Special Issue "Entropy and Its Applications across Disciplines"

A special issue of Entropy (ISSN 1099-4300).

Deadline for manuscript submissions: closed (31 December 2017).

Special Issue Editors

Prof. Amos Maritan
Website
Guest Editor
Department of Physics and Astronomy, University of Padova, Via Marzolo 8, 35131, Padova, Italy
Interests: statistical mechanics; biological physics; ecology; complex systems; neuroscience
Special Issues and Collections in MDPI journals
Dr. Samir Suweis
Website
Guest Editor
Department of Physics and Astronomy, University of Padova, Via Marzolo 8, 35131, Padova, Italy
Interests: ecosystem organizations; ecological networks; stochastic modelling of ecosystems dynamics and hydrological processes; sustainability and ecosystems services
Dr. Jordi Hidalgo
Website
Guest Editor
Department of Physics and Astronomy, University of Padova, Via Marzolo 8, 35131, Padova, Italy
Interests: critical phenomena; information theory; stochastic processes

Special Issue Information

Dear Colleagues,

The entropy concept was born initially in thermodynamics and is credited to the work of Rudolf Clausius. It was successively interpreted in terms of probability/statistics by Ludwig Boltzmann and J. Willard Gibbs, and ultimately led to the formulation of equilibrium statistical mechanics. The principle of maximum entropy (MaxEnt) allows an elegant derivation of the various statistical ensembles as emphasized by Jaynes by using the information entropy introduced by Shannon.

Entropy and the MaxEnt principle are now commonly used in many disciplines for the analysis of both complex equilibrium and non-equilibrium systems and is being increasingly employed in a variety of contexts, such as ecology, spectral analysis, electron microscopy, and neuroscience for inference from incomplete data. In all these applications, one is faced with problems related to the level of description of the system or coarse graining, which interestingly influence the final results.

This Special Issue invites contributions from leading groups to present original results or review the state-of-the-art of the use of entropy or the MaxEnt principle in their individual disciplines. This will lead to a cross-fertilization of ideas and techniques, and illuminate the use of these powerful techniques across disciplines.

Prof. Dr. Amos Maritan
Dr. Samir Suweis
Dr. Jordi Hidalgo
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Equilibrium & non-equlibrium statistical physics
  • microscopic thermodynamics
  • information theory in complex systems
  • quantitive biology & ecology, neuroscience

Published Papers (15 papers)

