Developing Entropy of Open Finite-Level Systems

A method to compute the time dependence of theentropy in the reduced dynamics is suggested. As a testit is applied to the Jaynes-Cummings model.     

The Entropy Formula for SRB-Measures of Lattice Dynamical Systems

We give a detailed proof of the entropy formula for SRB-measures of coupled hyperbolic attractors over integer lattices. We show that the topological pressure for the potential function of the SRB-measure is zero.     

Conditional Entropy and the Rokhlin Metric on an Orthomodular Lattice with Bayessian State

The present paper deals with the study of conditional entropy and its properties in a quantum space (L,s), where L is an orthomodular lattice and s is a Bayessian state on L. First, we obtained a pseudo-metric on the family of all partitions of the couple (B,s), where B is a Boolean algebra and s is a state on B. This pseudo-metric turns out to be a metric (called the Rokhlin metric) by using a new notion of s-refinement and by identifying those partitions of (B,s) which are s-equivalent. The present theory has then been extended to the quantum space (L,s), where L is an orthomodular lattice and s is a Bayessian state on L. Applying the theory of commutators and Bell inequalities, it is shown that the couple (L,s) can be equivalently replaced by a couple (B,s ₀), where B is a Boolean algebra and s ₀ is a state on B.     

Expressing the Entropy of Lattice Systems as Sums of Conditional Entropies

Whether a system is to be considered complex or not depends on how one searches for correlations. We propose a general scheme for calculation of entropies in lattice systems that has high flexibility in how correlations are successively taken into account. Compared to the traditional approach for estimating the entropy density, in which successive approximations build on step-wise extensions of blocks of symbols, we show that one can take larger steps when collecting the statistics necessary to calculate the entropy density of the system. In one dimension this means that, instead of a single sweep over the system in which states are read sequentially, one take several sweeps with larger steps so that eventually the whole lattice is covered. This means that the information in correlations is captured in a different way, and in some situations this will lead to a considerably much faster convergence of the entropy density estimate as a function of the size of the configurations used in the estimate. The formalism is exemplified with both an example of a free energy minimisation scheme for the two-dimensional Ising model, and an example of increasingly complex spatial correlations generated by the time evolution of elementary cellular automaton rule 60.     

Coherent Transport and Dynamical Entropy for Fermionic Systems

This paper consists of two parts. First we set up a general scheme of local traps in a homogeneous deterministic quantum system. The current of particles caught by the trap is linked to the dynamical behaviour of the trap states. In this way, transport properties in a homogeneous system are related to spectral properties of a coherent dynamics. Next we apply the scheme to a system of Fermions in the one-particle approximation. We obtain in particular lower bounds for the dynamical entropy in terms of the current induced by the trap.     

Entropy and ionic conductivity

It is known that the ionic conductivity can be obtained by using the diffusion constant and the Einstein relation. We derive it here by extracting it from the steady electric current which we calculate in three ways, using statistics analysis, an entropy method, and an entropy production approach.     

Entropy Production: From Open Volume-Preserving to Dissipative Systems

We generalize Gaspard's method for computing the -entropy production rate in Hamiltonian systems to dissipative systems with attractors considered earlier by Tél, Vollmer, and Breymann. This approach leads to a natural definition of a coarse-grained Gibbs entropy which is extensive, and which can be expressed in terms of the SRB measures and volumes of the coarse-graining sets which cover the attractor. One can also study the entropy and entropy production as functions of the degree of resolution of the coarse-graining process, and examine the limit as the coarse-graining size approaches zero. We show that this definition of the Gibbs entropy leads to a positive rate of irreversible entropy production for reversible dissipative systems. We apply the method to the case of a two-dimensional map, based upon a model considered by Vollmer, Tél, and Breymann, that is a deterministic version of a biased-random walk. We treat both volume-preserving and dissipative versions of the basic map, and make a comparison between the two cases. We discuss the -entropy production rate as a function of the size of the coarse-graining cells for these biased-random walks and, for an open system with flux boundary conditions, show regions of exponential growth and decay of the rate of entropy production as the size of the cells decreases. This work describes in some detail the relation between the results of Gaspard, those of of Tél, Vollmer, and Breymann, and those of Ruelle, on entropy production in various systems described by Anosov or Anosov-like maps.     

Entropy balance in distributed reversible Gray-Scott model

A practical way to calculate the entropy change in the distributed media composed of reversible Gray-Scott model is demonstrated. The entropy change is given as the sum of the entropy production and the divergence of entropy flow. The divergence of entropy is calculated based on the chemical potential of steady state. It becomes evident that: (i) the entropy change for the emergence of dissipative structures in the open system can be positive or negative, (ii) most of the entropy produced inside the system is thrown out to the environment when dissipative structures are developing, (iii) the entropy production and the divergence of entropy flow balance completely, when the system shows static steady states, (iv) the entropy change behaves as if it is the time derivative of the entropy production. Prior to these calculations of entropy balance, the features of emergent patterns in the two-dimensional system are examined in terms of entropy production solely. The results imply that the entropy production can be an index for us to discriminate spatial patterns, but is not a global thermodynamic potential for the evolution of dissipative structures.     

