计入固液界面作用的润滑热力学模型与分析

摩擦与润滑过程是典型的能量耗散过程, 在机理上与非平衡热力学中的熵增、耗散结构等理论颇有相似之处. 通过热力学分析可以对一些典型的摩擦磨损过程做出合理的机理揭示与推测. 本文利用热力学理论对典型的润滑过程进行了建模分析. 采用分离压模型表征和计入了微尺度下的固液界面作用, 揭示分析了润滑热力学模型与润滑状态Stribeck曲线的联系. 从分析计算结果来看, 润滑Stribeck曲线的摩擦系数最低点与系统热力学上的熵增率最低点具有相当好的对应关系, 而润滑状态从弹流润滑向薄膜润滑的转变过程, 可以用耗散结构理论加以机理解释. 文中的热力学模型和方法能够有效地体现出润滑过程中多物理要素跨尺度非线性耦合的作用, 对实际工程与实验有着重要的指导作用.     

Nonequilibrium quantum impurities: from entropy production to information theory

Nonequilibrium steady-state currents, unlike their equilibrium counterparts, continuously dissipate energy into their physical surroundings leading to entropy production and time-reversal symmetry breaking. This Letter discusses these issues in the context of quantum impurity models. We use simple thermodynamic arguments to define the rate of entropy production sigma and show that sigma has a simple information-theoretic interpretation in terms of nonequilibrium distribution functions. This allows us to show that the entropy production is strictly positive for any nonequilibrium steady state. We conclude by applying these ideas to the resonance level model and the Kondo model.     

Effects of Gaussian thermal fluctuations on the thermodynamic of microtubules in Landau-Ginzburg-Wilson model

This paper investigates microtubule thermodynamic properties dependence on gaussian thermal fluctuations using the Landau-Ginzburg-Wilson model. After solving the self-consistent equation for thermal fluctuations, we observed its increasing behavior as a function of temperature for different dimensionality 1, 2 and 3. Thermodynamic properties such as Shannon entropy, thermodynamic entropy, heat capacity and chemical potential have been computed. We found out that under thermal fluctuations, heat capacity and chemical potential exhibit negative values that can refer to the coexistence of first and second order phase transitions during MT dynamic instability. We also found that thermodynamic properties are highly affected at low temperatures. Moreover, thermodynamic entropy locally displays the conversion of the heat into work through the negentropy. We analyzed the behavior of the polarization according to fluctuations and found that thermal fluctuations modulate the polarization and depolarization of tubulin dimers which is very important in information processing in microtubules.     

Thermodynamics based on the principle of least abbreviated action: Entropy production in a network of coupled oscillators

We present some novel thermodynamic ideas based on the Maupertuis principle. By considering Hamiltonians written in terms of appropriate action-angle variables we show that thermal states can be characterized by the action variables and by their evolution in time when the system is nonintegrable. We propose dynamical definitions for the equilibrium temperature and entropy as well as an expression for the nonequilibrium entropy valid for isolated systems with many degrees of freedom. This entropy is shown to increase in the relaxation to equilibrium of macroscopic systems with short-range interactions, which constitutes a dynamical justification of the Second Law of Thermodynamics. Several examples are worked out to show that this formalism yields the right microcanonical (equilibrium) quantities. The relevance of this approach to nonequilibrium situations is illustrated with an application to a network of coupled oscillators (Kuramoto model). We provide an expression for the entropy production in this system finding that its positive value is directly related to dissipation at the steady state in attaining order through synchronization.     

Econophysics and the Entropic Foundations of Economics

This paper examines relations between econophysics and the law of entropy as foundations of economic phenomena. Ontological entropy, where actual thermodynamic processes are involved in the flow of energy from the Sun through the biosphere and economy, is distinguished from metaphorical entropy, where similar mathematics used for modeling entropy is employed to model economic phenomena. Areas considered include general equilibrium theory, growth theory, business cycles, ecological economics, urban–regional economics, income and wealth distribution, and financial market dynamics. The power-law distributions studied by econophysicists can reflect anti-entropic forces is emphasized to show how entropic and anti-entropic forces can interact to drive economic dynamics, such as in the interaction between business cycles, financial markets, and income distributions.     

Entropy, entropy flux and entropy rate of granular materials

The aim of this work is to analyze the entropy, entropy flux and entropy rate of granular materials within the frameworks of the Boltzmann equation and continuum thermodynamics. It is shown that the entropy inequality for a granular gas that follows from the Boltzmann equation differs from the one of a simple fluid due to the presence of a term which can be identified as the entropy density rate. From the knowledge of a non-equilibrium distribution function-valid for processes closed to equilibrium-it is obtained that the entropy density rate is proportional to the internal energy density rate divided by the temperature, while the entropy flux is equal to the heat flux vector divided by the temperature. A thermodynamic theory of a granular material is also developed whose objective is the determination of the basic fields of mass density, momentum density and internal energy density. The constitutive laws are restricted by the principle of material frame indifference and by the entropy principle. Through the exploitation of the entropy principle with Lagrange multipliers, it is shown that the results obtained from the kinetic theory for granular gases concerning the entropy density rate and entropy flux are valid in general for processes close to equilibrium of granular materials, where linearized constitutive equations hold.     

