Positivity of Entropy Production

We discuss the positivity of the mean entropy production for stochastic systems driven from equilibrium, as it was defined in refs. 7 and 8. Non-zero entropy production is closely linked with violation of the detailed balance condition. This connection is rigorously obtained for spinflip dynamics. We remark that the positivity of entropy production depends on the choice of time-reversal transformation, hence on the choice of the dynamical variables in the system of interest.     

Quantum entropy production as a measure of irreversibility

We consider conservative quantum evolutions possibly interrupted by macroscopic measurements. When started in a nonequilibrium state, the resulting path-space measure is not time-reversal invariant and the weight of time-reversal breaking equals the exponential of the entropy production. The mean entropy production can then be expressed via a relative entropy on the level of histories. This gives a partial extension of the result for classical systems, that the entropy production is given by the source term of time-reversal breaking in the path-space measure.     

Hurst-Kolmogorov dynamics as a result of extremal entropy production

It is demonstrated that extremization of entropy production of stochastic representations of natural systems, performed at asymptotic times (zero or infinity) results in constant derivative of entropy in logarithmic time and, in turn, in Hurst-Kolmogorov processes. The constraints used include preservation of the mean, variance and lag-1 autocovariance at the observation time step, and an inequality relationship between conditional and unconditional entropy production, which is necessary to enable physical consistency. An example with real world data illustrates the plausibility of the findings.     

Evolution of entropy in the Gay-Lussac experiment

Local entropy conservation is closely connected with the existence of an adiabatic invariant. As a particular case the Gay-Lussac experiment is analyzed. No entropy production takes place before the gas has reached the opposite wall. Subsequent shock formation strongly violates the adiabatic invariant, thus triggering intense entropy increase at standard densities. In the case of infinite mean free path the gas indefinitely persists in a state of constant entropy.     

熵产生率公式及其应用

导出了6N维和6维相空间的熵产生率，即熵增加定律的一个统计公式：P=kD(Δ_{qθ)²，即熵产生率P等于扩散系数D、离开平衡率θ的空间梯度平方的平均值与Boltzm ann常数k 三者之乘积.指明非平衡系统的宏观熵产生是由其微观状态数密度在空间随机地不均匀离开 平衡引起的.作为公式的应用,研究了气体自由膨胀、布朗运动及固体变形和断裂三个非平衡 态课题，给出了它们的熵产生及其一次和二次时间变化率，得到了不可逆过程的系统内对应 的微观结构变化是不均匀的推论.进而导 关键词： 熵产生率 微观状态数密度 离开平衡率 随机扩散}     

A Scheme for Information Erasure in a Double-Well Potential

We design an experimental scheme to realize one-bit information erasure and restoring processes by considering an overdamped colloidal particle in a double-well optical trap, which is added by a controllable laser tweezer. Using the Monte Carlo method, we simulate numerically the Langevin equation to calculate the mean work spent during the entire process and validate the entropy production fluctuation theory. Our result shows that the distribution of entropy production becomes narrow with increasing temperature and becomes stationary, represents the diminishing extent of irreversibility.     

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.     

Quantum transmission processes and their entropies

In classical information theory, one of the most important theorems are the coding theorems, which were discussed by calculating the mean entropy and the mean mutual entropy defined by the classical dynamical entropy (Kolmogorov-Sinai). The quantum dynamical entropy was first studied by Emch [13] and Connes-Stormer [11]. After that, several approaches for introducing the quantum dynamical entropy are done [10, 3, 8, 39, 15, 44, 9, 27, 28, 2, 19, 45]. The efficiency of information transmission for the quantum processes is investigated by using the von Neumann entropy [22] and the Ohya mutual entropy [24]. These entropies were extended to S- mixing entropy by Ohya [26, 27] in general quantum systems. The mean entropy and the mean mutual entropy for the quantum dynamical systems were introduced based on the S- mixing entropy. In this paper, we discuss the efficiency of information transmission to calculate the mean mutual entropy with respect to the modulated initial states and the connected channel for the quantum dynamical systems.     