Interface motion in a planar spin-flip model derived from exclusion on the line

We consider a two-dimensional spin-flip model, which can be interpreted as the limit of the Ising model at low temperature and a small nonzero external field. In the hydrodynamic limit and for a special class of initial conditions, the motion of the interface is governed by a nonlinear partial differential equation with a lattice-distorted curvature term. In our proofs we use results about the hydrodynamic behavior of the weakly asymmetric exclusion process on the integers and also on the nonnegative integers with a trap at the boundary.     

Dynein-Inspired Multilane Exclusion Process with Open Boundary Conditions

Motivated by the sidewise motions of dynein motors shown in experiments, we use a variant of the exclusion process to model the multistep dynamics of dyneins on a cylinder with open ends. Due to the varied step sizes of the particles in a quasi-two-dimensional topology, we observe the emergence of a novel phase diagram depending on the various load conditions. Under high-load conditions, our numerical findings yield results similar to the TASEP model with the presence of all three standard TASEP phases, namely the low-density (LD), high-density (HD), and maximal-current (MC) phases. However, for medium- to low-load conditions, for all chosen influx and outflux rates, we only observe the LD and HD phases, and the maximal-current phase disappears. Further, we also measure the dynamics for a single dynein particle which is logarithmically slower than a TASEP particle with a shorter waiting time. Our results also confirm experimental observations of the dwell time distribution: The dwell time distribution for dyneins is exponential in less crowded conditions, whereas a double exponential emerges under overcrowded conditions.     

Affordable,entropy-consistent Euler flux functions II: Entropy production at shocks

In this paper, an entropy-consistent flux is developed, continuing from the work of the previous paper. To achieve entropy consistency, a second and third-order differential terms are added to the entropy-conservative flux. This new flux function is tested on several one dimensional problems and compared with the original Roe flux. The new flux function exactly preserves the stationary contact discontinuity and does not capture the unphysical rarefaction shock. For steady shock problems, the new flux predicts a slightly more diffused profile whereas for unsteady cases, the captured shock is very similar to those produced by the Roe- flux. The shock stability is also studied in one dimension. Unlike the original Roe flux, the new flux is completely stable which will provide as a candidate to combat multidimensional shock instability, particularly the carbuncle phenomenon.     

Discriminating Bacterial Infection from Other Causes of Fever Using Body Temperature Entropy Analysis

Body temperature is usually employed in clinical practice by strict binary thresholding, aiming to classify patients as having fever or not. In the last years, other approaches based on the continuous analysis of body temperature time series have emerged. These are not only based on absolute thresholds but also on patterns and temporal dynamics of these time series, thus providing promising tools for early diagnosis. The present study applies three time series entropy calculation methods (Slope Entropy, Approximate Entropy, and Sample Entropy) to body temperature records of patients with bacterial infections and other causes of fever in search of possible differences that could be exploited for automatic classification. In the comparative analysis, Slope Entropy proved to be a stable and robust method that could bring higher sensitivity to the realm of entropy tools applied in this context of clinical thermometry. This method was able to find statistically significant differences between the two classes analyzed in all experiments, with sensitivity and specificity above 70% in most cases.     

Entropy of amorphous ice as determined by a new thermodynamic method

Abstract

The difference of the entropies of ice Ih and high-density amorphous ice and of low-density and high-density amorphous ice have been measured by a new direct method as about 2.1 and 1.1 J K^?1 mol^?1 respectively.     

Evolution of the Entropy and Renyi Difference Information during Self-Organization of Open Additive Systems

Evolution of the entropy and Renyi difference information is considered during transitions between stationary states in the space of control parameters for additive self-organization systems. S- and I-theorems on changes in the Renyi additive measures are proved under the Gibbs condition for the effective Hamiltonian. In the group approach, one- and two-parameter entropies and difference information of six types are obtained depending on the distribution seminorm.__________Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 42–47, March, 2005.     

Shocks and Excitation Dynamics in a Driven Diffusive Two-Channel System

We consider classical hard-core particles hopping stochastically on two parallel chains in the same or opposite directions with an inter- and intra-chain interaction. We discuss general questions concerning elementary excitations in these systems, shocks and rarefaction waves. From microscopical considerations we derive the collective velocities and shock stability conditions. The findings are confirmed by comparison to Monte Carlo data of a multi-parameter class of simple two lane driven diffusion models, which have the stationary state of a product form on a ring. Going to the hydrodynamic limit, we point out the analogy of our results to the ones known in the theory of differential equations of two conservation laws. We discuss the singularity problem and find a dissipative term that selects the physical solution.     

Entropy of an Arbitrarily Accelerating Black Hole

The entropy of an arbitrarily accelerating black hole is studied. As the metric is neither axisymmetric nor stationary, its entropy is difficult to calculate. We overcome the difficulty via introduction of a new coordinate system in which ₀₀ is zero at the event horizon's surface r = r _h , and calculate the entropy locally via the improved brick-wall model, that is, the thin film model with the locally thermal equilibrium satisfied. The results confirm that the entropy is proportional to its area both in the stationary space-time and non-stationary one.