This page is intentionally left blank Towards a Thermodynamic Theory for Ecological Systems 2004 Amsterdam – Boston – Heidelberg – London – New York – Oxford Paris – San Diego – San Francisco – Singapore – Sydney – Tokyo Sven Erik Jørgensen DFU, Environmental Chemistry Universitetsparken 2 2100 Copenhagen Denmark Yuri M. Svirezhev Potsdam Institute for Climate Impact Research PO Box 601203 14412 Potsdam Germany q 2004 Elsevier Ltd. All rights reserved. This work is protected under copyright by Elsevier Ltd, and the following terms and conditions apply to its use: Photocopying Single photocopies of single chapters may be made for personal use as allowed by national copyright laws. Permission of the Publisher and payment of a fee is required for all other photocopying, including multiple or systematic copying, copying for advertising or promotional purposes, resale, and all forms of document delivery. Special rates are available for educational institutions that wish to make photocopies for non-profit educational classroom use. Permissions may be sought directly from Elsevier’s Rights Department in Oxford, UK: phone (+44) 1865 843830, fax (+44) 1865 853333, e-mail: permissions@elsevier.com. Requests may also be completed on-line via the Elsevier homepage (http://www.elsevier.com/locate/permissions). In the USA, users may clear permissions and make payments through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA; phone: (+1) (978) 7508400, fax: (+1) (978) 7504744, and in the UK through the Copyright Licensing Agency Rapid Clearance Service (CLARCS), 90 Tottenham Court Road, London W1P 0LP, UK; phone: (+44) 20 7631 5555; fax: (+44) 20 7631 5500. Other countries may have a local reprographic rights agency for payments. Derivative Works Tables of contents may be reproduced for internal circulation, but permission of the Publisher is required for external resale or distribution of such material. Permission of the Publisher is required for all other derivative works, including compilations and translations. Electronic Storage or Usage Permission of the Publisher is required to store or use electronically any material contained in this work, including any chapter or part of a chapter. Except as outlined above, no part of this work may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without prior written permission of the Publisher. Address permissions requests to: Elsevier’s Rights Department, at the fax and e-mail addresses noted above. Notice No responsibility is assumed by the Publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. Because of rapid advances in the medical sciences, in particular, independent verification of diagnoses and drug dosages should be made. First edition 2004 Library of Congress Cataloging in Publication Data A catalog record is available from the Library of Congress. British Library Cataloguing in Publication Data A catalogue record is available from the British Library. ISBN: 0 08 044166 1 (hardbound) ISBN: 0 08 044167 X (paperback) W 1 The paper used in this publication meets the requirements of ANSI/NISO Z39.48-1992 (Permanence of Paper). Printed in The Netherlands. ELSEVIER B.V. Sara Burgerhartstraat 25 P.O. Box 211, 1000 AE Amsterdam, The Netherlands ELSEVIER Inc. 525 B Street, Suite 1900 San Diego, CA 92101-4495 USA ELSEVIER Ltd The Boulevard, Langford Lane Kidlington, Oxford OX5 1GB UK ELSEVIER Ltd 84 Theobalds Road London WC1X 8RR UK “Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense.” Buddha “Beware of Mathematicians and those that make hollow prophesy. There is a danger that they made a deal with Devil In order to disconcert Souls and bring the entire Humankind to Hell.” St. Augustine of Hippo This page is intentionally left blank CONTENTS PREFACE xiii CHAPTER 1: THERMODYNAMICS AS A METHOD: A PROBLEM OF STATISTICAL DESCRIPTION 1 1.1 Literary introduction . 1 1.2 Ontic openness . 5 1.3 The scope of this volume . . . 9 CHAPTER 2: THE LAWS OF CLASSICAL THERMODYNAMICS AND THEIR APPLICATION TO ECOLOGY 13 2.1 Introduction 13 2.2 Matter and energy in mechanics and thermodynamics. Energy conservation as the first law of thermodynamics. Fundamental Gibbs Equation 16 2.3 Entropy and the second law of thermodynamics. Nernst’s theorem . . . . 20 2.4 Maximal work which the system can perform on its environment. Characteristic functions or thermodynamic potentials . . . 23 2.5 Chemical equilibrium, chemical affinity and standard energies of biochemical reactions. Function of dissipation 26 2.6 Illustrations of thermodynamics in ecology . . 