Impacts of Uniform Magnetic Field and Internal Heated Vertical Plate on Ferrofluid Free Convection and Entropy Generation in a Square Chamber

The heat transfer enhancement and fluid flow control in engineering systems can be achieved by addition of ferric oxide nanoparticles of small concentration under magnetic impact. To increase the technical system life cycle, the entropy generation minimization technique can be employed. The present research deals with numerical simulation of magnetohydrodynamic thermal convection and entropy production in a ferrofluid chamber under the impact of an internal vertical hot sheet. The formulated governing equations have been worked out by the in-house program based on the finite volume technique. Influence of the Hartmann number, Lorentz force tilted angle, nanoadditives concentration, dimensionless temperature difference, and non-uniform heating parameter on circulation structures, temperature patterns, and entropy production has been scrutinized. It has been revealed that a transition from the isothermal plate to the non-uniformly warmed sheet illustrates a rise of the average entropy generation rate, while the average Nusselt number can be decreased weakly. A diminution of the mean entropy production strength can be achieved by an optimal selection of the Lorentz force tilted angle.     

冷库预冷流动传热物理场分布研究

冷库预冷是传统的果蔬采后预冷方法,前人研究通过数值模拟使冷库预冷过程的流场和温度场可视化,本文进一步分析空气流速、局部平均空气龄、温度、熵产、?损和(煨)耗散等物理场的分布特性,指出其间存在密切联系.塑料筐周围的空气流速和流向与内部的局部平均空气龄有关,并影响内部的传热速率.传热熵产率、传热?损率和(煨)耗散率的分布特...     

Entropy Production in Exactly Solvable Systems

The rate of entropy production by a stochastic process quantifies how far it is from thermodynamic equilibrium. Equivalently, entropy production captures the degree to which global detailed balance and time-reversal symmetry are broken. Despite abundant references to entropy production in the literature and its many applications in the study of non-equilibrium stochastic particle systems, a comprehensive list of typical examples illustrating the fundamentals of entropy production is lacking. Here, we present a brief, self-contained review of entropy production and calculate it from first principles in a catalogue of exactly solvable setups, encompassing both discrete- and continuous-state Markov processes, as well as single- and multiple-particle systems. The examples covered in this work provide a stepping stone for further studies on entropy production of more complex systems, such as many-particle active matter, as well as a benchmark for the development of alternative mathematical formalisms.     

Symmetry of the Linearized Boltzmann Equation II

This is the second part of the study by the author on the symmetry of the linearized Boltzmann equation. The issue of the present part is the entropy production and the Onsager–Casimir reciprocity relation in the steady non-equilibrium systems. After the discussions on the definition of the entropy, entropy flow, and entropy production in the non-equilibrium gas systems, the expression of the entropy production in the steady state is presented. Then, for the systems weakly perturbed from a uniform equilibrium state, the entropy production is shown to be expressed in terms of the solution of the linearized Boltzmann equation. The thermodynamic forces and fluxes and the kinetic coefficients are defined solely from the expression of the entropy production. The conventional-type Onsager–Casimir relation is shown to hold for the entire range of the Knudsen number in bounded- and unbounded-domain systems, provided that the state of the gas in a far field is a local Maxwellian satisfying the Boltzmann equation for the latter. As to the other unbounded-domain systems, a nonconventional reciprocity is shown to hold.     

The Role of the Total Entropy Production in the Dynamics of Open Quantum Systems in Detection of Non-Markovianity

The interaction between system and environment is a fundamental concept in the theory of open quantum systems. As a result of the interaction, an amount of correlation (both classical and quantum) emerges between the system and the environment. In this work, we recall the quantity that will be very useful to describe the emergence of the correlation between the system and the environment, namely, the total entropy production. Appearance of total entropy production is due to the entanglement production between the system and the environment. In this work, we discuss about the role of the total entropy production for detecting the non-Markovianity. By utilizing the relation between the total entropy production and total correlation between subsystems, one can see a temporary decrease of total entropy production is a signature of non-Markovianity. We apply our criterion for the special case, where the composite system has initial correlation with environment.     

