scholarly journals Möbius Transforms, Cycles and q-triplets in Statistical Mechanics

Entropy ◽  
2019 ◽  
Vol 21 (12) ◽  
pp. 1155 ◽  
Author(s):  
Jean Pierre Gazeau ◽  
Constantino Tsallis
Keyword(s):  
Statistical Mechanics ◽  
Complex Systems ◽  
Physical Properties ◽  
Real Number ◽  
Möbius Transforms ◽  
Complex Phenomena

In the realm of Boltzmann-Gibbs (BG) statistical mechanics and its q-generalisation for complex systems, we analysed sequences of q-triplets, or q-doublets if one of them was the unity, in terms of cycles of successive Möbius transforms of the line preserving unity ( q = 1 corresponds to the BG theory). Such transforms have the form q ↦ ( a q + 1 - a ) / [ ( 1 + a ) q - a ] , where a is a real number; the particular cases a = - 1 and a = 0 yield, respectively, q ↦ ( 2 - q ) and q ↦ 1 / q , currently known as additive and multiplicative dualities. This approach seemingly enables the organisation of various complex phenomena into different classes, named N-complete or incomplete. The classification that we propose here hopefully constitutes a useful guideline in the search, for non-BG systems whenever well described through q-indices, of new possibly observable physical properties.

Introduction: What Is Complexity?

2017 ◽  
Author(s):  
Paul Charbonneau
Keyword(s):  
Complex Systems ◽  
Computational Model ◽  
Computer Programs ◽  
Dissipative Systems ◽  
Ant Colonies ◽  
Natural Complex ◽  
Hands On ◽  
Complex Phenomena ◽  
Natural Complexity

This book investigates complex systems that are idealizations of naturally occurring phenomena characterized by the autonomous generation of structures and patterns at macroscopic scales. It provides material and guidance to allow the reader to learn about complexity through hands-on experimentation with complex systems with the aid of computer programs. Each chapter thus presents a simple computational model of natural complex phenomena ranging from avalanches and earthquakes to solar flares, epidemics, and ant colonies. This introductory chapter explains what complexity is, with emphasis on the fact that defining it is not a simple endeavor, and that it is not the same as randomness or chaos. It also shows that open dissipative systems are complex and clarifies what natural complexity means. Finally, it describes the computer programs listed in this book and suggests materials for further reading about complexity.

Statistical Mechanics and Information Theory for Complex Systems

2018 ◽  
Author(s):  
Stefan Thurner ◽  
Rudolf Hanel ◽  
Peter Klimekl
Keyword(s):  
Information Theory ◽  
Statistical Mechanics ◽  
Complex Systems ◽  
Maximum Entropy Principle ◽  
Distribution Functions ◽  
Complex Processes ◽  
Entropy Principle ◽  
Path Dependent ◽  
Statistical Systems ◽  
Dependent Processes

Most complex systems are statistical systems. Statsitical mechanics and information theory usually do not apply to complex systems because the latter break the assumptions of ergodicity, independence, and multinomial statistics. We show that it is possible to generalize the frameworks of statistical mechanics and information theory in a meaningful way, such that they become useful for understanding the statistics of complex systems.We clarify that the notion of entropy for complex systems is strongly dependent on the context where it is used, and differs if it is used as an extensive quantity, a measure of information, or as a tool for statistical inference. We show this explicitly for simple path-dependent complex processes such as Polya urn processes, and sample space reducing processes.We also show it is possible to generalize the maximum entropy principle to path-dependent processes and how this can be used to compute timedependent distribution functions of history dependent processes.

scholarly journals From Big Data to Econophysics and Its Use to Explain Complex Phenomena

2020 ◽  
Vol 13 (7) ◽  
pp. 153 ◽  
Author(s):  
Paulo Ferreira ◽  
Éder J.A.L. Pereira ◽  
Hernane B.B. Pereira
Keyword(s):  
Big Data ◽  
Complex Systems ◽  
Complex Networks ◽  
Power Laws ◽  
Research Field ◽  
Research Topic ◽  
Data Availability ◽  
Introductory Paper ◽  
Complex Phenomena

Big data has become a very frequent research topic, due to the increase in data availability. In this introductory paper, we make the linkage between the use of big data and Econophysics, a research field which uses a large amount of data and deals with complex systems. Different approaches such as power laws and complex networks are discussed, as possible frameworks to analyze complex phenomena that could be studied using Econophysics and resorting to big data.

Complex Systems Concepts in Simulations

2009 ◽  
pp. 452-461
Author(s):  
David Gibson
Keyword(s):  
Complex System ◽  
Complex Systems ◽  
Postsecondary Education ◽  
Teaching And Learning ◽  
System Simulation ◽  
Development Project ◽  
Department Of Education ◽  
Simulation Engine ◽  
Complex Phenomena ◽  
Core Characteristics

This chapter discusses how a teaching simulation can embody core characteristics of a complex system. It employs examples of specific frameworks and strategies used in simSchool, a research and development project supported by two programs of the U. S. Department of Education: Preparing Tomorrow’s Teachers to Use Technology (2004-2006), and currently, the Fund for the Improvement of Postsecondary Education (2006-2009). The chapter assumes that a complex system simulation engine and representation is needed in teaching simulations because teaching and learning are complex phenomena. The chapter’s two goals are to introduce core ideas of complex systems and to illustrate with examples from simSchool, a simulation of teaching and learning.

A Complex Systems Account of the Covid-19 Pandemic: Illustrations from India

2021 ◽  
Author(s):  
Sayan Das
Keyword(s):  
Complex Systems ◽  
Systems Thinking ◽  
Social Consequences ◽  
Control Measures ◽  
Wicked Problem ◽  
Complex World ◽  
Caring Science ◽  
Complex Systems Thinking ◽  
The World ◽  
Complex Phenomena

The Covid-19 pandemic in India and the rest of the world was followed by tremendous health and social consequences. Worldwide the pandemic created challenges that were unpredictable and elusive to our existing ways of thinking. The paper posits that a complex systems thinking is needed to make sense of the society-wide ramifications of a ‘wicked’ problem like the pandemic and devise appropriate resolutions. A complex systems thinking conceptualizes our society as emergent from irreducible interdependencies across individuals, communities and systems and the pandemic as a complex systems problem that has consequences both immediate and future. The paper uses the complexity lens to explore the unanticipated repercussions of the pandemic control measures that further accentuated pandemic induced socio-economic disruptions, and secondly, the domain of Covid-19 treatment in India, as examples, to demonstrate that while devising a response to complex phenomena like the pandemic more needs to be accounted for than what meets the eye. It thus calls for a more caring science that understands and respects our shared existence and wellbeing and makes use of diverse, democratic and decentralised processes to forge shared pathways for navigating our complex world.

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