30 2.7 Ecosystem as a biochemical reactor 36 2.8 Summary of the important ecological issues . 39 CHAPTER 3: SECOND AND THIRD LAW OF THERMODYNAMICS IN OPEN SYSTEMS 41 3.1 Open systems and their energy balance . 41 3.2 The second law of thermodynamics interpreted for open systems 43 3.3 Prigogine’s theorem and the evolutionary criterion by Glansdorff–Prigogine . 47 3.4 The third law of thermodynamics applied on open systems . . . 50 3.5 Thermodynamics of living organisms . . . 53 3.6 Quantification of openness and allometric principles 56 3.7 The temperature range needed for life processes . . . 62 3.8 Natural conditions for life . . 63 CHAPTER 4: ENTROPY, PROBABILITY AND INFORMATION 69 4.1 Entropy and probability 69 4.2 Entropy and information . . . 70 4.3 The system as a text and its information entropy . . 72 4.4 Diversity of biological communities 75 4.5 Simple statistical models of biological communities 77 4.6 Information analysis of the global vegetation pattern . . . 80 4.7 Diversity of the biosphere . . . 84 4.8 Information and evolutionary paradigm: selection of information . . . . . 87 4.9 Genetic information contained in an organism: hierarchy of information and its redundancy . . 90 4.10 Summary of the important ecological issues . 91 CHAPTER 5: WORK, EXERGY AND INFORMATION 95 5.1 The work done by a system imbedded into an environment . . . 95 5.2 What is exergy? Different interpretations of the exergy concept 100 5.3 Thermodynamic machines . . 102 5.4 Exergy far from thermodynamic equilibrium 106 5.5 Exergy and information 111 5.6 Exergy of solar radiation . . . 115 5.7 How to calculate the exergy of living organic matter? . . . 118 5.8 Other methods for the exergy calculation 122 5.9 Why have living systems such a high level of exergy? . . . 124 5.10 Summary of the important ecological issues . 125 CHAPTER 6: STABILITY IN MATHEMATICS, THERMODYNAMICS AND ECOLOGY 127 6.1 Introduction. Stability concepts in ecology and mathematics . . 127 6.2 Stability concept in thermodynamics and thermodynamic measures of stability . . 128 6.3 Model approach to definitions of stability: formal definitions and interpretations . . 133 6.4 Thermodynamics and dynamical systems 135 6.5 On stability of zero equilibrium and its thermodynamic interpretation 137 6.6 Stability of non-trivial equilibrium and one class of Lyapunov functions . . 139 6.7 Lyapunov function and exergy . . . 141 6.8 One more Lyapunov function 142 Contentsviii 6.9 What kind of Lyapunov function we could construct if one or several equilibrium coordinates tends to zero . . 143 6.10 Once more ecological example . . . 144 6.11 Problems of thermodynamic interpretation for ecological models . . . . . 147 6.12 Complexity versus stability . . 150 6.13 Summary of the ecological important issues . 151 CHAPTER 7: MODELS OF ECOSYSTEMS: THERMODYNAMIC BASIS AND METHODS. I. TROPHIC CHAINS 153 7.1 Introduction 153 7.2 General thermodynamic model of ecosystem 154 7.3 Ecosystem’s organisation: trophic chains 159 7.4 Dynamic equations of the trophic chain 163 7.5 Prigogine-like theorems and the length of trophic chain . 165 7.6 The closed chains with conservation of matter. Thermodynamic cost of biogeochemical cycle 169 7.7 Complex behaviour: cycles and chaos . . 174 7.8 What kind of exergy dynamics takes place when the enrichment and thermal pollution impact on the ecosystem? . 177 7.9 Embodied energy (emergy) . . 182 7.10 Summary of the ecological important issues . 186 CHAPTER 8: MODELS OF ECOSYSTEMS: THERMODYNAMIC BASIS AND METHODS. II. COMPETITION AND TROPHIC LEVEL 189 8.1 Introduction 189 8.2 Thermodynamics of a competing community 189 8.3 Community trajectory as a trajectory of steepest ascent . 195 8.4 Extreme properties of the potential W and other potential functions. Entropy production and Prigogine-like theorem 198 8.5 The system of two competing species . . . 205 8.6 Phenomenological thermodynamics of interacting populations 208 8.7 Community in the random environment and variations of Malthusian parameters 212 8.8 Summary of the ecological important issues . 219 CHAPTER 9: THERMODYNAMICS OF ECOLOGICAL NETWORKS . 221 9.1 Introduction 221 9.2 Topology of trophic network and qualitative stability . . . 223 9.3 Dynamic models of trophic networks and compartmental schemes . . . 225 9.4 Ecosystem as a metabolic cycle . . . 227 Contents ix 9.5 MacArthur’s diversity index, trophic diversity and ascendancy as measures of organisation . 