小系统的非平衡统计力学与随机热力学

热力学是一个古老的课题,古典热力学以宏观的具有大粒子数的系统为研究对象,自17世纪以来,科学家们构建了热力学的完备公理化体系。将热力学推广至小系统是近三十年来的研究前沿。文章介绍小系统的非平衡统计力学以及小系统的随机热力学。作为研究案例,利用时间依赖的谐振子势场控制单个粒子来构造随机热机的类卡诺循环,并发现该热机最大功率对应的效率等于1-,其中T_c和T_h分别对应于低温热库和高温热库的温度。     

Nonequilibrium thermodynamics of multicomponent systems

A general formalism of nonequilibrium thermodynamics of multicomponent fluids is given. Reversible parts of balance equations for the extensive variables are constructed in such a way that the growth rate of the extensive variables are related to their conjugate intensive parameters in an antisymmetric manner. This enables us to give the balance equation for the diffusional flow which plays an important role in the study of superfluidity and complex fluids.     

On Hamilton systems with even and odd poisson brackets

We present a new bound for the decay rate of a metastable state (in the context of the Fokker-Planck equation) and indicate circumstances under which this bound provides a good estimate. The estimate is used to study the conjectured relation =k Im F between decay rate and free energy analytic continuation. A counterexample as well as an explanation for the relation's usual validity are provided.     

Nonequilibrium thermodynamics of lasing and bistable optical systems

A simple model of nonlinear optical systems exhibiting instability—such as in laser action and in bistable absorption—is presented that provides a prototype of nonequilibrium thermodynamics on a statistical basis. The adiabatic reduction of the atomic degrees of freedom in a revised Langevin treatment establishes a fully consistent framework in which the active electromagnetic field mode is in contact with two thermal reservoirs (the cavity and the atoms) as well as being acted upon by an external field. The results are summarized by the first and second laws,dE=W+Q _c +Q _A anddS Q_c/¯T_c+Q_A/¯T_A, with the statistical mechanical representations of the entities therein exhibiting the nature of the mode; i.e., (a) a heat-engine structure operating between two reservoirs of temperatures¯T _c > 0 and¯T _A < 0 for the laser, and (b) a nonlinear response against external work balanced by a single reservoir (¯ T _c = ¯T _A ) for the absorptive bistability.Originally presented at the Taniguchi Symposium, October 1979.⁴⁴     

Nonequilibrium thermodynamics and fluctuation relations for small systems

In this review, we give a retrospect of the recent progress in nonequilibrium statistical mechanics and thermodynamics in small dynamical systems. For systems with only a few number of particles, fluctuations and nonlinearity become significant and contribute to the nonequilibrium behaviors of the systems, hence the statistical properties and thermodynamics should be carefully studied. We review recent developments of this topic by starting from the Gallavotti–Cohen fluctuation theorem, and then to the Evans–Searles transient fluctuation theorem, Jarzynski free-energy equality, and the Crooks fluctuation relation. We also investigate the nonequilibrium free energy theorem for trajectories involving changes of the heat bath temperature and propose a generalized free-energy relation. It should be noticed that the non-Markovian property of the heat bath may lead to the violation of the free-energy relation.     

On nonlinear irreversible processes II: The case of even and odd variables

The nonlinear generalization of the theory of Onsager and Machlup presented in a previous paper is extended to the case in which both of even and odd variables exist simultaneously.The generalization of Onsager's principle of least dissipation for the general nonlinear process is presented based on the diffusion and the semi-classical approximations.     

Nonequilibrium thermodynamics of spacetime

It has previously been shown that the Einstein equation can be derived from the requirement that the Clausius relation dS=deltaQ/T hold for all local acceleration horizons through each spacetime point, where is one-quarter the horizon area change in Planck units and deltaQ and T are the energy flux across the horizon and the Unruh temperature seen by an accelerating observer just inside the horizon. Here we show that a curvature correction to the entropy that is polynomial in the Ricci scalar requires a nonequilibrium treatment. The corresponding field equation is derived from the entropy balance relation dS=deltaQ/T+diS, where diS is a bulk viscosity entropy production term that we determine by imposing energy-momentum conservation. Entropy production can also be included in pure Einstein theory by allowing for shear viscosity of the horizon.     

Nonequilibrium evolution thermodynamics of vacancies

An alternative approach, nonequilibrium evolution thermodynamics, is compared with the classical Landau approach. A statistical justification of the approach is done with the help of a probability distribution function on an example of a solid with vacancies. Two kinds of kinetic equations are derived in terms of the internal energy and the modified free energy.     

Nonequilibrium thermodynamics of wealth condensation

We analyze wealth condensation for a wide class of stochastic economy models on the basis of the economic analog of thermodynamic potentials, termed transfer potentials. The economy model is based on three common transfers modes of wealth: random transfer, profit proportional to wealth and motivation of poor agents to work harder. The economies never reach steady state. Wealth condensation is the result of stochastic tunneling through a metastable transfer potential. In accordance with reality, both wealth and income distribution transiently show Pareto tails for high-income subjects. For metastable transfer potentials, exponential wealth condensation is a robust feature. For example with 10% annual profit 1% of the population owns 50% of the wealth after 50 years. The time to reach such a strong wealth condensation is a hyperbolic function of the annual profit rate.     