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Open AccessFeature PaperArticle
Nonequilibrium Entropic Bounds for Darwinian Replicators
Entropy 2018, 20(2), 98; https://doi.org/10.3390/e20020098 - 31 Jan 2018
Cited by 3
Abstract
Life evolved on our planet by means of a combination of Darwinian selection and innovations leading to higher levels of complexity. The emergence and selection of replicating entities is a central problem in prebiotic evolution. Theoretical models have shown how populations of different [...] Read more.
Life evolved on our planet by means of a combination of Darwinian selection and innovations leading to higher levels of complexity. The emergence and selection of replicating entities is a central problem in prebiotic evolution. Theoretical models have shown how populations of different types of replicating entities exclude or coexist with other classes of replicators. Models are typically kinetic, based on standard replicator equations. On the other hand, the presence of thermodynamical constraints for these systems remain an open question. This is largely due to the lack of a general theory of statistical methods for systems far from equilibrium. Nonetheless, a first approach to this problem has been put forward in a series of novel developements falling under the rubric of the extended second law of thermodynamics. The work presented here is twofold: firstly, we review this theoretical framework and provide a brief description of the three fundamental replicator types in prebiotic evolution: parabolic, malthusian and hyperbolic. Secondly, we employ these previously mentioned techinques to explore how replicators are constrained by thermodynamics. Finally, we comment and discuss where further research should be focused on. Full article
(This article belongs to the Special Issue Entropy and Its Applications across Disciplines)
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Open AccessArticle
Self-Organization of Genome Expression from Embryo to Terminal Cell Fate: Single-Cell Statistical Mechanics of Biological Regulation
Entropy 2018, 20(1), 13; https://doi.org/10.3390/e20010013 - 28 Dec 2017
Cited by 6
Abstract
A statistical mechanical mean-field approach to the temporal development of biological regulation provides a phenomenological, but basic description of the dynamical behavior of genome expression in terms of autonomous self-organization with a critical transition (Self-Organized Criticality: SOC). This approach reveals the basis of [...] Read more.
A statistical mechanical mean-field approach to the temporal development of biological regulation provides a phenomenological, but basic description of the dynamical behavior of genome expression in terms of autonomous self-organization with a critical transition (Self-Organized Criticality: SOC). This approach reveals the basis of self-regulation/organization of genome expression, where the extreme complexity of living matter precludes any strict mechanistic approach. The self-organization in SOC involves two critical behaviors: scaling-divergent behavior (genome avalanche) and sandpile-type critical behavior. Genome avalanche patterns—competition between order (scaling) and disorder (divergence) reflect the opposite sequence of events characterizing the self-organization process in embryo development and helper T17 terminal cell differentiation, respectively. On the other hand, the temporal development of sandpile-type criticality (the degree of SOC control) in mouse embryo suggests the existence of an SOC control landscape with a critical transition state (i.e., the erasure of zygote-state criticality). This indicates that a phase transition of the mouse genome before and after reprogramming (immediately after the late 2-cell state) occurs through a dynamical change in a control parameter. This result provides a quantitative open-thermodynamic appreciation of the still largely qualitative notion of the epigenetic landscape. Our results suggest: (i) the existence of coherent waves of condensation/de-condensation in chromatin, which are transmitted across regions of different gene-expression levels along the genome; and (ii) essentially the same critical dynamics we observed for cell-differentiation processes exist in overall RNA expression during embryo development, which is particularly relevant because it gives further proof of SOC control of overall expression as a universal feature. Full article
(This article belongs to the Special Issue Entropy and Its Applications across Disciplines)
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Open AccessArticle
Remarks on the Maximum Entropy Principle with Application to the Maximum Entropy Theory of Ecology
Entropy 2018, 20(1), 11; https://doi.org/10.3390/e20010011 - 27 Dec 2017
Cited by 7
Abstract
In the first part of the paper we work out the consequences of the fact that Jaynes’ Maximum Entropy Principle, when translated in mathematical terms, is a constrained extremum problem for an entropy function H ( p ) expressing the uncertainty associated with [...] Read more.
