Next Issue
Previous Issue

E-Mail Alert

Add your e-mail address to receive forthcoming issues of this journal:

Journal Browser

Journal Browser

Table of Contents

Entropy, Volume 19, Issue 7 (July 2017)

  • Issues are regarded as officially published after their release is announced to the table of contents alert mailing list.
  • You may sign up for e-mail alerts to receive table of contents of newly released issues.
  • PDF is the official format for papers published in both, html and pdf forms. To view the papers in pdf format, click on the "PDF Full-text" link, and use the free Adobe Readerexternal link to open them.
Cover Story (view full-size image) What happens when information is processed by applying a function f to a variable S? The data [...] Read more.
View options order results:
result details:
Displaying articles 1-87
Export citation of selected articles as:
Open AccessArticle Pretreatment and Wavelength Selection Method for Near-Infrared Spectra Signal Based on Improved CEEMDAN Energy Entropy and Permutation Entropy
Entropy 2017, 19(7), 380; https://doi.org/10.3390/e19070380
Received: 26 June 2017 / Revised: 14 July 2017 / Accepted: 22 July 2017 / Published: 24 July 2017
Cited by 2 | PDF Full-text (2085 KB) | HTML Full-text | XML Full-text
Abstract
The noise of near-infrared spectra and spectral information redundancy can affect the accuracy of calibration and prediction models in near-infrared analytical technology. To address this problem, the improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) and permutation entropy (PE) were used
[...] Read more.
The noise of near-infrared spectra and spectral information redundancy can affect the accuracy of calibration and prediction models in near-infrared analytical technology. To address this problem, the improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) and permutation entropy (PE) were used to propose a new method for pretreatment and wavelength selection of near-infrared spectra signal. The near-infrared spectra of glucose solution was used as the research object, the improved CEEMDAN energy entropy was then used to reconstruct spectral data for removing noise, and the useful wavelengths are selected based on PE after spectra segmentation. Firstly, the intrinsic mode functions of original spectra are obtained by improved CEEMDAN algorithm. The useful signal modes and noisy signal modes were then identified by the energy entropy, and the reconstructed spectral signal is the sum of useful signal modes. Finally, the reconstructed spectra were segmented and the wavelengths with abundant glucose information were selected based on PE. To evaluate the performance of the proposed method, support vector regression and partial least square regression were used to build the calibration model using the wavelengths selected by the new method, mutual information, successive projection algorithm, principal component analysis, and full spectra data. The results of the model were evaluated by the correlation coefficient and root mean square error of prediction. The experimental results showed that the improved CEEMDAN energy entropy can effectively reconstruct near-infrared spectra signal and that the PE can effectively solve the wavelength selection. Therefore, the proposed method can improve the precision of spectral analysis and the stability of the model for near-infrared spectra analysis. Full article
(This article belongs to the Special Issue Permutation Entropy & Its Interdisciplinary Applications)
Figures

Figure 1

Open AccessArticle An Application of Pontryagin’s Principle to Brownian Particle Engineered Equilibration
Entropy 2017, 19(7), 379; https://doi.org/10.3390/e19070379
Received: 3 July 2017 / Revised: 19 July 2017 / Accepted: 20 July 2017 / Published: 24 July 2017
Cited by 1 | PDF Full-text (550 KB) | HTML Full-text | XML Full-text
Abstract
We present a stylized model of controlled equilibration of a small system in a fluctuating environment. We derive the optimal control equations steering in finite-time the system between two equilibrium states. The corresponding thermodynamic transition is optimal in the sense that it occurs
[...] Read more.
We present a stylized model of controlled equilibration of a small system in a fluctuating environment. We derive the optimal control equations steering in finite-time the system between two equilibrium states. The corresponding thermodynamic transition is optimal in the sense that it occurs at minimum entropy if the set of admissible controls is restricted by certain bounds on the time derivatives of the protocols. We apply our equations to the engineered equilibration of an optical trap considered in a recent proof of principle experiment. We also analyze an elementary model of nucleation previously considered by Landauer to discuss the thermodynamic cost of one bit of information erasure. We expect our model to be a useful benchmark for experiment design as it exhibits the same integrability properties of well-known models of optimal mass transport by a compressible velocity field. Full article
(This article belongs to the Special Issue Thermodynamics and Statistical Mechanics of Small Systems)
Figures

