Algebraical Entropy and Arrow of Time

Usually, it is supposed that irreversibility of time appears only in macrophysics. Here, we attempt to introduce the microphysical arrow of time assuming that at a fundamental level nature could be non-associative. Obtaining numerical results of a measurement, which requires at least three ingredients: object, device and observer, in the non-associative case depends on ordering of operations and is ambiguous. We show that use of octonions as a fundamental algebra, in any measurement, leads to generation of unavoidable 18.6 bit relative entropy of the probability density functions of the active and passive transformations, which correspond to the groups G2 and SO(7), respectively. This algebraical entropy can be used to determine the arrow of time, analogically as thermodynamic entropy does.     

Time-Reversal, Irreversibility and Arrow of Time in Quantum Mechanics

The aim of this paper is to analyze time-asymmetric quantum mechanics with respect of its validity as a non time-reversal invariant, time-asymmetric theory as well as of its ability to determine an arrow of time.     

Causal Paradoxes: A Conflict Between Relativity and the Arrow of Time

It is often argued that superluminal velocities and nontrivial space-time topologies, allowed by the theory of relativity, may lead to causal paradoxes. By emphasizing that the notion of causality assumes the existence of a time arrow (TA) that points from the past to the future, the apparent paradoxes appear to be an artefact of the wrong tacit assumption that the relativistic coordinate TA coincides with the physical TA. The latter should be identified with the thermodynamic TA, which, by being absolute and irrotational, does not lead to paradoxes.     

Time Travel and the Reality of Spontaneity

Contrary to the informed consensus, time travel implies spontaneity (as distinct from chance) so that time travel can only be of the second kind.A preliminary version of this paper was presented at a Seminar on ‘Reality in Physics and Philosophy,’ S. N. Bose National Centre for the Basic Sciences, Calcutta, 24-25, Feb 1996.     

The Direction of Time: From the Global Arrow to the Local Arrow

In this paper we discuss the traditional approaches to the problem of the arrow of time. On the basis of this discussion we adopt a global and nonentropic approach, according to which the arrow of time has a global origin and is an intrinsic, geometrical feature of space-time. Finally, we show how the global arrow is translated into local terms as a local time-asymmetric flux of energy.     

Deterministic quantum evolution through modification of the hypotheses of statistical mechanics

It is claimed that for all apparatus capable of performing macroscopic measurements of microscopic systems there exist special internal states for which deterministic quantum evolution alone yields a particular macroscopic outcome rather than a superposition of macroscopically distinct outcomes. We maintain that these special states are distributed uniformly (in a certain sense) among the set of all states. It is hypothesized that for all actually performed experiments the initial conditions lie among the special states. We postulate that in the absence of precise information on apparatus initial conditions one should give equal weight to those microstates that are consistent with the macroscopic stateand are special in the sense used above. Evidence is presented for this postulate's recovering the usual quantum probabilities. This theory is fully deterministic, has no collapsing wave functions, and offers a resolution of the quantum measurement problem through a revision of the usual statistical mechanical handling of initial conditions. It requires a single wave function for the entire universe and an all encompassing conspiracy to arrange the right sort of special wave function for each experiment. In other words, an apparatus is in an appropriate microstate for the experiment that will actually happen even if an ostensibly random process is used to determine that experiment from among apparent alternatives. Although we do not provide physical or philosophical justification for our central hypothesis, some perspective is given by examining the notions implicit in the usual principles of thermodynamics.     

A set of Boussinesq-type equations for interfacial internal waves in two-layer stratified fluid

Many new forms of Boussinesq-type equations have been developed to extend the range of applicability of the classical Boussinesq equations to deeper water in the study of the surface waves. One approach was used by Nwogu (1993. J. Wtrw. Port Coastal and Oc. Eng. 119, 618--638) to improve the linear dispersion characteristics of the classical Boussinesq equations by using the velocity at an arbitrary level as the velocity variable in derived equations and obtain a new form of Boussinesq-type equations, in which the dispersion property can be optimized by choosing the velocity variable at an adequate level. In this paper, a set of Boussinesq-type equations describing the motions of the interfacial waves propagating alone the interface between two homogeneous incompressible and inviscid fluids of different densities with a free surface and a variable water depth were derived using a method similar to that used by Nwogu (1993. J. Wtrw. Port Coastal and Oc. Eng. 119, 618--638) for surface waves. The equations were expressed in terms of the displacements of free surface and density-interface, and the velocity vectors at arbitrary vertical locations in the upper layer and the lower layer (or depth-averaged velocity vector across each layer) of a two-layer fluid. As expected, the equations derived in the present work include as special cases those obtained by Nwogu (1993, J. Wtrw. Port Coastal and Oc. Eng. 119, 618-638) and Peregrine (1967, J. Fluid Mech. 27, 815-827) for surface waves when the density of the upper fluid is taken as zero.     

