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Dissipative Mechanics Using Complex-Valued Hamiltonians
Dissipative Mechanics Using Complex-Valued Hamiltonians S. G. Rajeev Department of Physics and Astronomy University of Rochester, Rochester, New York 14627 March 18, 2018 Abstract We show that a large class of dissipative systems can be brought to a canonical form by introducing complex co-ordinates in phase space and a complex-valued hamiltonian. A naive canonical quantization of these sys- tems lead to non-hermitean hamiltonian operators. The excited states are arXiv:quant-ph/0701141v1 19 Jan 2007 unstable and decay to the ground state . We also compute the tunneling amplitude across a potential barrier. 1 1 Introduction In many physical situations, loss of energy of the system under study to the out- side environment cannot be ignored. Often, the long time behavior of the system is determined by this loss of energy, leading to interesting phenomena such as attractors. There is an extensive literature on dissipative systems at both the classical and quantum levels (See for example the textbooks [1, 2, 3]). Often the theory is based on an evolution equation of the density matrix of a ‘small system’ coupled to a ‘reservoir’ with a large number of degrees of freedom, after the reservoir has been averaged out. In such approaches the system is described by a mixed state rather than a pure state: in quantum mechanics by a density instead of a wavefunction and in classical mechanics by a density function rather than a point in the phase space. There are other approaches that do deal with the evolution equations of a pure state. The canonical formulation of classical mechanics does not apply in a direct way to dissipative systems because the hamiltonian usually has the meaning of energy and would be conserved. -
An Ab Initio Definition of Life Pertaining to Astrobiology Ian Von Hegner
An ab initio definition of life pertaining to Astrobiology Ian von Hegner To cite this version: Ian von Hegner. An ab initio definition of life pertaining to Astrobiology. 2019. hal-02272413v2 HAL Id: hal-02272413 https://hal.archives-ouvertes.fr/hal-02272413v2 Preprint submitted on 15 Oct 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. HAL archives-ouvertes.fr | CCSD, August, 2019. An ab initio definition of life pertaining to Astrobiology Ian von Hegner Aarhus University Abstract Many definitions of life have been put forward in the course of time, but none have emerged to entirely encapsulate life. Putting forward an adequate definition is not a simple matter to do, despite many people seeming to believe they have an intuitive understanding of what is meant when it is stated that something is life. However, it is important to define life, because we ourselves, individually and collectively, are life, which entails an importance in itself. Furthermore, humankind‘s capability to look for life on other planets is steadily becoming a real possibility. But in order to realize that search, a definition of life is required. -
Dissipative Structures in Educational Change: Prigogine and the Academy
Wichita State University Libraries SOAR: Shocker Open Access Repository Donald L. Gilstrap University Libraries Dissipative Structures in Educational Change: Prigogine and the Academy Donald L. Gilstrap Wichita State University Citation Gilstrap, Donald L. 2007. Dissipative structures in educational change: Prigogine and the academy. -- International Journal of Leadership in Education: Theory and Practice; v.10 no.1, pp. 49-69. A post-print of this paper is posted in the Shocker Open Access Repository: http://soar.wichita.edu/handle/10057/6944 Dissipative structures in educational change: Prigogine and the academy Donald L. Gilstrap This article is an interpretive study of the theory of irreversible and dissipative systems process transformation of Nobel Prize winning physicist Ilya Prigogine and how it relates to the phenomenological study of leadership and organizational change in educational settings. Background analysis on the works of Prigogine is included as a foundation for human inquiry and metaphor generation for open, dissipative systems in educational settings. International case study research by contemporary systems and leadership theorists on dissipative structures theory has also been included to form the