Figure 1

Open AccessFeature PaperArticle Cognition and Cooperation in Interfered Multiple Access Channels
Entropy 2017, 19(7), 378; https://doi.org/10.3390/e19070378
Received: 31 May 2017 / Revised: 17 July 2017 / Accepted: 20 July 2017 / Published: 24 July 2017
PDF Full-text (509 KB) | HTML Full-text | XML Full-text
Abstract
In this work, we investigate a three-user cognitive communication network where a primary two-user multiple access channel suffers interference from a secondary point-to-point channel, sharing the same medium. While the point-to-point channel transmitter—transmitter 3—causes an interference at the primary multiple access channel receiver,
[...] Read more.
In this work, we investigate a three-user cognitive communication network where a primary two-user multiple access channel suffers interference from a secondary point-to-point channel, sharing the same medium. While the point-to-point channel transmitter—transmitter 3—causes an interference at the primary multiple access channel receiver, we assume that the primary channel transmitters—transmitters 1 and 2—do not cause any interference at the point-to-point receiver. It is assumed that one of the multiple access channel transmitters has cognitive capabilities and cribs causally from the other multiple access channel transmitter. Furthermore, we assume that the cognitive transmitter knows the message of transmitter 3 in a non-causal manner, thus introducing the three-user multiple access cognitive Z-interference channel. We obtain inner and outer bounds on the capacity region of the this channel for both causal and strictly causal cribbing cognitive encoders. We further investigate different variations and aspects of the channel, referring to some previously studied cases. Attempting to better characterize the capacity region we look at the vertex points of the capacity region where each one of the transmitters tries to achieve its maximal rate. Moreover, we find the capacity region of a special case of a certain kind of more-capable multiple access cognitive Z-interference channels. In addition, we study the case of full unidirectional cooperation between the 2 multiple access channel encoders. Finally, since direct cribbing allows us full cognition in the case of continuous input alphabets, we study the case of partial cribbing, i.e., when the cribbing is performed via a deterministic function. Full article
(This article belongs to the Special Issue Network Information Theory)
Figures

Figure 1

Open AccessArticle Investigation of Oriented Magnetic Field Effects on Entropy Generation in an Inclined Channel Filled with Ferrofluids
Entropy 2017, 19(7), 377; https://doi.org/10.3390/e19070377
Received: 13 June 2017 / Revised: 10 July 2017 / Accepted: 18 July 2017 / Published: 23 July 2017
Cited by 1 | PDF Full-text (363 KB) | HTML Full-text | XML Full-text
Abstract
Dispersion of super-paramagnetic nanoparticles in nonmagnetic carrier fluids, known as ferrofluids, offers the advantages of tunable thermo-physical properties and eliminate the need for moving parts to induce flow. This study investigates ferrofluid flow characteristics in an inclined channel under inclined magnetic field and
[...] Read more.
Dispersion of super-paramagnetic nanoparticles in nonmagnetic carrier fluids, known as ferrofluids, offers the advantages of tunable thermo-physical properties and eliminate the need for moving parts to induce flow. This study investigates ferrofluid flow characteristics in an inclined channel under inclined magnetic field and constant pressure gradient. The ferrofluid considered in this work is comprised of Cu particles as the nanoparticles and water as the base fluid. The governing differential equations including viscous dissipation are non-dimensionalised and discretized with Generalized Differential Quadrature Method. The resulting algebraic set of equations are solved via Newton-Raphson Method. The work done here contributes to the literature by searching the effects of magnetic field angle and channel inclination separately on the entropy generation of the ferrofluid filled inclined channel system in order to achieve best design parameter values so called entropy generation minimization is implemented. Furthermore, the effect of magnetic field, inclination angle of the channel and volume fraction of nanoparticles on velocity and temperature profiles are examined and represented by figures to give a thorough understanding of the system behavior. Full article
(This article belongs to the Special Issue Entropy Generation in Nanofluid Flows)
Figures