The Distance Modulus Determined from Carmeli’s Cosmology Fits the Accelerating Universe Data of the High-redshift Type Ia Supernovae Without Dark Matter

The velocity of the Hubble expansion has been added to General Relativity by Moshe Carmeli and this resulted in new equations of motion for the expanding universe. For the first time the observational magnitude–redshift data derived from the high-z supernova teams has been analysed in the framework of the Carmeli theory and the fit to that theory is achieved without the inclusion of any dark matter. Best fits to the data yield an averaged matter density for the universe at the present epoch Ω_m ≈ 0.021, which falls well within the measured values of the baryonic matter density. And the best estimate of Ω_Λ+ Ω_m ≈ 1.021 at the present epoch. The analysis also clearly distinguishes that the Hubble expansion of the universe is speed-limited.     

The Matter of Time

About a century ago, in the spirit of ancient atomism, the quantum of light was renamed the photon to suggest that it is the fundamental element of everything. Since the photon carries energy in its period of time, a flux of photons inexorably embodies a flow of time. Thus, time comprises periods as a trek comprises legs. The flows of quanta naturally select optimal paths (i.e., geodesics) to level out energy differences in the least amount of time. The corresponding flow equations can be written, but they cannot be solved. Since the flows affect their driving forces, affecting the flows, and so on, the forces (i.e., causes) and changes in motions (i.e., consequences) are inseparable. Thus, the future remains unpredictable. However, it is not all arbitrary but rather bounded by free energy. Eventually, when the system has attained a stationary state where forces tally, there are no causes and no consequences. Since there are no energy differences between the system and its surroundings, the quanta only orbit on and on. Thus, time does not move forward either but circulates.     

On the Algebra of Arrow Diagrams

The purpose of this Letter is to develop further the Gauss diagram approach to finite-type link invariants. In this context we introduce Gauss diagrams counterparts to chord diagrams, 4T relation, weight systems arising from Lie algebras, and an algebra of unitrivalent graphs modulo the STU relation. The counterparts, respectively, are arrow diagrams, 6T relation, weights arising from the solutions of the classical Yang–Baxter equation, and an algebra of acyclic arrow graphs (modulo an oriented version of the STU relation). The algebra encodes, in a graphical form, the main properties of Lie bialgebras, similarly to the well-known relation of the algebra of unitrivalent graphs to Lie algebras. We show that the oriented and relations hold, and that is isomorphic to the algebra of arrow diagrams. As an application, we consider an appropriate link-homotopy version of the algebra . Using this algebra, we construct a Gauss diagram invariants of string links up to link-homotopy, with values both in the algebra and in . We observe that this construction gives the universal Milnor's link-homotopy -invariants.     

Stochasticity,decoherence and an arrow of time from the discretization of time?

Certain intriguing consequences of the discreteness of time on the time evolution of dynamical systems are discussed. In the discrete-time classical mechanics proposed here, there is an arrow of time that follows from the fact that the replacement of the time derivative by the backward difference operator alone can preserve the non-negativity of the phase space density. It is seen that, even for free particles, all the degrees of freedom are correlated in principle. The forward evolution of functions of phase space variables by a finite number of time steps, in this discrete-time mechanics, depends on the entire continuous-time history in the interval [0, ∞]. In this sense, discrete time evolution is nonlocal in time from a continuous-time point of view. A corresponding quantum mechanical treatment is possible via the density matrix approach. The interference between nondegenerate quantum mechanical states decays exponentially. This decoherence is present, in principle, for all systems; however, it is of practical importance only in macroscopic systems, or in processes involving large energy changes.     

