Entropy generation minimization (finite time thermodynamics, or thermodynamic optimization) is the method that combines into simple models the most basic concepts of heat transfer, fluid mechanics, and thermodynamics. These simple models are used in the optimization of real (irreversible) devices and processes, subject to finite‐size and finite‐time constraints. The review traces the development and adoption of the method in several sectors of mainstream thermal engineering and science: cryogenics, heat transfer, education, storage systems, solar power plants, nuclear and fossil power plants, and refrigerators. Emphasis is placed on the fundamental and technological importance of the optimization method and its results, the pedagogical merits of the method, and the chronological development of the field.

Entropy generation minimization: The new thermodynamics of finite-size devices and finite-time processes

Abstract The historical background, research development, and the state-of-the-art of finite time thermodynamic theory and applications are reviewed from the point of view of both physics and engineering. The emphasis is on the performance optimization of thermodynamic processes and devices with finite-time and/or finite-size constraints, including heat engines, refrigerators, heat pumps, chemical reactions and some other processes, with respect to the following aspects: the study of Newton's law systems, an analysis of the effect of heat resistance and other irreversible loss models on the performance, an analysis of the effect of heat reservoir models on the performance, as well as the application for real thermodynamic processes and devices. It is pointed out that the generalized thermodynamic optimization theory is the development direction of finite thermodynamics in the future.

Finite Time Thermodynamic Optimization or Entropy Generation Minimization of Energy Systems

Motivation: A major challenge of systems biology is to infer biochemical interactions from large-scale observations, such as transcriptomics, proteomics and metabolomics. We propose to use a partial correlation analysis to construct approximate Undirected Dependency Graphs from such large-scale biochemical data. This approach enables a distinction between direct and indirect interactions of biochemical compounds, thereby inferring the underlying network topology.

Results: The method is first thoroughly evaluated with a large set of simulated data. Results indicate that the approach has good statistical power and a low False Discovery Rate even in the presence of noise in the data. We then applied the method to an existing data set of yeast gene expression. Several small gene networks were inferred and found to contain genes known to be collectively involved in particular biochemical processes. In some of these networks there are also uncharacterized ORFs present, which lead to hypotheses about their functions.

Availability: Programs running in MS-Windows and Linux for applying zeroth, first, second and third order partial correlation analysis can be downloaded at: http://mendes.vbi.vt.edu/tiki-index.php?page=Software

Supplementary information: Supplementary information can be found at: URL to be decided

Discovery of meaningful associations in genomic data using partial correlation coefficients

Recent experiments on the chlorite-iodide-malonic acid-starch reaction in a gel reactor give the first evidence of the existence of the symmetry breaking, reaction-diffusion structures predicted by Turing in 1952. A five-variable model that describes the temporal behavior of the system is reduced to a two-variable model, and its spatial behavior is analyzed. Structures have been found with wavelengths that are in good agreement with those observed experimentally. The gel plays a key role by binding key iodine species, thereby creating the necessary difference in the effective diffusion coefficients of the activator and inhibitor species, iodide and chlorite ions, respectively.

https://science.sciencemag.org/content/sci/251/4994/650.full.pdf

Modeling of turing structures in the chlorite--iodide--malonic Acid--starch reaction system.