interpretive framework for exploring alternative models of leadership theory in far from equilibrium educational settings. Interpretive analysis explores the metaphorical significance, connectedness, and inference of dissipative systems and helps further our knowledge of human-centered transformations in schools and colleges. Introduction Over the course of the past 30 years, educational institutions have undergone dramatic shifts, leading teachers and administrators in new and sometimes competing directions. We are all too familiar with rising enrolments and continual setbacks in financial resources. Perhaps this has never been more evident, particularly in the USA, than with the recent changes in educational and economic policies. -
Entropy and Life
Entropy and life Research concerning the relationship between the thermodynamics textbook, states, after speaking about thermodynamic quantity entropy and the evolution of the laws of the physical world, that “there are none that life began around the turn of the 20th century. In 1910, are established on a firmer basis than the two general American historian Henry Adams printed and distributed propositions of Joule and Carnot; which constitute the to university libraries and history professors the small vol- fundamental laws of our subject.” McCulloch then goes ume A Letter to American Teachers of History proposing on to show that these two laws may be combined in a sin- a theory of history based on the second law of thermo- gle expression as follows: dynamics and on the principle of entropy.[1][2] The 1944 book What is Life? by Nobel-laureate physicist Erwin Schrödinger stimulated research in the field. In his book, Z dQ Schrödinger originally stated that life feeds on negative S = entropy, or negentropy as it is sometimes called, but in a τ later edition corrected himself in response to complaints and stated the true source is free energy. More recent where work has restricted the discussion to Gibbs free energy because biological processes on Earth normally occur at S = entropy a constant temperature and pressure, such as in the atmo- dQ = a differential amount of heat sphere or at the bottom of an ocean, but not across both passed into a thermodynamic sys- over short periods of time for individual organisms. tem τ = absolute temperature 1 Origin McCulloch then declares that the applications of these two laws, i.e. -
Role of Nonlinear Dynamics and Chaos in Applied Sciences
v.;.;.:.:.:.;.;.^ ROLE OF NONLINEAR DYNAMICS AND CHAOS IN APPLIED SCIENCES by Quissan V. Lawande and Nirupam Maiti Theoretical Physics Oivisipn 2000 Please be aware that all of the Missing Pages in this document were originally blank pages BARC/2OOO/E/OO3 GOVERNMENT OF INDIA ATOMIC ENERGY COMMISSION ROLE OF NONLINEAR DYNAMICS AND CHAOS IN APPLIED SCIENCES by Quissan V. Lawande and Nirupam Maiti Theoretical Physics Division BHABHA ATOMIC RESEARCH CENTRE MUMBAI, INDIA 2000 BARC/2000/E/003 BIBLIOGRAPHIC DESCRIPTION SHEET FOR TECHNICAL REPORT (as per IS : 9400 - 1980) 01 Security classification: Unclassified • 02 Distribution: External 03 Report status: New 04 Series: BARC External • 05 Report type: Technical Report 06 Report No. : BARC/2000/E/003 07 Part No. or Volume No. : 08 Contract No.: 10 Title and subtitle: Role of nonlinear dynamics and chaos in applied sciences 11 Collation: 111 p., figs., ills. 13 Project No. : 20 Personal authors): Quissan V. Lawande; Nirupam Maiti 21 Affiliation ofauthor(s): Theoretical Physics Division, Bhabha Atomic Research Centre, Mumbai 22 Corporate authoifs): Bhabha Atomic Research Centre, Mumbai - 400 085 23 Originating unit : Theoretical Physics Division, BARC, Mumbai 24 Sponsors) Name: Department of Atomic Energy Type: Government Contd...(ii) -l- 30 Date of submission: January 2000 31 Publication/Issue date: February 2000 40 Publisher/Distributor: Head, Library and Information Services Division, Bhabha Atomic Research Centre, Mumbai 42 Form of distribution: Hard copy 50 Language of text: English 51 Language of summary: English 52 No. of references: 40 refs. 53 Gives data on: Abstract: Nonlinear dynamics manifests itself in a number of phenomena in both laboratory and day to day dealings. -
The Teleodynamics of Language, Culture, Technology and Science (LCT&S)