Chiral anomalies in even and odd dimensions

Odd dimensional Yang-Mills theories with an extra topological mass term, defined by the Chern-Simons secondary characteristic, are discussed. It is shown in detail how the topological mass affects the equal time charge commutation relations and how the modified commutation relations are related to non-abelian chiral anomalies in even dimensions. We also study the SU(3) chiral model (Wess-Zumino model) in four dimensions and we show how a gauge invariant interaction with an external SU(3) vector potential can be defined with the help of the Chern-Simons characteristic in five dimensions.     

Phase properties of odd and even circular states

Phase properties of the even and odd circular states are studied within the Hermitian phase formalism of Pegg and Barnett. Exact analytical formulas for the distribution function and the variance of the phase operator are obtained and used to examine whether or not the even and odd circular states exhibit photon-number squeezing and phase squeezing.     

Nonclassical properties of odd and even elliptical states

As a generalization of the optical circular states, elliptical states which are quantum superposition of coherent states on an ellipse in the α plane are constructed. The statistical properties of the states are investigated by using sub-Poissonian photon statistics, quadrature squeezing, Wigner function and phase distribution. It is shown that the elliptical states exhibit stronger quadrature squeezing. The interference fringes between the coherent states form the elliptic annuli of Fock states in the Wigner function picture. The phase distribution is no longer uniform as the circular states. An experimental scheme is proposed for generating equidistant coherent-state superpositions on an ellipse for the motion of the center of mass of a trapped ion.     

Quantum coherence between states with even and odd numbers of electrons

Systems with variable numbers of electrons are described in which the states representing coherent superpositions of states with even and odd numbers of electrons may occur. An experiment is suggested which generalizes the experiment of Nakamura et al. and may provide direct evidence of such coherence and, thereby, justify the reality of a superspace.     

Nonequilibrium thermodynamics of nonisothermal activation: Escape over mesoscopic barriers: I. The stochastic process

It is argued that in noisy “macroscopic” systems (e.g. Josephson junctions) the effective potential for the pertinent degree of freedom (e.g. the magnetic flux) generally depends on the specimen's - local - temperature and, hence, that it should be given a thermodynamical (rather than the usual mechanical) significance. A Brownian motion theory of the ensuing nonequilibrium thermodynamics will be presented, which generalizes Kramers' model for thermal activation to include nonisothermal effects. Inter alia it is shown how in the steady state the thermodynamic fluctuation potential (the “availability”) arises as the natural generalization of either the Gibbs or the Helmholtz free energy.     

奇偶相干态的SU2变换

本文以奇偶相干态为基矢,通过SU_2变换,构造了a~2的各正交归一本征态组,并讨论了它们的非经典效应与SU_2群参数的关系.     

双曲正弦、余弦算符与奇偶相干态

利用Fock空间的平移算符引入了双曲正弦和余弦算符,该算符作用在真空态上给出奇相干态和偶相干态的一种新表示形式,并讨论了奇、偶相干态的准概率分布函数和非经典特性．     

偶奇相干态的q-类比

在偶奇相干态的基础上,构造出偶、奇q-相干态,并讨论了它们的光统计特性.计算分析表明:偶奇q-相干态的光统计特性,是完全不相同的.     

The even and odd supersymmetric Hunter-Saxton and Liouville equations

It is shown that two different supersymmetric extensions of the Harry Dym equation lead to two different negative hierarchies of the supersymmetric integrable equations. While the first one yields the known even supersymmetric Hunter-Saxton equation, the second one is a new odd supersymmetric Hunter-Saxton equation. It is further proved that these two supersymmetric extensions of the Hunter-Saxton equation are reciprocally transformed to two different supersymmetric extensions of the Liouville equation.     

Intrinsic excitonic luminescence in odd and even numbered oligothiophenes

The emission properties of crystalline oligothiophenes (OTs) are investigated and related to the different selection rules arising from the number of rings. In odd OT crystals the purely electronic emission is absent since the molecular A1-1B(1) transition dipoles cancel at the bottom of the excitonic band. On the contrary, in crystals of even OTs this transition is allowed due to the constructive interference of the off-axis components of the molecular transition dipole. It possesses a polarization in the herringbone plane and exhibits superradiant behavior.     

Classification of the Yang-Mills anomalies in even and odd dimension

The general solution to the Wess-Zumino consistency equation is constructed. It does not depend on the antighost, nor on the sources, but only on the gauge and ghost fields through the geometrical combination $\text{A}\text{?}\text{= A}{}_{\mathrm{\mu }}\text{d}\text{x}{}^{\mathrm{\mu }}\text{+c}$. In dimension d, the anomalies with ghost number g are related to the off-BRS (d+s)-closed exterior forms $\text{I(}\text{A}\text{?}\text{, F)}$, of degree d + g + 1 and at most g-linear in $\text{A}\text{?}\text{.}$