In the first part of the paper we work out the consequences of the fact that Jaynes’ Maximum Entropy Principle, when translated in mathematical terms, is a constrained extremum problem for an entropy function H ( p ) expressing the uncertainty associated with the probability distribution p. Consequently, if two observers use different independent variables p or g ( p ) , the associated entropy functions have to be defined accordingly and they are different in the general case. In the second part we apply our findings to an analysis of the foundations of the Maximum Entropy Theory of Ecology (M.E.T.E.) a purely statistical model of an ecological community. Since the theory has received considerable attention by the scientific community, we hope to give a useful contribution to the same community by showing that the procedure of application of MEP, in the light of the theory developed in the first part, suffers from some incongruences. We exhibit an alternative formulation which is free from these limitations and that gives different results. Full article
(This article belongs to the Special Issue Entropy and Its Applications across Disciplines)
Open AccessArticle
Stochastic Thermodynamics: A Dynamical Systems Approach
Entropy 2017, 19(12), 693; https://doi.org/10.3390/e19120693 - 17 Dec 2017
Cited by 1
Abstract
In this paper, we develop an energy-based, large-scale dynamical system model driven by Markov diffusion processes to present a unified framework for statistical thermodynamics predicated on a stochastic dynamical systems formalism. Specifically, using a stochastic state space formulation, we develop a nonlinear stochastic [...] Read more.
In this paper, we develop an energy-based, large-scale dynamical system model driven by Markov diffusion processes to present a unified framework for statistical thermodynamics predicated on a stochastic dynamical systems formalism. Specifically, using a stochastic state space formulation, we develop a nonlinear stochastic compartmental dynamical system model characterized by energy conservation laws that is consistent with statistical thermodynamic principles. In particular, we show that the difference between the average supplied system energy and the average stored system energy for our stochastic thermodynamic model is a martingale with respect to the system filtration. In addition, we show that the average stored system energy is equal to the mean energy that can be extracted from the system and the mean energy that can be delivered to the system in order to transfer it from a zero energy level to an arbitrary nonempty subset in the state space over a finite stopping time. Full article
(This article belongs to the Special Issue Entropy and Its Applications across Disciplines)
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Open AccessArticle
Is an Entropy-Based Approach Suitable for an Understanding of the Metabolic Pathways of Fermentation and Respiration?
Entropy 2017, 19(12), 662; https://doi.org/10.3390/e19120662 - 04 Dec 2017
Cited by 3
Abstract
Lactic fermentation and respiration are important metabolic pathways on which life is based. Here, the rate of entropy in a cell associated to fermentation and respiration processes in glucose catabolism of living systems is calculated. This is done for both internal and external [...] Read more.
Lactic fermentation and respiration are important metabolic pathways on which life is based. Here, the rate of entropy in a cell associated to fermentation and respiration processes in glucose catabolism of living systems is calculated. This is done for both internal and external heat and matter transport according to a thermodynamic approach based on Prigogine’s formalism. It is shown that the rate of entropy associated to irreversible reactions in fermentation processes is higher than the corresponding one in respiration processes. Instead, this behaviour is reversed for diffusion of chemical species and for heat exchanges. The ratio between the rates of entropy associated to the two metabolic pathways has a space and time dependence for diffusion of chemical species and is invariant for heat and irreversible reactions. In both fermentation and respiration processes studied separately, the total entropy rate tends towards a minimum value fulfilling Prigogine’s minimum dissipation principle and is in accordance with the second principle of thermodynamics. The applications of these results could be important for cancer detection and therapy. Full article
(This article belongs to the Special Issue Entropy and Its Applications across Disciplines)
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Open AccessFeature PaperArticle
On Maximum Entropy and Inference
Entropy 2017, 19(12), 642; https://doi.org/10.3390/e19120642 - 28 Nov 2017
Cited by 4
Abstract
Maximum entropy is a powerful concept that entails a sharp separation between relevant and irrelevant variables. It is typically invoked in inference, once an assumption is made on what the relevant variables are, in order to estimate a model from data, that affords [...] Read more.
Maximum entropy is a powerful concept that entails a sharp separation between relevant and irrelevant variables. It is typically invoked in inference, once an assumption is made on what the relevant variables are, in order to estimate a model from data, that affords predictions on all other (dependent) variables. Conversely, maximum entropy can be invoked to retrieve the relevant variables (sufficient statistics) directly from the data, once a model is identified by Bayesian model selection. We explore this approach in the case of spin models with interactions of arbitrary order, and we discuss how relevant interactions can be inferred. In this perspective, the dimensionality of the inference problem is not set by the number of parameters in the model, but by the frequency distribution of the data. We illustrate the method showing its ability to recover the correct model in a few prototype cases and discuss its application on a real dataset. Full article
