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Entropy, Time and Evolution II

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A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Time".

Deadline for manuscript submissions: closed (10 November 2023) | Viewed by 18760

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Prof. Dr. Leonid M. Martyushev

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1. Technical Physics Department, Ural Federal University, 19 Mira St., 620002 Ekaterinburg, Russia
2. Institute of Industrial Ecology, Russian Academy of Sciences, 20 S. Kovalevskaya St., 620219 Ekaterinburg, Russia
Interests: fundamental problems of nature (irreversibility, asymmetry and scale of time, evolution, etc.); non-equilibrium thermodynamics; the second law of thermodynamics and entropy; maximum entropy production in physics, chemistry and biology; growth processes in nature (experiment, theory and simulation); morphological stability (crystal growth and fluid flow); pattern formation (dendrites, viscous fingers, etc.)
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Dear Colleagues,

We, and the world around us, constantly develop and evolve. The Universe and stars as well as societies and living beings pass through sequential stages from birth to maturity and death. This is a continuous process: one is replaced with the other. The one that has appeared repeats the old in some way, while being new in the other. We, and the world around us, develop directionally and irreversibly.

From long ago, humanity has used time to describe this movement and, specifically, its directionality and duration. The greatest minds of the past were interested in this concept and studied time: St. Augustine, Newton, Kant, Bergson, Einstein, et al. However, time—one of the most complex and controversial concepts used by people—is still not fully defined and understood.

Entropy, another concept, appeared more than 150 years ago in thermodynamics and then penetrated and developed in other branches of science. This quantity is used to study the evolution of various objects by representatives of numerous sciences: physics, chemistry, biology, computer science, linguistics and economics, among others. There are a number of important statements formulated for this quantity in science. Most notably, these are the second law of thermodynamics and the principles of minimum and maximum entropy production. Entropy is considered to be a measure of irreversibility, directionality of a process, and it is similar to time in this respect. However, despite being difficult to introduce and measure for some systems, entropy is simpler than the concept of time.

The following question arise in this regard: To what extent are time and entropy related? Authors are invited submit articles seeking to answer this and related questions to this Special Issue.

Prof. Dr. Leonid M. Martyushev
Guest Editor

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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 submissions that pass pre-check are 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.

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Keywords

time in natural sciences
temporal asymmetries
entropy, entropy production
second law of thermodynamics
maximum and minimum entropy production
evolution of the universe, stars, planet system, climate, etc.
evolution of ecological systems, biological objects, etc.
evolution of networks, economics, languages, etc.

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Entropy, Time and Evolution in Entropy (11 articles)

Published Papers (7 papers)

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Research

14 pages, 566 KiB

Open AccessArticle

Quasi-Equilibrium States and Phase Transitions in Biological Evolution

by Artem Romanenko and Vitaly Vanchurin

Entropy 2024, 26(3), 201; https://doi.org/10.3390/e26030201 - 27 Feb 2024

Cited by 1 | Viewed by 1773

Abstract

We developed a macroscopic description of the evolutionary dynamics by following the temporal dynamics of the total Shannon entropy of sequences, denoted by S, and the average Hamming distance between them, denoted by H. We argue that a biological system can persist in the so-called quasi-equilibrium state for an extended period, characterized by strong correlations between S and H, before undergoing a phase transition to another quasi-equilibrium state. To demonstrate the results, we conducted a statistical analysis of SARS-CoV-2 data from the United Kingdom during the period between March 2020 and December 2023. From a purely theoretical perspective, this allowed us to systematically study various types of phase transitions described by a discontinuous change in the thermodynamic parameters. From a more-practical point of view, the analysis can be used, for example, as an early warning system for pandemics. Full article

(This article belongs to the Special Issue Entropy, Time and Evolution II)