The organization, regulation and dynamical responses of biological systems are in many cases too complex to allow intuitive predictions and require the support of mathematical modeling for quantitative assessments and a reliable understanding of system functioning. All steps of constructing mathematical models for biological systems are challenging, but arguably the most difficult task among them is the estimation of model parameters and the identification of the structure and regulation of the underlying biological networks. Recent advancements in modern high-throughput techniques have been allowing the generation of time series data that characterize the dynamics of genomic, proteomic, metabolic, and physiological responses and enable us, at least in principle, to tackle estimation and identification tasks using 'top-down' or 'inverse' approaches. While the rewards of a successful inverse estimation or identification are great, the process of extracting structural and regulatory information is technically difficult. The challenges can generally be categorized into four areas, namely, issues related to the data, the model, the mathematical structure of the system, and the optimization and support algorithms. Many recent articles have addressed inverse problems within the modeling framework of Biochemical Systems Theory (BST). BST was chosen for these tasks because of its unique structural flexibility and the fact that the structure and regulation of a biological system are mapped essentially one-to-one onto the parameters of the describing model. The proposed methods mainly focused on various optimization algorithms, but also on support techniques, including methods for circumventing the time consuming numerical integration of systems of differential equations, smoothing overly noisy data, estimating slopes of time series, reducing the complexity of the inference task, and constraining the parameter search space. Other methods targeted issues of data preprocessing, detection and amelioration of model redundancy, and model-free or model-based structure identification. The total number of proposed methods and their applications has by now exceeded one hundred, which makes it difficult for the newcomer, as well as the expert, to gain a comprehensive overview of available algorithmic options and limitations. To facilitate the entry into the field of inverse modeling within BST and related modeling areas, the article presented here reviews the field and proposes an operational 'work-flow' that guides the user through the estimation process, identifies possibly problematic steps, and suggests corresponding solutions based on the specific characteristics of the various available algorithms. The article concludes with a discussion of the present state of the art and with a description of open questions.

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Recent Developments in Parameter Estimation and Structure Identification of Biochemical and Genomic Systems

Statistical properties of chaos in Chebyshev maps

In this article we elaborate on the structure of the generalized Lotka-Volterra (GLV) form for nonlinear differential equations. We discuss here the algebraic properties of the GLV family, such as the invariance under quasimonomial transformations and the underlying structure of classes of equivalence. Each class possesses a unique representative under the classical quadratic Lotka-Volterra form. We show how other standard modeling forms of biological interest, such as S-systems or mass-action systems, are naturally embedded into the GLV form, which thus provides a formal framework for their comparison and for the establishment of transformation rules. We also focus on the issue of recasting of general nonlinear systems into the GLV format. We present a procedure for doing so and point at possible sources of ambiguity that could make the resulting Lotka-Volterra system dependent on the path followed. We then provide some general theorems that define the operational and algorithmic framework in which this is not the case.

Lotka-Volterra representation of general nonlinear systems.

In this paper we elaborate on the structure of the Generalized Lotka-Volterra (GLV) form for nonlinear differential equations. We discuss here the algebraic properties of the GLV family, such as the invariance under quasimonomial transformations and the underlying structure of classes of equivalence. Each class possesses a unique representative under the classical quadratic Lotka-Volterra form. We show how other standard modelling forms of biological interest, such as S-systems or mass-action systems are naturally embedded into the GLV form, which thus provides a formal framework for their comparison, and for the establishment of transformation rules. We also focus on the issue of recasting of general nonlinear systems into the GLV format. We present a procedure for doing so, and point at possible sources of ambiguity which could make the resulting Lotka-Volterra system dependent on the path followed. We then provide some general theorems that define the operational and algorithmic framework in which this is not the case.

Lotka-Volterra representation of general nonlinear systems

Nonpolynomial vector fields under the Lotka-Volterra normal form

It is sometimes desirable to produce for a nonlinear system of ODEs a new representation of simpler structural form, but it is well known that this goal may imply an increase in the dimension of the system. This is what happens if in this new representation the vector field has a lower degree of nonlinearity or a smaller number of nonlinear contributions. Until now both issues have been treated separately, rather unsystematically and, in some cases, at the expense of an excessive increase in the number of dimensions. We unify here the treatment of both issues in a common algebraic framework. This allows us to proceed algorithmically in terms of simple matrix operations.

Victor Fairén

Papers

Statistical properties of chaos in Chebyshev maps

Lotka-Volterra representation of general nonlinear systems.

Lotka-Volterra representation of general nonlinear systems

Nonpolynomial vector fields under the Lotka-Volterra normal form

Algebraic recasting of nonlinear systems of ODEs into universal formats