(This article belongs to the Special Issue Entropy and Its Applications across Disciplines)
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Open AccessArticle
Thermodynamics, Statistical Mechanics and Entropy
Entropy 2017, 19(11), 603; https://doi.org/10.3390/e19110603 - 10 Nov 2017
Cited by 10
Abstract
The proper definition of thermodynamics and the thermodynamic entropy is discussed in the light of recent developments. The postulates for thermodynamics are examined critically, and some modifications are suggested to allow for the inclusion of long-range forces (within a system), inhomogeneous systems with [...] Read more.
The proper definition of thermodynamics and the thermodynamic entropy is discussed in the light of recent developments. The postulates for thermodynamics are examined critically, and some modifications are suggested to allow for the inclusion of long-range forces (within a system), inhomogeneous systems with non-extensive entropy, and systems that can have negative temperatures. Only the thermodynamics of finite systems are considered, with the condition that the system is large enough for the fluctuations to be smaller than the experimental resolution. The statistical basis for thermodynamics is discussed, along with four different forms of the (classical and quantum) entropy. The strengths and weaknesses of each are evaluated in relation to the requirements of thermodynamics. Effects of order 1 / N , where N is the number of particles, are included in the discussion because they have played a significant role in the literature, even if they are too small to have a measurable effect in an experiment. The discussion includes the role of discreteness, the non-zero width of the energy and particle number distributions, the extensivity of models with non-interacting particles, and the concavity of the entropy with respect to energy. The results demonstrate the validity of negative temperatures. Full article
(This article belongs to the Special Issue Entropy and Its Applications across Disciplines)
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Open AccessArticle
Single-Cell Reprogramming in Mouse Embryo Development through a Critical Transition State
Entropy 2017, 19(11), 584; https://doi.org/10.3390/e19110584 - 02 Nov 2017
Cited by 1
Abstract
Our previous work on the temporal development of the genome-expression profile in single-cell early mouse embryo indicated that reprogramming occurs via a critical transition state, where the critical-regulation pattern of the zygote state disappears. In this report, we unveil the detailed mechanism of [...] Read more.
Our previous work on the temporal development of the genome-expression profile in single-cell early mouse embryo indicated that reprogramming occurs via a critical transition state, where the critical-regulation pattern of the zygote state disappears. In this report, we unveil the detailed mechanism of how the dynamic interaction of thermodynamic states (critical states) enables the genome system to pass through the critical transition state to achieve genome reprogramming right after the late 2-cell state. Self-organized criticality (SOC) control of overall expression provides a snapshot of self-organization and explains the coexistence of critical states at a certain experimental time point. The time-development of self-organization is dynamically modulated by changes in expression flux between critical states through the cell nucleus milieu, where sequential global perturbations involving activation-inhibition of multiple critical states occur from the middle 2-cell to the 4-cell state. Two cyclic fluxes act as feedback flow and generate critical-state coherent oscillatory dynamics. Dynamic perturbation of these cyclic flows due to vivid activation of the ensemble of low-variance expression (sub-critical state) genes allows the genome system to overcome a transition state during reprogramming. Our findings imply that a universal mechanism of long-term global RNA oscillation underlies autonomous SOC control, and the critical gene ensemble at a critical point (CP) drives genome reprogramming. Identification of the corresponding molecular players will be essential for understanding single-cell reprogramming. Full article
(This article belongs to the Special Issue Entropy and Its Applications across Disciplines)
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Open AccessArticle
A Behavioural Analysis of Complexity in Socio-Technical Systems under Tension Modelled by Petri Nets
Entropy 2017, 19(11), 572; https://doi.org/10.3390/e19110572 - 25 Oct 2017
Cited by 3
Abstract
Complexity analysis of dynamic systems provides a better understanding of the internal behaviours that are associated with tension and efficiency, which in the socio-technical systems may lead to innovation. One of the popular approaches for the assessment of complexity is associated with self-similarity. [...] Read more.