Information entropy of a dynamical system driven by quasimonochromatic noise

This paper shows the Fokker-Planck equation of a dynamical system driven by quasimonochromatic noise. Based on the Fokker-Planck equation and the definition of Shannon's information entropy, the exact time dependence of entropy flux and entropy production for the system is calculated. The relationship between the properties of quasimonochromatic noise and dissipative parameter and their effects on entropy flux and entropy production are discussed.     

A decomposed equation for local entropy and entropy production in volume-preserving coarse-grained systems

In this study an equation for the local entropy is derived based on the formulation of a master equation and is applied to volume-preserving maps. The equation consists of the following terms: unsteady, convection, diffusion, probability-weighted phase space volume expansion rate, nonnegative entropy production, and residuals. The decomposition makes it possible to evaluate entropy production in terms of microscopic dynamics and is expected to be applicable to many coarse-grained systems on the phase space. When it is applied to two volume-preserving multibaker chain systems it is confirmed that the summation of the nonnegative entropy production on each site numerically coincides with the entropy production introduced by Gilbert et al. [T. Gilbert, J.R. Dorfman, P. Gaspard, Entropy production, fractals, and relaxation to equilibrium, Phys. Rev. Lett. 85 (2000) 1606-1609] and the phenomenological expression both in nonequilibrium steady and unsteady states. The coincidence is brought about by the fact that the residual terms vanish in the thermodynamic limit when they are integrated on each site. It follows that the entropy production is dominated by the nonnegative entropy production term and becomes positive in nonequilibrium states.     

Entropy Production in Nonlinear,Thermally Driven Hamiltonian Systems

We consider a finite chain of nonlinear oscillators coupled at its ends to two infinite heat baths which are at different temperatures. Using our earlier results about the existence of a stationary state, we show rigorously that for arbitrary temperature differences and arbitrary couplings, such a system has a unique stationary state. (This extends our earlier results for small temperature differences.) In all these cases, any initial state will converge (at an unknown rate) to the stationary state. We show that this stationary state continually produces entropy. The rate of entropy production is strictly negative when the temperatures are unequal and is proportional to the mean energy flux through the system     

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.     

非平衡热力学中传热过程熵产表达式的修正

熵产是非平衡热力学中的核心物理量,传统上表示为广义力(驱动力)与广义流的乘积.这种表达存在两方面缺陷:一是广义力与广义流的拆分具有任意性;更重要的是,以其计算热波传递时熵产可以为负值,从而违反热力学第二定律.本文基于热质理论分析表明,传热过程的熵产实质上是由热质流体的热质能耗散引起的,所以熵产中的力不是驱动力而是阻力,并且具有力的量纲.由此提出的熵产修正表达式,不仅在计算热波传递过程中熵产恒为正值,与扩展不可逆热力学中的熵产表达式一致,而且不存在力和流拆分的任意性.     

Generalized thermostatistics based on the Sharma-Mittal entropy and escort mean values

A generalized thermostatistics is developed for an entropy measure introduced by Sharma and Mittal. A maximum-entropy scheme involving the maximization of the Sharma and Mittal entropy under appropriate constraints expressed as escort mean values is advanced. Maximum-entropy distributions exhibiting a power law behavior in the asymptotic limit are obtained. Thus, results previously derived for the Renyi entropy and the Tsallis entropy are generalized. In addition, it is shown that for almost deterministic systems among all possible composable entropies with kernels that are described by power laws the Sharma-Mittal entropy is the only entropy measure that gives rise to a thermostatistics based on escort mean values and admitting of a partition function. Received 27 June 2002 Published online 31 December 2002