Estimating dissipation from single stationary trajectories

In this Letter we show that the time reversal asymmetry of a stationary time series provides information about the entropy production of the physical mechanism generating the series, even if one ignores any detail of that mechanism. We develop estimators for the entropy production which can detect nonequilibrium processes even when there are no measurable flows in the time series.     

Brownian diode: Molecular motor based on a semi-permeable Brownian particle with internal potential drop

A model of an autonomous isothermal Brownian motor with an internal propulsion mechanism is considered. The motor is a Brownian particle which is semi-transparent for molecules of surrounding ideal gas. Molecular passage through the particle is controlled by a potential similar to that in the transition rate theory, i.e. characterized by two stationary states with a finite energy difference separated by a potential barrier. The internal potential drop maintains the diode-like asymmetry of molecular fluxes through the particle, which results in the particle?s stationary drift.     

Brownian Particle in a Poisson-Shot-Noise Active Bath: Exact Statistics,Effective Temperature,and Inference

The dynamics of an overdamped Brownian particle in a thermal bath that contains a dilute solution of active particles is studied. The particle moves in a harmonic potential and experiences Poisson shot-noise kicks with specified amplitude distribution due to moving active particles in the bath. From the Fokker–Planck equation for the particle dynamics, the stationary solution for the displacement distribution is derived along with the moments characterizing mean, variance, skewness, and kurtosis, as well as finite-time first and second moments. An effective temperature is also computed through the fluctuation–dissipation theorem and show that equipartition theorem holds for all zero-mean kick distributions, including those leading to non-Gaussian stationary statistics. For the case of Gaussian-distributed active kicks, a re-entrant behavior from non-Gaussian to Gaussian stationary states and a heavy-tailed leptokurtic distribution across a wide range of parameters are found as seen in recent experimental studies. Further analysis reveals statistical signatures of the irreversible dynamics of the particle displacement in terms of the time asymmetry of cross-correlation functions. Fruits of the work is the development of an compact inference scheme that may allow experimentalists to extract the rate and moments of underlying shot-noise solely from the statistics the particle position.     

Temporal asymmetry as precondition of experience. The foundation of the arrow of time

Knowledge as knowledge of facts is based on the appearance of time as fundamental difference between past and future. Taking asymmetry in time as precondition of experience, the time symmetry of the basic laws of physics has to be explained. We give an explanation founded on the abstraction leading from semigroups to groups and the essential role of the concept of groups to define stationary states and observables. We then present a short outline of the construction of an abstract quantum theory as theory of knowledge based on the asymmetry between facts and possibilities. It is well known that the second law of thermodynamics cannot be derived from theH-theorem without a further hypothesis. We show that the application of the concept of probability to the past yields inconsistency of theH-theorem and a derivation of the second law via a Boltzmann-type hypothesis. The question remains whether the distinction of facts and possibilities as precondition of a theory of knowledge is rooted in a theory of cognition itself.     

Dynamical evolution of a two-level atom in a monomode chaotic field

The dynamical evolution of a two-level atom interacting with a monochromatic chaotic field is expressed in terms of a series of functions of the field photon number n. The series are evaluated in the approximation of large 〈n〉, by using the Stirling numbers of the second kind and their properties. The calculated mean values of atomic parameters show a time behaviour that is quite different from an exponential decay to the steady state. In particular they reach values below the steady state values and then evolve towards the stationary conditions with positive derivative. An evaluation of the decay time in the present scheme is also given for excited atomic states.     

Clocking ultrafast wave packet dynamics in molecules through UV-induced symmetry breaking

We investigate the use of UV-pump-UV-probe schemes to trace the evolution of nuclear wave packets in excited molecular states by analyzing the asymmetry of the electron angular distributions resulting from dissociative ionization. The asymmetry results from the coherent superposition of gerade and ungerade states of the remaining molecular ion in the region where the nuclear wave packet launched by the pump pulse in the neutral molecule is located. Hence, the variation of this asymmetry with the time delay between the pump and the probe pulses parallels that of the moving wave packet and, consequently, can be used to clock its field-free evolution. The performance of this method is illustrated for the H(2) molecule.     

Relaxation of Plasma Electrons towards Stationary States as Related to Different Initial Energy Distributions and for a Wide Range of the Final Electric Field Strength

Starting from former investigations concerning the collision dominated relaxation of the electron component in weakly ionized inert gas plasma we generalize the results obtained. Also in the present paper we use the same adaquate kinetic equation for the electron energy distribution function. On one side the influence of non-stationary, analytically given initial energy distributions on the relaxation behaviour and on the resulting adjustment time of stationary states was investigated. On the other side the calculation, especially of the adjustment time, was extended to a whole variety of final stationary states ranging from those determined only by energy loss due to elastic collisions to those determined only by exciting collisions. The adjustment time obtained varies by about four orders of magnitude within this wide range of final stationary states.     

