MEP) principle. The known result is reproduced in a similar form.     

Entropy Production Rate Changes in Lysogeny/Lysis Switch Regulation of Bacteriophage Lambda

According to the chemical kinetic model of lysogeny/lysis switch in Escherichia coli (E. coli) infected by bacteriophage λ, the entropy production rates of steady states are calculated. The results show that the lysogenic state has lower entropy production rate than lytic state, which provides an explanation on why the lysogenic state of λ phage is so stable. We also notice that the entropy production rates of both lysogenic state and lytic state are lower than that of saddle-point and bifurcation state, which is consistent with the principle of minimum entropy production for living organism in nonequilibrium stationary state. Subsequently, the relations between CI and Cro degradation rates at two bifurcations and the changes of entropy production rate with CI and Cro degradation are deduced. The theory and method can be used to calculate entropy change in other molecular network.     

Entropy balance in distributed reversible Gray-Scott model

A practical way to calculate the entropy change in the distributed media composed of reversible Gray-Scott model is demonstrated. The entropy change is given as the sum of the entropy production and the divergence of entropy flow. The divergence of entropy is calculated based on the chemical potential of steady state. It becomes evident that: (i) the entropy change for the emergence of dissipative structures in the open system can be positive or negative, (ii) most of the entropy produced inside the system is thrown out to the environment when dissipative structures are developing, (iii) the entropy production and the divergence of entropy flow balance completely, when the system shows static steady states, (iv) the entropy change behaves as if it is the time derivative of the entropy production. Prior to these calculations of entropy balance, the features of emergent patterns in the two-dimensional system are examined in terms of entropy production solely. The results imply that the entropy production can be an index for us to discriminate spatial patterns, but is not a global thermodynamic potential for the evolution of dissipative structures.     

Entropy production and thermal conductivity of a dilute gas

It is known that the thermal conductivity of a dilute gas can be derived by using kinetic theory. We present here a new derivation by starting with two known entropy production principles: the steepest entropy ascent (SEA) principle and the maximum entropy production (MEP) principle. A remarkable feature of the new derivation is that it does not require the specification of the existence of the temperature gradient. The known result is reproduced in a similar form.     

Dynamics of Entropy Production Rate in Two Coupled Bosonic Modes Interacting with a Thermal Reservoir

The Markovian time evolution of the entropy production rate is studied as a measure of irreversibility generated in a bipartite quantum system consisting of two coupled bosonic modes immersed in a common thermal environment. The dynamics of the system is described in the framework of the formalism of the theory of open quantum systems based on completely positive quantum dynamical semigroups, for initial two-mode squeezed thermal states, squeezed vacuum states, thermal states and coherent states. We show that the rate of the entropy production of the initial state and nonequilibrium stationary state, and the time evolution of the rate of entropy production, strongly depend on the parameters of the initial Gaussian state (squeezing parameter and average thermal photon numbers), frequencies of modes, parameters characterising the thermal environment (temperature and dissipation coefficient), and the strength of coupling between the two modes. We also provide a comparison of the behaviour of entropy production rate and Rényi-2 mutual information present in the considered system.     

Entropy generation in radiative motion of tangent hyperbolic nanofluid in presence of activation energy and nonlinear mixed convection

In this communication, an optimization of entropy generation is performed through thermodynamics second law. Tangent hyperbolic nanomaterial model is used which describes the important slip mechanism namely Brownian and thermophoresis diffusions. MHD fluid is considered. The novel binary chemical reaction model is implemented to characterize the impact of activation energy. Nonlinear mixed convection, dissipation and Joule heating are considered. Appropriate similarity transformations are implemented to get the required coupled ODEs system. The obtained system is tackled for series solutions by homotopy method. Graphs are constructed to analyze the impact of different flow parameters on entropy number, nanoparticle volume concentration, temperature and velocity fields. Total entropy generation rate is calculated via various flow variables. It is noticed from obtained results that entropy number depend up thermal irreversibility, viscous dissipation and Joule heating irreversibility and concentration irreversibility. Decreasing behavior of concentration is witnessed for higher estimations of chemical reaction variable. Entropy number is more for higher Hartmann number, Weissenberg number and chemical reaction variable while contrast behavior is noted for Bejan number.     

不同目的热优化目标函数:热量传递势容损耗与熵产

热量传递势容(势容)反映了物体的导热能力,在导热过程中势容有损耗,对应于势容损耗最小的导热过程效率最高,传热速率最大。熵反映了过程的不可逆性,在导热过程中熵有增加(熵产),对应于熵产最小的过程是系统做有用功的能力((?))损失最小的过程。以势容损耗和熵产为目标函数,分别对导热平板和圆形导热管进行了导热优化计算。以势容损耗作为目标函数的优化,要求沿传热方向温度的梯度为常数,结果是系统具有最大的导热能力。以熵产作为目标函数的优化,要求沿传热方向温度的自然对数的梯度为常数,结果是系统具有最小的(?)损耗。     

Free energy and entropy production in planar Couette flow far from equilibrium

The macroscopic thermodynamic stability of a system of 108 diatomic molecules undergoing planar Couette flow far from equilibrium is reported. The system is perturbed from the steady state using a nondissipative variable colour field which induces a polarization in the system. It is found that the steady state for the system corresponds to an extremum in the generalized free energy and entropy production. However, while the free energy is always a minimum, the entropy production may be either a minimum or a maximum depending upon the direction of the colour field. These results, for a molecular system, are fundamentally different from those for an equivalent atomic system.     

Optimum design of infrared detector's micro-cooler with entropy generation minimization

In this paper, an optimization of Joule-Thomson micro coolers, used in the infrared detector is performed based on minimization of irreversibility. These types of coolers have various applications in many industrial and non-industrial devices. One of the major applications of these coolers is the micro cooling system in infrared detectors. In this paper, the considerable cooling system is divided into some layer, include of the hot gas layer, cold gas layer, the buffer layer, top layer and upper layer and each layer divided into some cell. Then the energy balance (include of convective heat transfer and enthalpy flow) was applied to each cell and set of governed equations was solved with the suitable method. The comparison of the current study with experimental results shows the good accuracy of performing modeling. In the next section, irreversibility analysis was performed and the total entropy generation rate was evaluated. In the last section, optimization of the considered system is performed for minimizing of entropy generation and volume.     

Entropy,information and Maxwell’s demon after quantum mechanics

The problem of the subjective nature of entropy and its relation to information and irreversibility is examined in the light of the quantum measurement problem. The main thesis of the paper is that state collapse during a measurement and hence entropy increase in the observed universe is seen by observers who are only able to observe a restricted manifold of states determined by their concepts, language, etc., in short by their level of perception. The thesis leads to the assertion that any universe with a structure must evolve.