Complexity analysis of dynamic systems provides a better understanding of the internal behaviours that are associated with tension and efficiency, which in the socio-technical systems may lead to innovation. One of the popular approaches for the assessment of complexity is associated with self-similarity. The dynamic component of dynamic systems represents the relationships and interactions among the inner elements (and its surroundings) and fully describes its behaviour. The approach used in this work addresses complexity analysis in terms of system behaviour, i.e., the so-called behavioural analysis of complexity. The self-similarity of a system (structural or behavioural) can be determined, for example, using fractal geometry, whose toolbox provides a number of methods for the measurement of the so-called fractal dimension. Other instruments for measuring the self-similarity in a system, include the Hurst exponent and the framework of complex system theory in general. The approach introduced in this work defines the complexity analysis in a social-technical system under tension. The proposed procedure consists of modelling the key dynamic components of a discrete event dynamic system by any definition of Petri nets. From the stationary probabilities, one can then decide whether the system is self-similar using the abovementioned tools. In addition, the proposed approach allows for finding the critical values (phase transitions) of the analysed systems. Full article
(This article belongs to the Special Issue Entropy and Its Applications across Disciplines)
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Open AccessArticle
Is Cetacean Intelligence Special? New Perspectives on the Debate
Entropy 2017, 19(10), 543; https://doi.org/10.3390/e19100543 - 13 Oct 2017
Cited by 1
Abstract
In recent years, the interpretation of our observations of animal behaviour, in particular that of cetaceans, has captured a substantial amount of attention in the scientific community. The traditional view that supports a special intellectual status for this mammalian order has fallen under [...] Read more.
In recent years, the interpretation of our observations of animal behaviour, in particular that of cetaceans, has captured a substantial amount of attention in the scientific community. The traditional view that supports a special intellectual status for this mammalian order has fallen under significant scrutiny, in large part due to problems of how to define and test the cognitive performance of animals. This paper presents evidence supporting complex cognition in cetaceans obtained using the recently developed intelligence and embodiment hypothesis. This hypothesis is based on evolutionary neuroscience and postulates the existence of a common information-processing principle associated with nervous systems that evolved naturally and serves as the foundation from which intelligence can emerge. This theoretical framework explaining animal intelligence in neural computational terms is supported using a new mathematical model. Two pathways leading to higher levels of intelligence in animals are identified, each reflecting a trade-off either in energetic requirements or the number of neurons used. A description of the evolutionary pathway that led to increased cognitive capacities in cetacean brains is detailed and evidence supporting complex cognition in cetaceans is presented. This paper also provides an interpretation of the adaptive function of cetacean neuronal traits. Full article
(This article belongs to the Special Issue Entropy and Its Applications across Disciplines)
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Open AccessArticle
Logical Entropy and Logical Mutual Information of Experiments in the Intuitionistic Fuzzy Case
Entropy 2017, 19(8), 429; https://doi.org/10.3390/e19080429 - 21 Aug 2017
Cited by 7
Abstract
In this contribution, we introduce the concepts of logical entropy and logical mutual information of experiments in the intuitionistic fuzzy case, and study the basic properties of the suggested measures. Subsequently, by means of the suggested notion of logical entropy of an IF-partition, [...] Read more.
In this contribution, we introduce the concepts of logical entropy and logical mutual information of experiments in the intuitionistic fuzzy case, and study the basic properties of the suggested measures. Subsequently, by means of the suggested notion of logical entropy of an IF-partition, we define the logical entropy of an IF-dynamical system. It is shown that the logical entropy of IF-dynamical systems is invariant under isomorphism. Finally, an analogy of the Kolmogorov–Sinai theorem on generators for IF-dynamical systems is proved. Full article
(This article belongs to the Special Issue Entropy and Its Applications across Disciplines)
Open AccessArticle
Invalid Microstate Densities for Model Systems Lead to Apparent Violation of Thermodynamic Law
Entropy 2017, 19(7), 314; https://doi.org/10.3390/e19070314 - 30 Jun 2017
Abstract
It is often incorrectly assumed that the number of microstates Ω ( E , V , N , . . . ) available to an isolated system can have arbitrary dependence on the extensive variables E , V , N , ... However, [...] Read more.