Information 2013, 4, 94-116; doi:10.3390/info4010094 OPEN ACCESS information ISSN 2078-2489 www.mdpi.com/journal/information Review The Teleodynamics of Language, Culture, Technology and Science (LCT&S) Robert K. Logan 1,2 1 Department of Physics, University of Toronto, 60 Street George, Toronto, ON M5S 1A7, Canada; E-Mail: [email protected]; Tel.: +1-416-361-5928 2 Strategic Innovation Lab OCAD University, Toronto, ON M5T 1W1, Canada Received: 8 November 2012; in revised form: 30 January 2013 / Accepted: 2 February 2013 / Published: 7 February 2013 Abstract: Logan [1] in his book The Extended Mind developed the hypothesis that language, culture, technology and science can be treated as organisms that evolve and reproduce themselves. This idea is extended by making use of the notion of teleodynamics that Deacon [2] introduced and developed in his book Incomplete Nature to explain the nature of life, sentience, mind and a self that acts in its own interest. It is suggested that language, culture, technology and science (LCT&S) like living organisms also act in their own self-interest, are self-correcting and are to a certain degree autonomous even though they are obligate symbionts with their human hosts. Specifically, it will be argued that LCT&S are essentially teleodynamic systems, which Deacon defines as “self-creating, self-maintaining, self-reproducing, individuated systems [2] (p. 325)”. Keywords: language; culture; technology; science; teleodynamics; morphodynamics; thermodynamics; organism; obligate symbiont 1. Introduction Although [teleodynamics] is the distinguishing characteristic of living processes, it is not necessarily limited to the biological—Deacon. Terrence Deacon [2] in his book, Incomplete Nature: How Mind Emerged from Matter attempts to develop a scientific theory of how properties such as information, value, purpose, meaning, and end-directed behavior emerged from physics and chemistry. -
Molecules, Information and the Origin of Life: What Is Next?
molecules Perspective Molecules, Information and the Origin of Life: What Is Next? Salvatore Chirumbolo 1,* and Antonio Vella 2 1 Department of Neurosciences, Biomedicine and Movement Sciences, University of Verona, 37134 Verona, Italy 2 Verona-Unit of Immunology, Azienda Ospedaliera Universitaria Integrata, 37134 Verona, Italy; [email protected] * Correspondence: [email protected]; Tel.: +39-0458027645 Abstract: How life did originate and what is life, in its deepest foundation? The texture of life is known to be held by molecules and their chemical-physical laws, yet a thorough elucidation of the aforementioned questions still stands as a puzzling challenge for science. Focusing solely on molecules and their laws has indirectly consolidated, in the scientific knowledge, a mechanistic (reductionist) perspective of biology and medicine. This occurred throughout the long historical path of experimental science, affecting subsequently the onset of the many theses and speculations about the origin of life and its maintenance. Actually, defining what is life, asks for a novel epistemology, a ground on which living systems’ organization, whose origin is still questioned via chemistry, physics and even philosophy, may provide a new key to focus onto the complex nature of the human being. In this scenario, many issues, such as the role of information and water structure, have been long time neglected from the theoretical basis on the origin of life and marginalized as a kind of scenic backstage. On the contrary, applied science and technology went ahead on considering molecules as the sole leading components in the scenery. Water physics and information dynamics may have a role in living systems much more fundamental than ever expected. -
Ordered Complexity from Dissipative and Chaotic Systems, Including the Human Brain and Society and the Universe; Relevance of the Second Law of Thermodynamics