Figure 1

Open AccessArticle A Novel Numerical Approach for a Nonlinear Fractional Dynamical Model of Interpersonal and Romantic Relationships
Entropy 2017, 19(7), 375; https://doi.org/10.3390/e19070375
Received: 28 May 2017 / Revised: 4 July 2017 / Accepted: 19 July 2017 / Published: 22 July 2017
Cited by 13 | PDF Full-text (1978 KB) | HTML Full-text | XML Full-text
Abstract
In this paper, we propose a new numerical algorithm, namely q-homotopy analysis Sumudu transform method (q-HASTM), to obtain the approximate solution for the nonlinear fractional dynamical model of interpersonal and romantic relationships. The suggested algorithm examines the dynamics of love
[...] Read more.
In this paper, we propose a new numerical algorithm, namely q-homotopy analysis Sumudu transform method (q-HASTM), to obtain the approximate solution for the nonlinear fractional dynamical model of interpersonal and romantic relationships. The suggested algorithm examines the dynamics of love affairs between couples. The q-HASTM is a creative combination of Sumudu transform technique, q-homotopy analysis method and homotopy polynomials that makes the calculation very easy. To compare the results obtained by using q-HASTM, we solve the same nonlinear problem by Adomian’s decomposition method (ADM). The convergence of the q-HASTM series solution for the model is adapted and controlled by auxiliary parameter ℏ and asymptotic parameter n. The numerical results are demonstrated graphically and in tabular form. The result obtained by employing the proposed scheme reveals that the approach is very accurate, effective, flexible, simple to apply and computationally very nice. Full article
(This article belongs to the Special Issue Complex Systems and Fractional Dynamics)
Figures

Figure 1

Open AccessArticle Comparative Analysis of Jüttner’s Calculation of the Energy of a Relativistic Ideal Gas and Implications for Accelerator Physics and Cosmology
Entropy 2017, 19(7), 374; https://doi.org/10.3390/e19070374
Received: 5 July 2017 / Revised: 20 July 2017 / Accepted: 21 July 2017 / Published: 22 July 2017
PDF Full-text (2462 KB) | HTML Full-text | XML Full-text
Abstract
Jüttner used the conventional theory of relativistic statistical mechanics to calculate the energy of a relativistic ideal gas in 1911. An alternative derivation of the energy of a relativistic ideal gas was published by Horwitz, Schieve and Piron in 1981 within the context
[...] Read more.
Jüttner used the conventional theory of relativistic statistical mechanics to calculate the energy of a relativistic ideal gas in 1911. An alternative derivation of the energy of a relativistic ideal gas was published by Horwitz, Schieve and Piron in 1981 within the context of parametrized relativistic statistical mechanics. The resulting energy in the ultrarelativistic regime differs from Jüttner’s result. We review the derivations of energy and identify physical regimes for testing the validity of the two theories in accelerator physics and cosmology. Full article
(This article belongs to the Special Issue Advances in Relativistic Statistical Mechanics)
Figures

Figure 1

Open AccessArticle Objective Weights Based on Ordered Fuzzy Numbers for Fuzzy Multiple Criteria Decision-Making Methods
Entropy 2017, 19(7), 373; https://doi.org/10.3390/e19070373
Received: 7 June 2017 / Revised: 16 July 2017 / Accepted: 20 July 2017 / Published: 21 July 2017
Cited by 1 | PDF Full-text (1403 KB) | HTML Full-text | XML Full-text
Abstract
Fuzzy multiple criteria decision-making (FMCDM) methods are techniques of finding the trade-off option out of all feasible alternatives that are characterized by multiple criteria and where data cannot be measured precisely, but can be represented, for instance, by ordered fuzzy numbers (OFNs). One
[...] Read more.
Fuzzy multiple criteria decision-making (FMCDM) methods are techniques of finding the trade-off option out of all feasible alternatives that are characterized by multiple criteria and where data cannot be measured precisely, but can be represented, for instance, by ordered fuzzy numbers (OFNs). One of the main steps in FMCDM methods consist in finding the appropriate criteria weights. A method based on the concept of Shannon entropy is one of many techniques for the determination of criteria weights when obtaining them from the decision-maker is not possible. The goal of the paper is to extend the notion of Shannon entropy to fuzzy data represented by OFNs. The proposed approach allows to obtain criteria weights as OFNs, which are normalized and sum to 1. Full article
(This article belongs to the Section Information Theory)
Figures