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52 pages, 9198 KiB

Open AccessArticle

Theoretical Improvements in Enzyme Efficiency Associated with Noisy Rate Constants and Increased Dissipation

by Davor Juretić and Željana Bonačić Lošić

Entropy 2024, 26(2), 151; https://doi.org/10.3390/e26020151 - 9 Feb 2024

Cited by 2 | Viewed by 2117

Abstract

Previous studies have revealed the extraordinarily large catalytic efficiency of some enzymes. High catalytic proficiency is an essential accomplishment of biological evolution. Natural selection led to the increased turnover number, k_cat, and enzyme efficiency, k_cat/K_M, of uni–uni enzymes, which convert a single substrate into a single product. We added or multiplied random noise with chosen rate constants to explore the correlation between dissipation and catalytic efficiency for ten enzymes: beta-galactosidase, glucose isomerase, β-lactamases from three bacterial strains, ketosteroid isomerase, triosephosphate isomerase, and carbonic anhydrase I, II, and T200H. Our results highlight the role of biological evolution in accelerating thermodynamic evolution. The catalytic performance of these enzymes is proportional to overall entropy production—the main parameter from irreversible thermodynamics. That parameter is also proportional to the evolutionary distance of β-lactamases PC1, RTEM, and Lac-1 when natural or artificial evolution produces the optimal or maximal possible catalytic efficiency. De novo enzyme design and attempts to speed up the rate-limiting catalytic steps may profit from the described connection between kinetics and thermodynamics. Full article

(This article belongs to the Special Issue Entropy, Time and Evolution II)

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31 pages, 3610 KiB

Open AccessArticle

An Entropy Generation Rate Model for Tropospheric Behavior That Includes Cloud Evolution

by Jainagesh A. Sekhar

Entropy 2023, 25(12), 1625; https://doi.org/10.3390/e25121625 - 5 Dec 2023

Cited by 1 | Viewed by 5918

Abstract

A postulate that relates global warming to higher entropy generation rate demand in the tropospheric is offered and tested. This article introduces a low-complexity model to calculate the entropy generation rate required in the troposphere. The entropy generation rate per unit volume is noted to be proportional to the square of the Earth’s average surface temperature for a given positive rate of surface warming. The main postulate is that the troposphere responds with mechanisms to provide for the entropy generation rate that involves specific cloud morphologies and wind behavior. A diffuse-interface model is used to calculate the entropy generation rates of clouds. Clouds with limited vertical development, like the high-altitude cirrus or mid-altitude stratus clouds, are close-to-equilibrium clouds that do not generate much entropy but contribute to warming. Clouds like the cumulonimbus permit rapid vertical cloud development and can rapidly generate new entropy. Several extreme weather events that the Earth is experiencing are related to entropy-generating clouds that discharge a high rate of rain, hail, or transfer energy in the form of lightning. The water discharge from a cloud can cool the surface below the cloud but also add to the demand for a higher entropy generation rate in the cloud and troposphere. The model proposed predicts the atmospheric conditions required for bifurcations to severe-weather clouds. The calculated vertical velocity of thunderclouds associated with high entropy generation rates matches the recorded observations. The scale of instabilities for an evolving diffuse interface is related to the entropy generation rate per unit volume. Significant similarities exist between the morphologies and the entropy generation rate correlations in vertical cloud evolution and directionally solidified grainy microstructures. Such similarities are also explored to explore a generalized framework of pattern evolution and establish the relationships with the corresponding entropy generation rate. A complex system like the troposphere can invoke multiple phenomena that dominate at different spatial scales to meet the demand for an entropy generation rate. A few such possibilities are presented in the context of rapid and slow changes in weather patterns. Full article

(This article belongs to the Special Issue Entropy, Time and Evolution II)

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13 pages, 328 KiB

Open AccessArticle

Parameters of State in the Global Thermodynamics of Binary Ideal Gas Mixtures in a Stationary Heat Flow

by Anna Maciołek, Robert Hołyst, Karol Makuch, Konrad Giżyński and Paweł J. Żuk

Entropy 2023, 25(11), 1505; https://doi.org/10.3390/e25111505 - 31 Oct 2023

Cited by 4 | Viewed by 1598

Abstract

In this paper, we formulate the first law of global thermodynamics for stationary states of the binary ideal gas mixture subjected to heat flow. We map the non-uniform system onto the uniform one and show that the internal energy [...] Read more.