Volume 6, Issue 8, August – 2021 International Journal of Innovative Science and Research Technology ISSN No:-2456-2165 Ordered Complexity from Dissipative and Chaotic Systems, Including the human brain and society and the Universe; Relevance of the Second Law of Thermodynamics Authors Sarbajit Roy, Shailendra Kumar Pandey, Vishal Kumar, Purushotam Kumar, Sudhir Kumar, Raman Kumar Mandal, Rajnish Kumar, Deepshikha Mishra. RamGovind Institute of Technology, Koderma, Jharkhand Abstract:- The paper connects the characteristics of a A living system is characterized by continual flow and dissipative system, which operates far from equilibrium, change in its equilibrium, a process which requires a chaotic system , depending upon initial conditions and thousands of chemical reactions. When these processes complexity, which forms from the holistic connection of come to a standstill, they induce chemical and thermal its parts .Consequent, the human brain, human society equilibrium, which also signifies a dead organism. Living and the universe itself are portrayed as dissipative, organisms continually maintain themselves in a state far chaotic and complex. Chaos is everywhere as is from equilibrium, which is a state of life. complexity. The paper analyzes the aspects of nonlinearity in system dynamics based on the ideas of Although far from equilibrium , the state is stable and Ilya Prigogine and attempts to forge a link between the over long periods of time. In spite of the ongoing flow of systems discussed . The Second Law of Thermodynamics components, the same structure is maintained . involving the total increase in entropy is elucidated as being universal and inherent in all events of the universe. To describe systems far from equilibrium, Prigogine The law may be considered as part of the evolutionary realized that classical thermodynamics was inappropriate, tool in the formation of complex organisms, galaxies and since its mathematical structure was linear. -
Thermodynamics and Life: an Evolutionary Point of View
N. Marchettini et al., Int. J. of Design & Nature and Ecodynamics. Vol. 3, No. 4 (2009) 249–258 THERMODYNAMICS AND LIFE: AN EVOLUTIONARY POINT OF VIEW N. MARCHETTINI1, E. SIMONCINI1 & E.B.P. TIEZZI2 1Department of Chemistry, University of Siena, Siena, Italy. 2Department of Mathematics and Informatics, University of Siena, Siena, Italy. ABSTRACT The complexity we observe in life forms, in their development and in biological evolution, is the result of the temporal and spatial constraints of a long evolutionary history made up of relations accumulating in time. This work assumes that space and time belong to different logical types: the fi rst being reversible and conservative and the second irreversible and evolutionary. Time and space are reciprocally irreducible quantities. We refer to the thermodynamics of the Nobel laureate in Chemistry, Ilya Prigogine, to perform a new point of view of life, in terms of evolutionary thermodynamics. Keywords: Dissipative Structures, Evolution, Information, life origins, Macrostates, Microstates,Tempos. 1 INTRODUCTION ON PRIGOGINE RESEARCH The historical–scientifi c moment that we are living in seems to be searching for, once again, a defi nition for a concept that has had complex consequences. The concept we will be talking about in this work is that of dissipative structures, as its ‘inventor’, Ilya Prigogine, has named it. The magnitude of Prigogine theory can be understood only if time is considered in its closed relation with life and evolution [1–4]. The comprehension of irreversible phenomena has undergone a revolution, thanks to the study of dissipative structures, of those systems, that is, far from equilibrium and open to the exterior, in which fl uctuations of energy can produce order out of chaos. -
The Entropocene
THE ENTROPOCENE Jeff Robbins Rutgers University 101 Murray Hall, New Brunswick, NJ 08901, USA ABSTRACT According to Eric Schneider and the late James Kay “nature abhors a gradient” as it seeks to degrade any and all differences that can make a difference. They also claim that life self-organized by creating a meta-order out of disordered orders, evolving as an increasingly efficient, effective, sustainable (order from order) means for degrading the huge sun to earth temperature gradient. They inject purpose into the scheme by claiming that life represents “order emerging from disorder in the service of more disorder.” Or, as Jeffrey Wicken succinctly put it in “Evolution and Thermodynamics: The New Paradigm,” “Organisms are remote-from-equilibrium systems that maintain their organizational structures by irreversibly degrading free energy through informed kinetic pathways acquired through evolution. Dissipation through structuring is the strategy of life.” In other words, life came about as an evolving means for giving the Second Law of Thermodynamics what it wants. Entropy. In my 2015 ISSS paper, “Anthropocene as Life’s State of the Art in Disorder Production: A Sustainability Conundrum,” I proposed that our species collectively is disorder producer summa cum laude. We are the most efficient, most effective, degrader of gradients, producer of entropy yet evolved. Calling our epoch, “the Anthropocene” doesn’t capture our essence. Our epoch is the Entropocene. We have turned the bio-geosphere from an accumulator of solar exergy (“free energy”, the measure of energy’s utility) as in fossil fuels, into a trapper of entropy a.k.a., global warming. -