Figure 1

Open AccessArticle Transfer Entropy for Nonparametric Granger Causality Detection: An Evaluation of Different Resampling Methods
Entropy 2017, 19(7), 372; https://doi.org/10.3390/e19070372
Received: 16 May 2017 / Revised: 14 July 2017 / Accepted: 17 July 2017 / Published: 21 July 2017
PDF Full-text (1296 KB) | HTML Full-text | XML Full-text
Abstract
The information-theoretical concept transfer entropy is an ideal measure for detecting conditional independence, or Granger causality in a time series setting. The recent literature indeed witnesses an increased interest in applications of entropy-based tests in this direction. However, those tests are typically based
[...] Read more.
The information-theoretical concept transfer entropy is an ideal measure for detecting conditional independence, or Granger causality in a time series setting. The recent literature indeed witnesses an increased interest in applications of entropy-based tests in this direction. However, those tests are typically based on nonparametric entropy estimates for which the development of formal asymptotic theory turns out to be challenging. In this paper, we provide numerical comparisons for simulation-based tests to gain some insights into the statistical behavior of nonparametric transfer entropy-based tests. In particular, surrogate algorithms and smoothed bootstrap procedures are described and compared. We conclude this paper with a financial application to the detection of spillover effects in the global equity market. Full article
(This article belongs to the Special Issue Entropic Applications in Economics and Finance)
Figures

Figure 1

Open AccessArticle A Quantized Kernel Learning Algorithm Using a Minimum Kernel Risk-Sensitive Loss Criterion and Bilateral Gradient Technique
Entropy 2017, 19(7), 365; https://doi.org/10.3390/e19070365
Received: 19 June 2017 / Revised: 8 July 2017 / Accepted: 13 July 2017 / Published: 20 July 2017
Cited by 14 | PDF Full-text (400 KB) | HTML Full-text | XML Full-text
Abstract
Recently, inspired by correntropy, kernel risk-sensitive loss (KRSL) has emerged as a novel nonlinear similarity measure defined in kernel space, which achieves a better computing performance. After applying the KRSL to adaptive filtering, the corresponding minimum kernel risk-sensitive loss (MKRSL) algorithm has been
[...] Read more.
Recently, inspired by correntropy, kernel risk-sensitive loss (KRSL) has emerged as a novel nonlinear similarity measure defined in kernel space, which achieves a better computing performance. After applying the KRSL to adaptive filtering, the corresponding minimum kernel risk-sensitive loss (MKRSL) algorithm has been developed accordingly. However, MKRSL as a traditional kernel adaptive filter (KAF) method, generates a growing radial basis functional (RBF) network. In response to that limitation, through the use of online vector quantization (VQ) technique, this article proposes a novel KAF algorithm, named quantized MKRSL (QMKRSL) to curb the growth of the RBF network structure. Compared with other quantized methods, e.g., quantized kernel least mean square (QKLMS) and quantized kernel maximum correntropy (QKMC), the efficient performance surface makes QMKRSL converge faster and filter more accurately, while maintaining the robustness to outliers. Moreover, considering that QMKRSL using traditional gradient descent method may fail to make full use of the hidden information between the input and output spaces, we also propose an intensified QMKRSL using a bilateral gradient technique named QMKRSL_BG, in an effort to further improve filtering accuracy. Short-term chaotic time-series prediction experiments are conducted to demonstrate the satisfactory performance of our algorithms. Full article
(This article belongs to the Special Issue Entropy in Signal Analysis)
Figures

Figure 1

Open AccessArticle Collaborative Service Selection via Ensemble Learning in Mixed Mobile Network Environments
Entropy 2017, 19(7), 358; https://doi.org/10.3390/e19070358
Received: 18 May 2017 / Revised: 4 July 2017 / Accepted: 10 July 2017 / Published: 20 July 2017
Cited by 3 | PDF Full-text (4148 KB) | HTML Full-text | XML Full-text
Abstract
Mobile Service selection is an important but challenging problem in service and mobile computing. Quality of service (QoS) predication is a critical step in service selection in 5G network environments. The traditional methods, such as collaborative filtering (CF), suffer from a series of
[...] Read more.
Mobile Service selection is an important but challenging problem in service and mobile computing. Quality of service (QoS) predication is a critical step in service selection in 5G network environments. The traditional methods, such as collaborative filtering (CF), suffer from a series of defects, such as failing to handle data sparsity. In mobile network environments, the abnormal QoS data are likely to result in inferior prediction accuracy. Unfortunately, these problems have not attracted enough attention, especially in a mixed mobile network environment with different network configurations, generations, or types. An ensemble learning method for predicting missing QoS in 5G network environments is proposed in this paper. There are two key principles: one is the newly proposed similarity computation method for identifying similar neighbors; the other is the extended ensemble learning model for discovering and filtering fake neighbors from the preliminary neighbors set. Moreover, three prediction models are also proposed, two individual models and one combination model. They are used for utilizing the user similar neighbors and servicing similar neighbors, respectively. Experimental results conducted in two real-world datasets show our approaches can produce superior prediction accuracy. Full article
(This article belongs to the Special Issue Information Theory and 5G Technologies)
Figures