U (S^{*}, V, N_{1}, N_{2}, f_{1}^{*}, f_{2}^{*})

is the function of the following parameters of state: a non-equilibrium entropy

S^{*}

, volume V, number of particles of the first component,

N_{1}

, number of particles of the second component

N_{2}

and the renormalized degrees of freedom. The parameters

f_{1}^{*}, f_{2}^{*}

N_{1}, N_{2}

satisfy the relation

(N_{1} / (N_{1} + N_{2})) f_{1}^{*} / f_{1} + (N_{2} / (N_{1} + N_{2})) f_{2}^{*} / f_{2} = 1

(

f_{1}

and

f_{2}

are the degrees of freedom for each component respectively). Thus, only 5 parameters of state describe the non-equilibrium state of the binary mixture in the heat flow. We calculate the non-equilibrium entropy

S^{*}

and new thermodynamic parameters of state

f_{1}^{*}, f_{2}^{*}

explicitly. The latter are responsible for heat generation due to the concentration gradients. The theory reduces to equilibrium thermodynamics, when the heat flux goes to zero. As in equilibrium thermodynamics, the steady-state fundamental equation also leads to the thermodynamic Maxwell relations for measurable steady-state properties. Full article

(This article belongs to the Special Issue Entropy, Time and Evolution II)

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17 pages, 925 KiB

Open AccessArticle

Complex Networks and Interacting Particle Systems

by Noam Abadi and Franco Ruzzenenti

Entropy 2023, 25(11), 1490; https://doi.org/10.3390/e25111490 - 27 Oct 2023

Viewed by 1956

Abstract

Complex networks is a growing discipline aimed at understanding large interacting systems. One of its goals is to establish a relation between the interactions of a system and the networks structure that emerges. Taking a Lennard-Jones particle system as an example, we show that when interactions are governed by a potential, the notion of structure given by the physical arrangement of the interacting particles can be interpreted as a binary approximation to the interaction potential. This approximation simplifies the calculation of the partition function of the system and allows to study the stability of the interaction structure. We compare simulated results with those from the approximated partition function and show how the network and system perspective complement each other. With this, we draw a direct connection between the interactions of a molecular system and the network structure it forms and assess the degree to which it describes the system. We conclude by discussing the advantages and limitations of this method for weighted networks, as well as how this concept might be extended to more general systems. Full article

(This article belongs to the Special Issue Entropy, Time and Evolution II)

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11 pages, 376 KiB

Open AccessFeature PaperArticle

Fundamental Relation for the Ideal Gas in the Gravitational Field and Heat Flow

by Robert Hołyst, Paweł J. Żuk, Karol Makuch, Anna Maciołek and Konrad Giżyński

Entropy 2023, 25(11), 1483; https://doi.org/10.3390/e25111483 - 26 Oct 2023

Cited by 2 | Viewed by 2881

Abstract

We formulate the first law of global thermodynamics for stationary states of the ideal gas in the gravitational field subjected to heat flow. We map the non-uniform system (described by profiles of the density and temperature) onto the uniform one and show that [...] Read more.

U (S^{*}, V, N, L, M^{*})

is the function of the following parameters of state: the non-equilibrium entropy

S^{*}

, volume V, number of particles, N, height of the column L along the gravitational force, and renormalized mass of a particle

M^{*}

. Each parameter corresponds to a different way of energy exchange with the environment. The parameter

M^{*}

changes internal energy due to the shift of the centre of mass induced by the heat flux. We give analytical expressions for the non-equilibrium entropy

S^{*}

and effective mass

M^{*}

. When the heat flow goes to zero,

S^{*}

approaches equilibrium entropy. Additionally, when the gravitational field vanishes, our fundamental relation reduces to the fundamental relation at equilibrium. Full article

(This article belongs to the Special Issue Entropy, Time and Evolution II)

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8 pages, 303 KiB

Open AccessArticle

The Time Evolution of Mutual Information between Disjoint Regions in the Universe

by Biswajit Pandey

Entropy 2023, 25(7), 1094; https://doi.org/10.3390/e25071094 - 21 Jul 2023

Cited by 1 | Viewed by 1469

Abstract

We study the time evolution of mutual information between mass distributions in spatially separated but casually connected regions in an expanding universe. The evolution of mutual information is primarily determined by the configuration entropy rate, which depends on the dynamics of the expansion and growth of density perturbations. The joint entropy between distributions from the two regions plays a negligible role in such evolution. Mutual information decreases with time in a matter-dominated universe, whereas it stays constant in a

Λ

-dominated universe. The

Λ

CDM model and some other models of dark energy predict a minimum in mutual information beyond which dark energy dominates the dynamics of the universe. Mutual information may have deeper connections to the dark energy and accelerated expansion of the universe. Full article

(This article belongs to the Special Issue Entropy, Time and Evolution II)

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