Self-Organization, Entropy Generation Rate, and Boundary Defects: A Control Volume Approach

Abstract

Self-organization that leads to the discontinuous emergence of optimized new patterns is related to entropy generation and the export of entropy. Compared to the original pattern that the new, self-organized pattern replaces, the new features could involve an abrupt change in the pattern-volume. There is no clear principle of pathway selection for self-organization that is known for triggering a particular new self-organization pattern. The new pattern displays different types of boundary-defects necessary for stabilizing the new order. Boundary-defects can contain high entropy regions of concentrated chemical species. On the other hand, the reorganization (or refinement) of an established pattern is a more kinetically tractable process, where the entropy generation rate varies continuously with the imposed variables that enable and sustain the pattern features. The maximum entropy production rate (MEPR) principle is one possibility that may have predictive capability for self-organization. The scale of shapes that form or evolve during self-organization and reorganization are influenced by the export of specific defects from the control volume of study. The control volume (CV) approach must include the texture patterns to be located inside the CV for the MEPR analysis to be applicable. These hypotheses were examined for patterns that are well-characterized for solidification and wear processes. We tested the governing equations for bifurcations (the onset of new patterns) and for reorganization (the fine tuning of existing patterns) with published experimental data, across the range of solidification morphologies and nonequilibrium phases, for metallic glass and featureless crystalline solids. The self-assembling features of surface-texture patterns for friction and wear conditions were also modeled with the entropy generation (MEPR) principle, including defect production (wear debris). We found that surface texture and entropy generation in the control volume could be predictive for self-organization. The main results of this study provide support to the hypothesis that self-organized patterns are a consequence of the maximum entropy production rate per volume principle. Patterns at any scale optimize a certain outcome and have utility. We discuss some similarities between the self-organization behavior of both inanimate and living systems, with ideas regarding the optimizing features of self-organized pattern features that impact functionality, beauty, and consciousness.

Investigating a Method for a Horizontal Comprehensive Eco-Compensation Standard of Interregional Ecological Regulating Services

“…Based on MEP, it is conceived that if the value of the ecological regulating services is visualized, the dynamic equilibrium state of the value surface is likely to form a normal bell-shaped distribution. The value curved surface expands around to form a dynamic and stable surface structure [48,49]. When it extends to the adjacent districts, the surface can be Entropy 2023, 25, 1319 5 of 23 calculated to obtain the ecological regulation output value, and the transmission relation of eco-compensation is formed naturally.…”

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

“…The behavior of open complex systems like the troposphere is difficult to model [7][8][9]. However, it is becoming recognized that the entropy generation rates, temperature distributions, chemical partitioning, fluid circulation patterns, and phase-boundary shapes are related [10], particularly when the system is at steady-state conditions [10][11][12][13][14][15][16][17][18][19][20][21][22] thereby allowing for new models to be explored such as the one presented in this article. The entropy generation rate has a relationship to pattern formations.…”

“…The entropy generation rate has a relationship to pattern formations. Patterns and shapes have been studied with changing entropy generation rate principles for galaxy clusters, Hele-Shaw cells, natural convection, smokestacks, evolutionary biological systems, and directional freezing [10,[13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. There is a scale at which free-energy dissipation and entropy generation are optimized by a system when it picks its dominant entropy generation mechanism [22].…”

In situphase formation during high-temperature synthesis in clad mechanocomposites based on the Ti–Al system

“…In this regard, for a deeper understanding of the behavior of such systems at the stages of synthesis, and in particular for understanding micro-and macro-kinetic processes, it is necessary to correlate experimental data with model combustion mechanisms in nanostructured heterogeneous systems. In this case, methods related to the mechanisms of self-organization of the structure can provide new insights into the mechanisms of synthesis in the mechanically activated and clad nanostructured systems (Sekhar, 2021). In particular, dissipative vibrational chemical reactions, i.e.…”