A DEFENSE of EQUILIBRIUM REASONING in ECONOMICS by Jennifer Soyun Jhun BA in Philosophy and Economics, Northwestern University
A DEFENSE OF EQUILIBRIUM REASONING IN ECONOMICS by Jennifer Soyun Jhun BA in Philosophy and Economics, Northwestern University, 2008 Submitted to the Graduate Faculty of The Kenneth P. Dietrich School of Arts and Sciences in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Pittsburgh 2016 UNIVERSITY OF PITTSBURGH KENNETH P. DIETRICH SCHOOL OF ARTS AND SCIENCES This dissertation was presented by Jennifer Soyun Jhun It was defended on May 27, 2016 and approved by Robert Batterman, Professor of Philosophy, University of Pittsburgh Sheldon Smith, Professor of Philosophy, University of California, Los Angeles Dissertation Advisor: Mark Wilson, Distinguished Professor of Philosophy, University of Pittsburgh Dissertation Advisor: James Woodward, Distinguished Professor of History and Philosophy of Science, University of Pittsburgh ii A DEFENSE OF EQUILIBRIUM REASONING IN ECONOMICS Jennifer Jhun, PhD University of Pittsburgh, 2016 Copyright © by Jennifer Jhun 2016 iii A DEFENSE OF EQUILIBRIUM REASONING IN ECONOMICS Jennifer Soyun Jhun, PhD University of Pittsburgh, 2016 Critics both within and outside of philosophy have challenged economics wholesale as unscientific. In particular, economics seems unable to predict future events because it relies on assumptions like equilibrium conditions, which stipulate that the economy tends to stay in its current state absent external forces. The popular background view that gives rise to this criticism is that the job of science is to uncover laws of nature, by appeal to which we can determine (usually deductively) the future behavior of a dynamical system as it evolves. I argue that lawlike statements in economics have a very different role than this: they provide a means of understanding in terms of how efficient a particular system is. -
Introduction to the Theory of Infinite-Dimensional Dissipative Systems
I. D. Chueshov Author: I. D. Chueshov This book provides an exhau - stive introduction to the scope Introduction to the Theory Title: Introduction to the Theory of InfiniteDimensional of InfiniteDimensional of main ideas and methods of the Dissipative Systems Dissipative Systems theory of infinite-dimensional dis - sipative dynamical systems which 966–7021–64–5 ISBN: 966–7021–64–5 has been rapidly developing in re - cent years. In the examples sys tems generated by nonlinear partial differential equations I.D.Chueshov I . D . Chueshov arising in the different problems of modern mechanics of continua are considered. The main goal of the book is to help the reader Introduction Theory Introduction to the Theory to master the basic strategies used Infinite-Dimensional of Infinite-Dimensional in the study of infinite-dimensional dissipative systems and to qualify Dissipative Dissipative him/her for an independent scien - Systems 2002 Systems tific research in the given branch. Experts in nonlinear dynamics will find many fundamental facts in the convenient and practical form » in this book. Universitylecturesincontemporarymathematics The core of the book is com - posed of the courses given by the author at the Department of Me chanics and Mathematics at Kharkov University during a number of years. This book con - tains a large number of exercises which make the main text more complete. It is sufficient to know the fundamentals of functional analysis and ordinary differential equations to read the book. CTA Translated by Constantin I. Chueshov ORDER You can ORDER this book from the Russian edition («ACTA», 1999) while visiting the website of «ACTA» Scientific Publishing House Translation edited by www.acta.com.ua http://www.acta.com.uawww.acta.com.ua/en/ Maryna B.