Ground-state energy and entropy of the two-dimensional Edwards-Anderson spin-glass model with different bond distributions

We study the two-dimensional Edwards-Anderson spin-glass model using a parallel tempering Monte Carlo algorithm. The ground-state energy and entropy are calculated for different bond distributions. In particular, the entropy is obtained by using a thermodynamic integration technique and an appropriate reference state, which is determined with the method of high-temperature expansion. This strategy provides accurate values of this quantity for finite-size lattices. By extrapolating to the thermodynamic limit, the ground-state energy and entropy of the different versions of the spin-glass model are determined.     

Entropy production in nonequilibrium systems at stationary states

We present a stochastic approach to nonequilibrium thermodynamics based on the expression of the entropy production rate advanced by Schnakenberg for systems described by a master equation. From the microscopic Schnakenberg expression we get the macroscopic bilinear form for the entropy production rate in terms of fluxes and forces. This is performed by placing the system in contact with two reservoirs with distinct sets of thermodynamic fields and by assuming an appropriate form for the transition rate. The approach is applied to an interacting lattice gas model in contact with two heat and particle reservoirs. On a square lattice, a continuous symmetry breaking phase transition takes place such that at the nonequilibrium ordered phase a heat flow sets in even when the temperatures of the reservoirs are the same. The entropy production rate is found to have a singularity at the critical point of the linear-logarithm type.     

Susceptible-infected-recovered epidemics in populations with heterogeneous contact rates

Heterogeneity of contact patterns is recognized as an important feature for realistic modeling of many epidemics. During an outbreak, the frequency of contacts can vary a great deal from person to person and period to period. Contact heterogeneity has been shown to have a large impact on epidemic thresholds and the final size of epidemics. We develop and apply a model which incorporates an arbitrary distribution of contact rates. The model consists of a low-dimensional system of ordinary differential equations which incorporates arbitrary heterogeneity by making use of generating functions of the contact rate distribution. We show further how this model can be applied to the study of simple intervention strategies, such as quarantine of public venues with probability proportional to size. The dynamic model allows us to investigate the effects of gradually implementing such strategies in response to an ongoing epidemic, and we investigate these strategies using data on the contact patterns within a large US city.     

TOLOMEO,a Novel Machine Learning Algorithm to Measure Information and Order in Correlated Networks and Predict Their State

We present ToloMEo (TOpoLogical netwOrk Maximum Entropy Optimization), a program implemented in C and Python that exploits a maximum entropy algorithm to evaluate network topological information. ToloMEo can study any system defined on a connected network where nodes can assume N discrete values by approximating the system probability distribution with a Pottz Hamiltonian on a graph. The software computes entropy through a thermodynamic integration from the mean-field solution to the final distribution. The nature of the algorithm guarantees that the evaluated entropy is variational (i.e., it always provides an upper bound to the exact entropy). The program also performs machine learning, inferring the system’s behavior providing the probability of unknown states of the network. These features make our method very general and applicable to a broad class of problems. Here, we focus on three different cases of study: (i) an agent-based model of a minimal ecosystem defined on a square lattice, where we show how topological entropy captures a crossover between hunting behaviors; (ii) an example of image processing, where starting from discretized pictures of cell populations we extract information about the ordering and interactions between cell types and reconstruct the most likely positions of cells when data are missing; and (iii) an application to recurrent neural networks, in which we measure the information stored in different realizations of the Hopfield model, extending our method to describe dynamical out-of-equilibrium processes.     

MaxEnt and dynamical information

The presence of a quantum critical point can significantly affect the thermodynamic properties of a material at finite temperatures. This is reflected, e.g., in the entropy landscape S(T, c) in the vicinity of a quantum critical point, yielding particularly strong variations for varying the tuning parameter c such as magnetic field. In this work we have studied the thermodynamic properties of the quantum compass model in the presence of a transverse field. The specific heat, entropy and cooling rate under an adiabatic demagnetization process have been calculated. During an adiabatic (de)magnetization process temperature drops in the vicinity of a field-induced zero-temperature quantum phase transitions. However close to field-induced quantum phase transitions we observe a large magnetocaloric effect.     

