On the rule of reversibility in channeling and blocking experiments

The macroscopic reversibility of the Fokker-Planck equation for charged particles in a crystal has been proven. It has been shown that at finite depths the reversibility rule fails because of a decrease of the particle transverse energy due to stopping.     

H-Theorems from Macroscopic Autonomous Equations

The H-theorem is an extension of the Second Law to a time-sequence of states that need not be equilibrium ones. In this paper we review and we rigourously establish the connection with macroscopic autonomy.If for a Hamiltonian dynamics for many particles, the macrostate evolves autonomously, then its entropy is non-decreasing as a consequence of Liouville's theorem. That observation, made since long, is here rigorously analyzed with special care to reconcile the application of Liouville's theorem (for a finite number of particles) with the condition of autonomous macroscopic evolution (sharp only in the limit of infinite scale separation); and to evaluate the presumed necessity of a semigroup property for the macroscopic evolution.     

Importance of reversibility in the quantum formalism

In this Letter I stress the role of causal reversibility (time symmetry), together with causality and locality, in the justification of the quantum formalism. First, in the algebraic quantum formalism, I show that the assumption of reversibility implies that the observables of a quantum theory form an abstract real C^{?} algebra, and can be represented as an algebra of operators on a real Hilbert space. Second, in the quantum logic formalism, I emphasize which axioms for the lattice of propositions (the existence of an orthocomplementation and the covering property) derive from reversibility. A new argument based on locality and Soler's theorem is used to derive the representation as projectors on a regular Hilbert space from the general quantum logic formalism. In both cases it is recalled that the restriction to complex algebras and Hilbert spaces comes from the constraints of locality and separability.     

The generalized theorem of reversibility in the optics of thin films

The author derives the generalized theorem of the reversibility of rays in thin films, based on the boundary conditions for the electromagnetic field vectors.     

Fluctuation theorem for stochastic systems

The fluctuation theorem describes the probability ratio of observing trajectories that satisfy or violate the second law of thermodynamics. It has been proved in a number of different ways for thermostatted deterministic nonequilibrium systems. In the present paper we show that the fluctuation theorem is also valid for a class of stochastic nonequilibrium systems. The theorem is therefore not reliant on the reversibility or the determinism of the underlying dynamics. Numerical tests verify the theoretical result.     

统计物理历史上的宏观不可逆性与微观可逆性之争

牛顿力学的时间可逆性与宏观热力学过程不可逆性的矛盾,很长时间以来一直是物理学和哲学中争论最多的问题之一．本文通过玻尔兹曼引入的H定理所引起的不可逆性之争,回顾了历史上关于这一问题的争论,并讨论了最近几十年关于这一问题研究的历史进展．在现代遍历性理论和混沌动力学的框架下,微观可逆与宏观不可逆之间的矛盾得到了很好的回答,并得到了很好的统一和解决.     

The universal macroscopic statistics and phase transitions of rank distributions

We establish a “Central Limit Theorem” for rank distributions, which provides a detailed characterization and classification of their universal macroscopic statistics and phase transitions. The limit theorem is based on the statistical notion of Lorenz curves, and is termed the “Lorenzian Limit Law” (LLL). Applications of the LLL further establish: (i) a statistical explanation for the universal emergence of Pareto’s law in the context of rank distributions; (ii) a statistical classification of universal macroscopic network topologies; (iii) a statistical classification of universal macroscopic socioeconomic states; (iv) a statistical classification of Zipf’s law, and a characterization of the “self-organized criticality” it manifests.     

The fluctuation–dissipation theorem

A system in equilibrium will in general exhibit microscopic fluctuations about the equilibrium state. The fluctuation–dissipation theorem relates the spectrum of these fluctuations to a solution of the macroscopic equation describing the approach to equilibrium from a non-equilibrium state. The aim here is to show exactly what the theorem is and how it is to be used. An account of the quantum version of the theorem is given in three parts, depending on the solution of the macroscopic equation used to express the fluctuations: the relaxation function, the response function or the Green function for continuous systems. Each part is illustrated with an example: charge fluctuations in an RLC circuit for the first two and electric field fluctuations in vacuum for the last.     

