Entropy-based Formulation Research Articles

Freight-transit tour synthesis entropy-based formulation: sharing infrastructure for buses and trucks

Freight-transit tour synthesis entropy-based formulation: sharing infrastructure for buses and trucks

Non-Markovianity through entropy-based quantum thermodynamics

We introduce a generalized approach to characterize the non-Markovianity of quantum dynamical maps via breakdown of monotonicity of thermodynamic functions. By adopting an entropy-based formulation of quantum thermodynamics, we use the relationship between heat and entropy to propose a measure of non-Markovianity based on the heat flow for single-qubit quantum evolutions. This measure can be applied for unital dynamical maps that do not invert the sign of the internal energy. Under certain conditions, it can also be extended for other thermodynamic functions, such as internal energy and work flows. In this context, a natural connection between heat and quantum coherence can be identified for dynamical maps that are both unital and incoherent. As applications, we explore dissipative and non-dissipative quantum dynamical processes, illustrating the compatibility between our thermodynamic quantifiers and the well-establish measure defined via quantum coherence.

Entropy-based formulation of thermodynamics in arbitrary quantum evolution

Given the evolution of an arbitrary open quantum system, we formulate a general and unambiguous method to separate the internal energy change of the system into an entropy-related contribution and a part causing no entropy change, identified as heat and work, respectively. We also demonstrate that heat and work admit geometric and dynamical descriptions by developing a universal dynamical equation for the given trajectory of the system. The dissipative and coherent parts of this equation contribute exclusively to heat and work, where the specific role of a work contribution from a counterdiabatic drive is underlined. Next we define an expression for the irreversible entropy production of the system which does not have explicit dependence on the properties of the ambient environment; rather, it depends on a set of the system's observables excluding its Hamiltonian and is independent of internal energy change. We illustrate our results with three examples.

An Entropy-Based Formulation for the Support of Sustainable Mass Customization 4.0

Industry 4.0, an information and communication umbrella of terms that includes the Internet of Things (IoT) and cyber-physical systems, aims to ensure the future of the manufacturing industry competing in a proper environment of mass customization: demand for short delivery time, high quality, and small-lot products. Within this context of an Industry 4.0 mass customization environment, success depends on its sustainability, where the latter can only be achieved by the manufacturing efficiency of the smart factory-based Industry 4.0 transforming processes. Even though Industry 4.0 is associated with an optimal resource and energy productivity/efficiency, it becomes necessary to answer if the integration of Industry 4.0 elements (like CPS) has a favorable sustainability payoff. This requires performing energy consumption what-if analyses. The original contribution of this paper is the use of the entropy-based formulation as an alternative way of performing the initial steps of the energy consumption what-if analyses. The usefulness of the proposed approach is demonstrated by comparing the results of a discrete-event simulation model of mass customization 4.0 environment and the values obtained by using the entropy-based formulation. The obtained results suggest that the entropy-based formulation acts as a fairly good trend indicator of the system’s performance parameters increase/decrease. The managerial implications of these findings are presented at the end of this document.

An Entropy-Based Formulation for Assessing the Complexity Level of a Mass Customization Industry 4.0 Environment

It has been stated that Industry 4.0’s goal is, among others, the sustainable success in a market characterized by exigent and informed consumers demanding personalized products and services, where the level of manufacturing complexity increases with level of product customization. Even though different manufacturing complexity measures have been developed, there seems to be a lack of a comprehensive metric that address both the mass customization variety-induced complexity, and the complexity derived from the adoption of the Industry 4.0 paradigm. The main original contribution of this paper is the development of an entropy-based (entropic) formulation to address this last issue. Its validity and usefulness is put to the test via a discrete-event simulation study of a mass customization production system operating within an Industry 4.0 context. Our findings show that the entropic formulation acts as a fairly good trend indicator of the system’s performance parameter increase/decrease, but not as an estimator of the final values. A discussion of the managerial implications of the obtained results is offered at the end of the paper.

A hybrid adaptive decision system for supply chain reconfiguration

Due to short product life cycle, it is expedient to reconfiguration an existing supply chain from time to time. Companies need to impose the standards on operational units for finding the best or the near best alternative configuration. Thus, it becomes imperative to effectively adapt various enablers in a supply chain by understanding the dynamics between them that help to reconfigure a supply chain for high levels of performance. This paper presents an integration of agent-based simulation and decision tree learning as the data mining techniques to determine adaptive decisions of operational units of a mobile phone supply chain. Agent-based simulation output is subjected to data mining analysis to understand system behaviour in terms of interactions and the factors influencing the performance. An entropy-based formulation is proposed as the basis for comparing different operational units in the supply chain. The insights obtained are then encapsulated as operational rules and guidelines supporting better decision-making.

Entropy Based Modelling for Estimating Demographic Trends.