TDM泵浦光纤拉曼放大器四波混频噪声的分析

四波混频作为一种噪声广泛存在于各种光放大器中,论文将对TDM泵浦方式的拉曼放大器的四波混频噪声进行分析和仿真,最后提出改善四波混频噪声的方法。     

平均最后通过时间和热核裂变速率

提出利用平均最后通过鞍点时间计算热核裂变速率,结果表明平均最后通过鞍点时间的倒数比平均首次通过断点时间的倒数更接近朗之万数值模拟值. The mean last passage time is introduced to instead of the mean first passage time for studying the decay of an induced-fissioning system. The stationary fission rate determined by the inverse of mean last passage time across the saddle point is agreement with the resulting rate of Langevin simulation and better than that of mean first passage time arriving at the scission point.     

On Hot Bangs and the Arrow of Time in Relativistic Quantum Field Theory

 A recently proposed method for the characterization and analysis of local equilibrium states in relativistic quantum field theory is applied to a simple model. Within this model states are identified which are locally (but not globally) in thermal equilibrium and it is shown that their local thermal properties evolve according to macroscopic equations. The largest space–time regions in which local equilibrium states can exist are timelike cones. Thus, although the model does not describe dissipative effects, such states fix in a natural manner a time direction. Moreover, generically they determine a distinguished space–time point where a singularity in the temperature (a hot bang) must have occurred if local equilibrium prevailed thereafter. The results illustrate how the breaking of the time reflection symmetry at macroscopic scales manifests itself in a microscopic setting. Received: 17 January 2003 / Accepted: 5 March 2003 Published online: 17 April 2003 Communicated by H. Araki and K. Fredenhagen     

Isochronous Systems, the Arrow of Time, and the Definition of Deterministic Chaos

It is shown how, given an arbitrary dynamical system, other systems can be manufactured which are isochronous (periodic in all their degrees of freedom with an arbitrarily assigned fixed period T) and whose dynamics coincides exactly with that of the original system over a fraction 1 ? ?? of that period where ?? is a number that can be arbitrarily assigned in the range 0 < ?? < 1. The treatment is in the context of autonomous dynamical systems whose equations of motion feature infinitely differentiable functions of the dependent variables. It is argued that this possibility suggests that it would be useful to devise measures of the degree of complexity of a dynamical system which are associated with finite portions of its time evolution??hence going beyond the standard characterizations of the chaotic behavior of a dynamical system (via its Lyapunov coefficients or its ergodic properties), requiring its observation over infinite time.     

On the nature of the so-called generic instabilities in dissipative relativistic hydrodynamics

It is shown that the so-called generic instabilities that appear in the framework of relativistic linear irreversible thermodynamics (LIT), describing the fluctuations of a simple fluid close to equilibrium, arise due to the coupling of heat with hydrodynamic acceleration which appears in Eckart’s formalism of relativistic irreversible thermodynamics. Further, we emphasize that such behavior should be interpreted as a contradiction to the postulates of LIT, namely a violation of Onsager’s hypothesis on the regression of fluctuations, and not as fluid instabilities. Such contradictions can be avoided within a relativistic linear framework if a Meixner-like approach to the phenomenological equations is employed.     

Electromagnetic Time Reversal Algorithms and Source Localization in Lossy Dielectric Media

The problem of reconstructing the spatial support of an extended radiating electric current source density in a lossy dielectric medium from transient boundary measurements of the electric fields is studied. A time reversal algorithm is proposed to localize a source density from loss-less wave-field measurements. Further, in order to recover source densities in a lossy medium, we first build attenuation operators thereby relating loss-less waves with lossy ones. Then based on asymptotic expansions of attenuation operators with respect to attenuation parameter, we propose two time reversal strategies for localization. The losses in electromagnetic wave propagation are incorporated using the Debye's complex permittivity, which is well-adopted for low frequencies (radio and microwave) associated with polarization in dielectrics.     

三体heritage混合相互作用和核转动惯量的变化

讨论了在费米子动力学对称模型中大形变区核转动惯量的变化机制.指出在无I1带和基带交叉的情况下,heritage混合本身也可以引起转动惯量的变化,但引起混合的相互作用形式是重要的,引入某种三体相互作用后能很好地解释实验事实.