Figure 1

Open AccessArticle Conformity, Anticonformity and Polarization of Opinions: Insights from a Mathematical Model of Opinion Dynamics
Entropy 2017, 19(7), 371; https://doi.org/10.3390/e19070371
Received: 29 May 2017 / Revised: 13 July 2017 / Accepted: 18 July 2017 / Published: 19 July 2017
Cited by 2 | PDF Full-text (850 KB) | HTML Full-text | XML Full-text
Abstract
Understanding and quantifying polarization in social systems is important because of many reasons. It could for instance help to avoid segregation and conflicts in the society or to control polarized debates and predict their outcomes. In this paper, we present a version of
[...] Read more.
Understanding and quantifying polarization in social systems is important because of many reasons. It could for instance help to avoid segregation and conflicts in the society or to control polarized debates and predict their outcomes. In this paper, we present a version of the q-voter model of opinion dynamics with two types of responses to social influence: conformity (like in the original q-voter model) and anticonformity. We put the model on a social network with the double-clique topology in order to check how the interplay between those responses impacts the opinion dynamics in a population divided into two antagonistic segments. The model is analyzed analytically, numerically and by means of Monte Carlo simulations. Our results show that the system undergoes two bifurcations as the number of cross-links between cliques changes. Below the first critical point, consensus in the entire system is possible. Thus, two antagonistic cliques may share the same opinion only if they are loosely connected. Above that point, the system ends up in a polarized state. Full article
(This article belongs to the Special Issue Statistical Mechanics of Complex and Disordered Systems)
Figures

Figure 1

Open AccessArticle Optimal Detection under the Restricted Bayesian Criterion
Entropy 2017, 19(7), 370; https://doi.org/10.3390/e19070370
Received: 8 May 2017 / Revised: 11 July 2017 / Accepted: 18 July 2017 / Published: 19 July 2017
PDF Full-text (1116 KB) | HTML Full-text | XML Full-text
Abstract
This paper aims to find a suitable decision rule for a binary composite hypothesis-testing problem with a partial or coarse prior distribution. To alleviate the negative impact of the information uncertainty, a constraint is considered that the maximum conditional risk cannot be greater
[...] Read more.
This paper aims to find a suitable decision rule for a binary composite hypothesis-testing problem with a partial or coarse prior distribution. To alleviate the negative impact of the information uncertainty, a constraint is considered that the maximum conditional risk cannot be greater than a predefined value. Therefore, the objective of this paper becomes to find the optimal decision rule to minimize the Bayes risk under the constraint. By applying the Lagrange duality, the constrained optimization problem is transformed to an unconstrained optimization problem. In doing so, the restricted Bayesian decision rule is obtained as a classical Bayesian decision rule corresponding to a modified prior distribution. Based on this transformation, the optimal restricted Bayesian decision rule is analyzed and the corresponding algorithm is developed. Furthermore, the relation between the Bayes risk and the predefined value of the constraint is also discussed. The Bayes risk obtained via the restricted Bayesian decision rule is a strictly decreasing and convex function of the constraint on the maximum conditional risk. Finally, the numerical results including a detection example are presented and agree with the theoretical results. Full article
(This article belongs to the Special Issue Maximum Entropy and Bayesian Methods)
Figures