It is often incorrectly assumed that the number of microstates Ω ( E , V , N , . . . ) available to an isolated system can have arbitrary dependence on the extensive variables E , V , N , ... However, this is not the case for systems which can, in principle, reach thermodynamic equilibrium since restrictions arise from the underlying equilibrium statistical mechanic axioms of independence and a priori equal probability of microstates. Here we derive a concise criterion specifying the condition on Ω which must be met in order for a system to be able, in principle, to reach thermodynamic equilibrium. Natural quantum systems obey this criterion and therefore can, in principle, reach thermodynamic equilibrium. However, models which do not respect this criterion will present inconsistencies when treated under equilibrium thermodynamic formalism. This has relevance to a number of recent models in which negative heat capacity and other violations of fundamental thermodynamic law have been reported. Full article
(This article belongs to the Special Issue Entropy and Its Applications across Disciplines)
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Open AccessReply
Maximum Entropy Theory of Ecology: A Reply to Harte
Entropy 2018, 20(5), 308; https://doi.org/10.3390/e20050308 - 24 Apr 2018
Cited by 3
Abstract
In a paper published in this journal, I addressed the following problem: under which conditions will two scientists, observing the same system and sharing the same initial information, reach the same probabilistic description upon the application of the Maximum Entropy inference principle (MaxEnt) [...] Read more.
In a paper published in this journal, I addressed the following problem: under which conditions will two scientists, observing the same system and sharing the same initial information, reach the same probabilistic description upon the application of the Maximum Entropy inference principle (MaxEnt) independent of the probability distribution chosen to set up the MaxEnt procedure. This is a minimal objectivity requirement which is generally asked for scientific investigation. In the same paper, I applied the findings to a critical examination of the application of MaxEnt made in Harte’s Maximum Entropy Theory of Ecology (METE). Prof. Harte published a comment to my paper and this is my reply. For the sake of the reader who may be unaware of the content of the papers, I have tried to make this reply self-contained and to skip technical details. However, I invite the interested reader to consult the previously published papers. Full article
(This article belongs to the Special Issue Entropy and Its Applications across Disciplines)
Open AccessComment
Maximum Entropy and Theory Construction: A Reply to Favretti
Entropy 2018, 20(4), 285; https://doi.org/10.3390/e20040285 - 14 Apr 2018
Cited by 4
Abstract
In the maximum entropy theory of ecology (METE), the form of a function describing the distribution of abundances over species and metabolic rates over individuals in an ecosystem is inferred using the maximum entropy inference procedure. Favretti shows that an alternative maximum entropy [...] Read more.
In the maximum entropy theory of ecology (METE), the form of a function describing the distribution of abundances over species and metabolic rates over individuals in an ecosystem is inferred using the maximum entropy inference procedure. Favretti shows that an alternative maximum entropy model exists that assumes the same prior knowledge and makes predictions that differ from METE’s. He shows that both cannot be correct and asserts that his is the correct one because it can be derived from a classic microstate-counting calculation. I clarify here exactly what the core entities and definitions are for METE, and discuss the relevance of two critical issues raised by Favretti: the existence of a counting procedure for microstates and the choices of definition of the core elements of a theory. I emphasize that a theorist controls how the core entities of his or her theory are defined, and that nature is the final arbiter of the validity of a theory. Full article
(This article belongs to the Special Issue Entropy and Its Applications across Disciplines)
Open AccessDiscussion
Quality Systems. A Thermodynamics-Related Interpretive Model
Entropy 2017, 19(8), 418; https://doi.org/10.3390/e19080418 - 17 Aug 2017
Cited by 3
Abstract
In the present paper, a Quality Systems Theory is presented. Certifiable Quality Systems are treated and interpreted in accordance with a Thermodynamics-based approach. Analysis is also conducted on the relationship between Quality Management Systems (QMSs) and systems theories. A measure of entropy is [...] Read more.
In the present paper, a Quality Systems Theory is presented. Certifiable Quality Systems are treated and interpreted in accordance with a Thermodynamics-based approach. Analysis is also conducted on the relationship between Quality Management Systems (QMSs) and systems theories. A measure of entropy is proposed for QMSs, including a virtual document entropy and an entropy linked to processes and organisation. QMSs are also interpreted in light of Cybernetics, and interrelations between Information Theory and quality are also highlighted. A measure for the information content of quality documents is proposed. Such parameters can be used as adequacy indices for QMSs. From the discussed approach, suggestions for organising QMSs are also derived. Further interpretive thermodynamic-based criteria for QMSs are also proposed. The work represents the first attempt to treat quality organisational systems according to a thermodynamics-related approach. At this stage, no data are available to compare statements in the paper. Full article
(This article belongs to the Special Issue Entropy and Its Applications across Disciplines)
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