Irreversibility and nonrecurrence

Zermelo and Loschmidt pointed out that the equations of classical mechanics are recurrent and reversible, while those of macroscopic physics are non-recurrent and irreversible. These observations cast doubt on the possibility of deriving the macroscopic equations from classical mechanics. Therefore an example is presented to show that nonrecurrent equations can be derived from recurrent ones, and another example to show that irreversible equations can be derived from reversible ones. The irreversible equation derived in the second example describes either decaying, growing, or undamped motions, depending upon the initial conditions. Thus the specification of initial conditions introduces the irreversibility. These demonstrations may help to clarify previous resolutions of the recurrence and reversibility paradoxes.     

Fluctuation Theorem for Currents and Schnakenberg Network Theory

A fluctuation theorem is proved for the macroscopic currents of a system in a nonequilibrium steady state, by using Schnakenberg network theory. The theorem can be applied, in particular, in reaction systems where the affinities or thermodynamic forces are defined globally in terms of the cycles of the graph associated with the stochastic process describing the time evolution.     

A Nonequilibrium Extension of the Clausius Heat Theorem

We generalize the Clausius (in)equality to overdamped mesoscopic and macroscopic diffusions in the presence of nonconservative forces. In contrast to previous frameworks, we use a decomposition scheme for heat which is based on an exact variant of the Minimum Entropy Production Principle as obtained from dynamical fluctuation theory. This new extended heat theorem holds true for arbitrary driving and does not require assumptions of local or close to equilibrium. The argument remains exactly intact for diffusing fields where the fields correspond to macroscopic profiles of interacting particles under hydrodynamic fluctuations. We also show that the change of Shannon entropy is related to the antisymmetric part under a modified time-reversal of the time-integrated entropy flux.     

Near-field optical microscope image formation: a theoretical and experimental study

A quantitative comparison between theory and experiment has been carried out for a collection-mode near-field optical microscope. A 30-nm (lateral dimension) cylindrical dielectric sample was imaged. This image was compared with the result of theoretical calculations that used a classical macroscopic nonglobal model based on the excitation theorem. Good agreement was obtained, with image inversion, edge enhancement, and edge asymmetry correctly predicted.     

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.     

Central limit theorem for mixing quantum systems and the CCR-algebra of fluctuations

We analyse macroscopic fluctuations of an infinite quantum system and introduce the CCR-C*-algebra of normal fluctuations. A non-commutative central limit theorem for mixing quantum systems is proved.     

Surface polariton response function approach to dispersion forces between macroscopic bodies

A new method for the calculation of dispersion forces between macroscopic bodies is developed. The basis idea here is to use the surface polariton response function and the fluctuation-dissipation theorem.     

Fluctuations in the diffusion of particles in a non-uniform medium

We study the thermal fluctuations of density and flow velocity of particles diffusing in a non-uniform medium with memory character. The fluctuation spectra are derived from the macroscopic equations with the aid of the generalized Nyquist theorem. A comparison is made with other methods.     

Optics in spatially dispersive media: The energy theorem and the boundary conditions

The optics of spatially dispersive media is developed starting from a macroscopic material equation in differential form. The energy theorem is reformulated exhibiting the energy density, energy flux and the absorption density of polaritons. The 6 boundary conditions needed at an interface between to spatially dispersive media are derived.     

Kirchhoff-Planck law for freely radiating bodies and fluctuation-dissipation theorem

The interrelation between the Kirchhoff-Planck law (KPL) and the fluctuation-dissipation theorem (FDT) is discussed. It is known that the KPL is valid for freely radiating atoms if (i) the occupation probability of the atomic levels is the Boltzmann equilibrium probability and if (ii) the induced emission is treated as negative absorption. It is shown that the assumption (ii) is also inherent in the definition of the generalized susceptability. The susceptability is directly connected with the corresponding correlation function (FDT). It is proofed that the attached dipole fluctuation spectrum in its normally ordered form and the classical Maxwell equations reproduce the KPL. This result serves as the guideline for the extension of this procedure to macroscopic systems (susceptability ε (ω)). The theory can be used to describe radiative heat transfer in inhomogeneous systems. The validity of this macroscopic theory implies the same assumptions as the validity of the KPL for freely radiating atoms. The freely radiating dielectric half-space is treated as a simple example.