Derivation of reference distribution functions for Tokamak-plasmas by statistical thermodynamics

A general approach for deriving the expression of reference distribution functions by statistical thermodynamics is illustrated, and applied to the case of a magnetically confined plasma. The local equilibrium is defined by imposing the minimum entropy production, which applies only to the linear regime near a stationary thermodynamically non-equilibrium state and the maximum entropy principle under the scale invariance restrictions. This procedure may be adopted for a system subject to an arbitrary number of thermodynamic forces, however, for concreteness, we analyze, afterwords, a magnetically confined plasma subject to three thermodynamic forces, and three energy sources: (i) the total Ohmic heat, supplied by the transformer coil; (ii) the energy supplied by neutral beam injection (NBI); and (iii) the RF energy supplied by ion cyclotron resonant heating (ICRH) system which heats the minority population. In this limit case, we show that the derived expression of the distribution function is more general than that one, which is currently used for fitting the numerical steady-state solutions obtained by simulating the plasma by gyro-kinetic codes. An application to a simple model of fully ionized plasmas submitted to an external source is discussed. Through kinetic theory, we fixed the values of the free parameters linking them with the external power supplies. The singularity at low energy in the proposed distribution function is related to the intermittency in the turbulent plasma.     

Reissner-Nordstrom几何中标量场的统计熵与能斯特定理

从Reissner-Nordstrom时空背景下的Klein-Gordon方程出发,利用改进的brick-wall方法膜模型,计算黑洞背景下标量场的自由能和熵.得到标量场的熵是由两部分组成的,根据熵是广延量的性质,得到黑洞熵是由两个子热力学系统贡献的.在此基础上给出了新的Bekenstein-Smarr公式.结果表明,用两个子热力学系统表达的熵,当黑洞的辐射温度趋于绝对零度时,黑洞的熵也趋于零,它满足能斯特定理,可视为黑洞的普朗克绝对熵. 关键词： brick-wall方法 膜模型 黑洞熵 能斯特定理     

Calibration Invariance of the MaxEnt Distribution in the Maximum Entropy Principle

The maximum entropy principle consists of two steps: The first step is to find the distribution which maximizes entropy under given constraints. The second step is to calculate the corresponding thermodynamic quantities. The second part is determined by Lagrange multipliers’ relation to the measurable physical quantities as temperature or Helmholtz free energy/free entropy. We show that for a given MaxEnt distribution, the whole class of entropies and constraints leads to the same distribution but generally different thermodynamics. Two simple classes of transformations that preserve the MaxEnt distributions are studied: The first case is a transform of the entropy to an arbitrary increasing function of that entropy. The second case is the transform of the energetic constraint to a combination of the normalization and energetic constraints. We derive group transformations of the Lagrange multipliers corresponding to these transformations and determine their connections to thermodynamic quantities. For each case, we provide a simple example of this transformation.     

Does a Computer Have an Arrow of Time?

Schulman (Entropy 7(4):221–233, 2005) has argued that Boltzmann’s intuition, that the psychological arrow of time is necessarily aligned with the thermodynamic arrow, is correct. Schulman gives an explicit physical mechanism for this connection, based on the brain being representable as a computer, together with certain thermodynamic properties of computational processes. Hawking (Physical Origins of Time Asymmetry, Cambridge University Press, Cambridge, 1994) presents similar, if briefer, arguments. The purpose of this paper is to critically examine the support for the link between thermodynamics and an arrow of time for computers. The principal arguments put forward by Schulman and Hawking will be shown to fail. It will be shown that any computational process that can take place in an entropy increasing universe, can equally take place in an entropy decreasing universe. This conclusion does not automatically imply a psychological arrow can run counter to the thermodynamic arrow. Some alternative possible explanations for the alignment of the two arrows will be briefly discussed.     

Magnetotransport in simple metals. An exactly soluble model

The magnetoconductivity tensors of a metal with a weakly anisotropic Fermi surface are determined from analytic solutions to the Boltzmann equation without any restrictions on the magnitude of the cyclotron frequency compared to the collision rate. Results are given for both a two- and a three-dimensional model, the former being analytically simpler to handle. The Hall coefficient and magnetoresistance are obtained as functions of the magnetic field, and we show by explicit calculation how the thermoelectric coefficients at high magnetic fields are determined by the thermodynamic entropy.     

Quantum Transport of Particles and Entropy

A unified view on macroscopic thermodynamics and quantum transport is presented. Thermodynamic processes with an exchange of energy between two systems necessarily involve the flow of other balancable quantities. These flows are first analyzed using a simple drift-diffusion model, which includes the thermoelectric effects, and connects the various transport coefficients to certain thermodynamic susceptibilities and a diffusion coefficient. In the second part of the paper, the connection between macroscopic thermodynamics and quantum statistics is discussed. It is proposed to employ not particles, but elementary Fermi- or Bose-systems as the elementary building blocks of ideal quantum gases. In this way, the transport not only of particles but also of entropy can be derived in a concise way, and is illustrated both for ballistic quantum wires, and for diffusive conductors. In particular, the quantum interference of entropy flow is in close correspondence to that of electric current.