In this paper, an entropy-based method is proposed to forecast the demographical changes of countries. We formulate the estimation of future demographical profiles as a constrained optimization problem, anchored on the empirically validated assumption that the entropy of age distribution is increasing in time. The procedure of the proposed method involves three stages, namely: 1) Prediction of the age distribution of a country’s population based on an “age-structured population model”; 2) Estimation the age distribution of each individual household size with an entropy-based formulation based on an “individual household size model”; and 3) Estimation the number of each household size based on a “total household size model”. The last stage is achieved by projecting the age distribution of the country’s population (obtained in stage 1) onto the age distributions of individual household sizes (obtained in stage 2). The effectiveness of the proposed method is demonstrated by feeding real world data, and it is general and versatile enough to be extended to other time dependent demographic variables.

An entropy-based formulation of irreversible processes based on contact structures

In this paper we propose an analytical formulation of the dynamical behaviour of complex and open physical systems which is formulated on the total thermodynamic phase space using the contact form associated with Gibbs’ relation. Starting from balance equations we construct control contact systems by using the entropy function to represent the thermodynamic properties. The contact Hamiltonian function generating the dynamical behaviour has then the units of an entropy variation. We consider complex thermodynamic systems, described by compartmental systems, and we construct the associated control contact system by composing the control contact formulation of every compartment. The contact Hamiltonian functions generating the dynamical behaviour are discussed with respect to two alternative formalisms used for describing coupled sets of reversible and irreversible processes, namely the GENERIC formulation and the Matrix formulation. This analysis is then illustrated on the elementary example of a coupled mechanical and thermodynamic system.

Traffic Modeling and College-Bus Routing Using Entropy Maximization

A method is presented by which traffic flow estimation between known origins and destinations can be evaluated based on a modified entropy model, and by which bus-routing optimization can be performed. The traffic flow analysis is performed by use of an entropy-based formulation of the vehicular movements of students within the domain under examination, while the perceived level of disorder caused by the numerous vehicle-student-trips in the domain under examination is subsequently used for the formulation of a policy and a bus-routing scheme in order to minimize the original entropy in the system. The entropy metric used in the scheduling optimization is related to the probability of student-trips by origin and destination, and an application of the method is illustrated via a case study of an urban university (with facilities in multiple locations) initiating bus service for its students.

Entropy as an assessment tool of supply chain information sharing

As the order fulfillment process needs to be managed in a seamless way, the level of information sharing among the partners of the supply chain needs to be increased. An entropy-based formulation is proposed as the basis of a methodology for comparing different information sharing approaches in a supply chain environment. A step-by-step comparison of two different information sharing approaches is presented to exemplify the use of the methodology. A computer simulation is used to validate the usefulness of the proposed methodology.

The MM, ME, ML, EL, EF and GMM approaches to estimation: a synthesis

The 20th century began on an auspicious statistical note with the publication of Karl Pearson's (Philos. Mag. Ser. 50 (1900) 157) goodness-of-fit test, which is regarded as one of the most important scientific breakthroughs. The basic motivation behind this test was to see whether an assumed probability model adequately described the data at hand. Pearson (Philos. Trans. Roy. Soc. London Ser. A 185 (1894) 71) also introduced a formal approach to statistical estimation through his method of moments (MM) estimation. Ronald A. Fisher, while he was a third year undergraduate at the Gonville and Caius College, Cambridge, suggested the maximum likelihood estimation (MLE) procedure as an alternative to Pearson's MM approach. In 1922 Fisher published a monumental paper that introduced such basic concepts as consistency, efficiency, sufficiency—and even the term “parameter” with its present meaning. Fisher (Philos. Trans. Roy. Soc. London Ser. A 222 (1922) 309) provided the analytical foundation of MLE and studied its efficiency relative to the MM estimator. Fisher (J. Roy. Statist. Soc. 87 (1924a) 442) established the asymptotic equivalence of minimum χ 2 and ML estimators and wrote in favor of using minimum χ 2 method rather than Pearson's MM approach. Recently, econometricians have found working under assumed likelihood functions restrictive, and have suggested using a generalized version of Pearson's MM approach, commonly known as the GMM estimation procedure as advocated in Hansen (Econometrica 50 (1982) 1029). Earlier, Godambe (Ann. Math. Statist. 31 (1960) 1208) and Durbin (J. Roy. Statist. Soc. Ser. B 22 (1960) 139) developed the estimating function (EF) approach to estimation that has been proven very useful for many statistical models. A fundamental result is that score is the optimum EF. Ferguson (Ann. Math. Statist. 29 (1958) 1046) considered an approach very similar to GMM and showed that estimation based on the Pearson χ 2 statistic is equivalent to efficient GMM. Golan et al. (Maximum Entropy Econometrics: Robust Estimation with Limited Data. Wiley, New York, 1996) developed entropy-based formulation that allowed them to solve a wide range of estimation and inference problems in econometrics. More recently, Imbens et al. (Econometrica 66 (1998) 333), Kitamura and Stutzer (Econometrica 65 (1997) 861) and Mittelhammer et al. (Econometric Foundations. Cambridge University Press, Cambridge, 2000) put GMM within the framework of empirical likelihood (EL) and maximum entropy (ME) estimation. It can be shown that many of these estimation techniques can be obtained as special cases of minimizing Cressie and Read (J. Roy. Statist. Soc. Ser. B 46 (1984) 440) power divergence criterion that comes directly from the Pearson (1900) χ 2 statistic. In this way we are able to assimilate a number of seemingly unrelated estimation techniques into a unified framework.