时间反演对称和非平衡统计定常态(Ⅰ)

本文是作者从微观量子统计理论出发应用微观可逆性原理讨论非平衡统计定常态普遍性质的第一部份。文中给出了非平衡量子统计格林函数(闭路格林函数)在定常态上关于时间反演对称的表达方式。把生成泛函技术和时间反演对称结合起来,得到了具有时间反演对称性的非平衡统计定常态上统计格林函数和顶点函数所满足的时间反演对称关系。 关键词：     

The Electron Relaxation to Stationary States in Collision Dominated Plasmas in Molecular Gases

The temporal collision dominated relaxation of electrons to new stationary states, starting from initial stationary states and due to jump-like changes of the electric field, was studied in the plasmas of the molecular gases N₂ and CO. Numerical solving of the time dependent Boltzmann equation for the electrons yields the temporal evolution of their energy distribution function and of resulting macroscopic quantities. The varying relaxation due to different values of the field strength in the final stationary state has been investigated considering the molecules of the plasma only as vibrationally non-excited and, in another case, including the additional impact of collisions with vibrationally excited molecules. The results obtained are discussed and, in particular, the relaxation times found for the transitions to the new stationary states are analysed on the basis of the energy transfer effectiveness by the collision processes. An approximative microphysical basis for the understanding of the main features of the relaxation in such complex molecular gas plasmas could be obtained.     

Theory of one-dimensional quantum pump based on a two-barrier structure

A 1D quantum pump based on a structure of two δ-functional harmonically oscillating potentials is considered. Such a structure can pump electrons from one bank to the other. An ac perturbation induces a steady-state current. The effect takes place in spatially asymmetric systems. Such an asymmetry is formed due to a difference in the initial heights of the barriers or in the amplitudes or phases of ac signals. The pump can operate in various modes depending on its parameters. It is shown that the current displays oscillations with a period such that the wavelength of incident or excited electrons is multiple to the separation of the δ-functions. Resonances at quasi-stationary states between the barriers, at zero energy, and with stationary states (in the case of wells) are investigated.     

Classical Limit of Expectation Values in a Wave Packet Involving Few Stationary States

Expectation values of physical quantities in a wave packet involving few stationary states in an infinite square well are calculated. Explicit results show that the expectation values in the classical limit go over to the corresponding classical quantity in the form of the arithmetic mean (in mathematical term, the Fejér's average) of the partial Fourier series converging to the classical quantity. The number of the stationary states is that of the partial Fourer series in the Fejér's average. The quantum uncertainty is then demonstrated to have a classical counterpart.     

Broken asymmetry of the human heartbeat: loss of time irreversibility in aging and disease

Time irreversibility, a fundamental property of nonequilibrium systems, should be of importance in assessing the status of physiological processes that operate over a wide range of scales. However, measurement of this property in living systems has been limited. We provide a computational method derived from basic physics assumptions to quantify time asymmetry over multiple scales and apply it to the human heartbeat time series in health and disease. We find that the multiscale time asymmetry index is highest for a time series from young subjects and decreases with aging or heart disease. Loss of time irreversibility may provide a new way of assessing the functionality of living systems that operate far from equilibrium.     

Information symmetries in irreversible processes

We study dynamical reversibility in stationary stochastic processes from an information-theoretic perspective. Extending earlier work on the reversibility of Markov chains, we focus on finitary processes with arbitrarily long conditional correlations. In particular, we examine stationary processes represented or generated by edge-emitting, finite-state hidden Markov models. Surprisingly, we find pervasive temporal asymmetries in the statistics of such stationary processes. As a consequence, the computational resources necessary to generate a process in the forward and reverse temporal directions are generally not the same. In fact, an exhaustive survey indicates that most stationary processes are irreversible. We study the ensuing relations between model topology in different representations, the process's statistical properties, and its reversibility in detail. A process's temporal asymmetry is efficiently captured using two canonical unifilar representations of the generating model, the forward-time and reverse-time ε-machines. We analyze example irreversible processes whose ε-machine representations change size under time reversal, including one which has a finite number of recurrent causal states in one direction, but an infinite number in the opposite. From the forward-time and reverse-time ε-machines, we are able to construct a symmetrized, but nonunifilar, generator of a process--the bidirectional machine. Using the bidirectional machine, we show how to directly calculate a process's fundamental information properties, many of which are otherwise only poorly approximated via process samples. The tools we introduce and the insights we offer provide a better understanding of the many facets of reversibility and irreversibility in stochastic processes.     

Estimation of stationary structural system parameters from non-stationary random vibration data: A locally stationary model method

Stationary structural system (building) natural frequency and damping parameters are estimated from a long non-stationary ambient vibration time series record. The non-stationary vibration record is decomposed into continuous, not necessarily equal duration, stationary time series segments by a locally stationary autoregressive (AR) model method. Estimates of the stationary structural system parameters are extracted from each of the locally stationary AR models. The final estimate of the structural system parameters is a time duration weighted average of the estimates in each stationary segment. Under reasonable conditions the theoretical variance of the structural system parameter estimates decreases with the duration of the long non-stationary record. The results of the analysis of a long duration non-stationary record are compared with the results of an earlier approach in which the long duration non-stationary record was decomposed into relatively short fixed duration vibration records and analyzed as stationary time series [1]. The variances of the damping parameter estimates achieved by the current method are one-half to one-quarter of those obtained by the earlier method. The sample variance of the structural system parameter estimates decreases with the reciprocal of the duration of the overall non-stationary record.     