Figure 1

Open AccessPerspective The History and Perspectives of Efficiency at Maximum Power of the Carnot Engine
Entropy 2017, 19(7), 369; https://doi.org/10.3390/e19070369
Received: 30 March 2017 / Revised: 5 July 2017 / Accepted: 14 July 2017 / Published: 19 July 2017
Cited by 3 | PDF Full-text (1312 KB) | HTML Full-text | XML Full-text
Abstract
Finite Time Thermodynamics is generally associated with the Curzon–Ahlborn approach to the Carnot cycle. Recently, previous publications on the subject were discovered, which prove that the history of Finite Time Thermodynamics started more than sixty years before even the work of Chambadal and
[...] Read more.
Finite Time Thermodynamics is generally associated with the Curzon–Ahlborn approach to the Carnot cycle. Recently, previous publications on the subject were discovered, which prove that the history of Finite Time Thermodynamics started more than sixty years before even the work of Chambadal and Novikov (1957). The paper proposes a careful examination of the similarities and differences between these pioneering works and the consequences they had on the works that followed. The modelling of the Carnot engine was carried out in three steps, namely (1) modelling with time durations of the isothermal processes, as done by Curzon and Ahlborn; (2) modelling at a steady-state operation regime for which the time does not appear explicitly; and (3) modelling of transient conditions which requires the time to appear explicitly. Whatever the method of modelling used, the subsequent optimization appears to be related to specific physical dimensions. The main goal of the methodology is to choose the objective function, which here is the power, and to define the associated constraints. We propose a specific approach, focusing on the main functions that respond to engineering requirements. The study of the Carnot engine illustrates the synthesis carried out and proves that the primary interest for an engineer is mainly connected to what we called Finite (physical) Dimensions Optimal Thermodynamics, including time in the case of transient modelling. Full article
(This article belongs to the Special Issue Carnot Cycle and Heat Engine Fundamentals and Applications)
Figures

Figure 1

Open AccessArticle Nonequilibrium Entropy in a Shock
Entropy 2017, 19(7), 368; https://doi.org/10.3390/e19070368
Received: 13 June 2017 / Revised: 12 July 2017 / Accepted: 14 July 2017 / Published: 19 July 2017
PDF Full-text (660 KB) | HTML Full-text | XML Full-text
Abstract
In a classic paper, Morduchow and Libby use an analytic solution for the profile of a Navier–Stokes shock to show that the equilibrium thermodynamic entropy has a maximum inside the shock. There is no general nonequilibrium thermodynamic formulation of entropy; the extension of
[...] Read more.
In a classic paper, Morduchow and Libby use an analytic solution for the profile of a Navier–Stokes shock to show that the equilibrium thermodynamic entropy has a maximum inside the shock. There is no general nonequilibrium thermodynamic formulation of entropy; the extension of equilibrium theory to nonequililbrium processes is usually made through the assumption of local thermodynamic equilibrium (LTE). However, gas kinetic theory provides a perfectly general formulation of a nonequilibrium entropy in terms of the probability distribution function (PDF) solutions of the Boltzmann equation. In this paper I will evaluate the Boltzmann entropy for the PDF that underlies the Navier–Stokes equations and also for the PDF of the Mott–Smith shock solution. I will show that both monotonically increase in the shock. I will propose a new nonequilibrium thermodynamic entropy and show that it is also monotone and closely approximates the Boltzmann entropy. Full article
(This article belongs to the Special Issue Entropy, Time and Evolution)
Figures

Figure 1

Open AccessFeature PaperArticle Reliable Approximation of Long Relaxation Timescales in Molecular Dynamics
Entropy 2017, 19(7), 367; https://doi.org/10.3390/e19070367
Received: 25 April 2017 / Revised: 13 July 2017 / Accepted: 13 July 2017 / Published: 18 July 2017
Cited by 2 | PDF Full-text (515 KB) | HTML Full-text | XML Full-text
Abstract
Many interesting rare events in molecular systems, like ligand association, protein folding or conformational changes, occur on timescales that often are not accessible by direct numerical simulation. Therefore, rare event approximation approaches like interface sampling, Markov state model building, or advanced reaction coordinate-based
[...] Read more.
Many interesting rare events in molecular systems, like ligand association, protein folding or conformational changes, occur on timescales that often are not accessible by direct numerical simulation. Therefore, rare event approximation approaches like interface sampling, Markov state model building, or advanced reaction coordinate-based free energy estimation have attracted huge attention recently. In this article we analyze the reliability of such approaches. How precise is an estimate of long relaxation timescales of molecular systems resulting from various forms of rare event approximation methods? Our results give a theoretical answer to this question by relating it with the transfer operator approach to molecular dynamics. By doing so we also allow for understanding deep connections between the different approaches. Full article
(This article belongs to the Special Issue Understanding Molecular Dynamics via Stochastic Processes)
Figures

Figure 1

Back to Top