Variations on a theme by Mark Kac

Mark Kac's theorem on the mean recurrence time in a stationary stochastic process in discrete time with discrete states is taken as the starting point for a series of variations, most of which are formulated in terms of 0–1 processes. Whereas the original theorem deals with the mean recurrence time of a given state under the condition that the state is realized at time 0, this condition is dropped in part of the variations; two others refer to the variance of the recurrence time and two to the Poincaré cycle of a dynamical system. Most variations consist in inequalities and formal identities for the mean first-arrival time and subsequent recurrence times for the given state.     

Phase probability density in subensembles of a quantum mode of a one-atom maser

The method of periodic trajectories is applied to the analysis of the phase states of a one-atom maser mode, information on which can be obtained from a series of consequent indirect phase-sensitive quantum measurements of atoms leaving the cavity. Such information allows one to study in detail the evolution of a maser mode in a stationary state. The evolution pattern is represented as a random sequence of subensembles in which the mode exists during different time intervals. An approximate stochastic recurrence relation is obtained, which allows us, using the Monte Carlo method, to generate a sequence of relative frequencies of detection of the states of a chosen basis in escaping atoms. Formulas for the phase probability density for subensembles of the mode are derived. These formulas are obtained using as initial data the average relative frequencies measured by an experimenter in a region of a stable trajectory.     

Relaxation of physical systems in relative-number state representation

The relaxation properties of physical systems in the Liouville space are investigated in terms of the relative-number state representation. An arbitrary state can be expressed by superposition of relative-number states. In the absence of an time-dependent external field, all components with non-zero relative-numbers decay to zero with time, and any stationary state can be expressed only in terms of zero relative-number states. The phase canonically conjugate to the relative-number is completely uncertain in a stationary state. It is thought that relaxation from an arbitrary initial state to a stationary state is described as some kind of phase relaxation process. Such a phase relaxation process is explicitly described by the phase operator formalism within the framework of the relative-number state representation.     

Distribution of return intervals of extreme events

The distribution of return intervals of extreme events is studied in time series characterized by finite-term correlations with non-exponential decay. Precisely, it has been analyzed the statistics of the return intervals of extreme values of the resistance fluctuations displayed by resistors with granular structure in nonequilibrium stationary states. The resistance fluctuations are calculated by Monte Carlo simulations using a resistor network approach. It has been found that for highly disordered networks, when the auto-correlation function displays a non-exponential and non-power-law decay, the distribution of return intervals of the extreme values is a stretched exponential, with exponent independent of the threshold.     

Interactive Statistical Mechanics and Nonlinear Filtering

This paper connects non-equilibrium statistical mechanics and optimal nonlinear filtering. The latter concerns the observation-conditional behaviour of Markov signal processes, and thus provides a tool for investigating statistical mechanics with partial observations. These allow entropy reduction, illustrating Landauer’s Principle in a quantitative way. The joint process comprising a signal and its nonlinear filter is irreversible in its invariant distribution, which therefore corresponds to a non-equilibrium stationary state of the associated joint system. Macroscopic entropy and energy flows are identified for this state. Since these are driven by observations internal to the system, they do not cause entropy increase, and so the joint system makes statistical mechanical sense in reverse time. Time reversal yields a dual system in which the signal and filter exchange roles. Despite the structural similarity of the original and dual systems, there is a substantial asymmetry in their complexities. This reveals the direction of time, despite the systems being in stationary states that do not produce entropy. This work was partially supported by Leverhulme Trust Research Fellowship 2003/0426, by MURI Grant F49620-02-1-0325 (Complex Adaptive Networks for Co-operative Control), by ARO-MURI Grant DAAD19-00-1-0466 (Data Fusion in Large Arrays of Microsensors (sensor web)) and by NSF-ITR Grant CCR-0325774 Collaborative Research: New Approaches to Experimental Design and Statistical Analysis of Genomic and Structural Biological Data from Multiple Sources.     

Synthesis of multivariate random vibration systems: A two-stage least squares AR-MA model approach

A parametric time series model procedure for the synthesis of multivariate stationary time series random vibrations is shown. The vibrations are assumed to be the outputs of a regularly sampled, random noise excited, differential equation model of a vivration system. The procedure is a two-stage least squares method for realizing a multivariate disrcrete time mixed autoregressive-moving average (AR-MA) model from a given stationary process matrix covariance function. The synthesis procedure and the problem of the minimal representation of multivariate output systems and the overparameterization of AR-MA models are discussed and illustrated.