229 9.6 How exergy helps to organise the ecosystem . 233 9.7 Some dynamic properties of trophic networks 235 9.8 Stability and reactions of a bog in the temperate zone . . 238 9.9 Summary of the ecological important issues . 241 CHAPTER 10: THERMODYNAMICS OF VEGETATION 243 10.1 Introduction. Energetics of photosynthesis . . 243 10.2 Thermodynamic model of a vegetation layer. Fluxes of heat, water vapour and other gases 244 10.3 Energy balance of a vegetation layer and the energy efficiency coefficient . . . 249 10.4 Thermodynamic model of vegetation: internal entropy production . . . 250 10.5 Vegetation as an active surface: the solar energy degradation and the entropy of solar energy . . 253 10.6 Vegetation as an active surface: exergy of solar radiation 255 10.7 Simplified energy and entropy balances in the ecosystem 261 10.8 Entropy overproduction as a criterion of the degradation of natural ecosystems under anthropogenic pressure . . 264 10.9 Energy and chemical loads or how to convolute the vector data 266 10.10 Summary of the ecological important issues . 269 CHAPTER 11: THERMODYNAMICS OF THE BIOSPHERE 271 11.1 Introduction 271 11.2 Comparative analysis of the energetics of the biosphere and technosphere . . . 273 11.3 Myth of sustainable development 276 11.4 Thermodynamics model of the biosphere. 1. Entropy balance . 277 11.5 Thermodynamics model of the biosphere. 2. Annual increment of entropy in the biosphere . 279 11.6 Exergy of solar radiation: global scale . . 281 11.7 Exergy of the biosphere 287 11.8 Exergy and the evolution . . . 290 11.9 Summary of the ecological important issues . 298 CHAPTER 12: TELEOLOGY AND EXTREME PRINCIPLES: A TENTATIVE FOURTH LAW OF THERMODYNAMICS 301 12.1 Introduction 301 12.2 The maximum power principle . . . 302 12.3 Hypothesis: a thermodynamic law of ecology 306 Contentsx 12.4 Supporting evidence . . 309 12.5 Other ecosystem theories 314 12.6 Toward a consistent ecosystem theory . . 316 12.7 Some final comments . 322 CHAPTER 13: APPLICATION OF EXERGY AS ECOLOGICAL INDICATOR AND GOAL FUNCTION IN ECOLOGICAL MODELLING 325 13.1 Introduction 325 13.2 Exergy and specific exergy as ecological indicators . 328 13.3 Assessment of ecosystem integrity. An example: a lake ecosystem . . . 333 13.4 Thermodynamics of controlled ecological processes and exergy 338 13.5 Modelling the selection of Darwin’s finches . . 341 13.6 Exergy of the global carbon cycle: how to estimate its potentital useful work 346 POSTSCRIPTUM 351 REFERENCES 355 Contents xi [...]... variables, and, as a special application, the role of stochasiticity and determinism in human history was given by Leo Tolstoy in his great novel “War and Peace” Let us cite these pages Towards a Thermodynamic Theory for Ecological Systems, pp 1–11 q 2004 Elsevier Ltd All Rights Reserved 2 Towards a Thermodynamic Theory for Ecological Systems “From the close of the year 1811 intensified arming and concentrating... same ecosystems and we need them all if we want to get a comprehensive view of ecosystems A map cannot, furthermore, give a complete picture We can always make the scale larger and larger and include more details, but we cannot get all the details for instance where all the cars of an area are situated just now, and if we could the picture would be invalid a few seconds later because we want to map... V2 Þ are the volume fractions of each subsystem in the total system We can see that the total density is a mean of subsystem densities Generally speaking, we can say that the system state (in relation to intensive parameters) 16 Towards a Thermodynamic Theory for Ecological Systems Fig 2.2 Cyclic process: x1 and x2 are state variables, “0” ¼ “4” are the initial and final states, “1”, “2” and “3” are... 14 Towards a Thermodynamic Theory for Ecological Systems Before applying the thermodynamic concepts and methods to ecological systems we have to tell our readers about them But before that, we shall try to answer the question: “What, strictly speaking, do we understand by the notions heat, energy and entropy?” We also have to define: “What is meant by a ‘system’?” The latter is a main word in the thermodynamic. .. Ladegaard, Joao Marques, Henning Mejer, Felix Mu€ller, Søren Nors Nielsen, Bernard C Patten, Vladimir Petukhov, Vicente Santiago, Wolf Steinborn, Alexey Voinov, Maciej Zalewski, Nikolai Zavalishin and J Zhang We are also grateful to Valentina Krysanova, Valery Pomaz, Alison Schlums, Stephen Sitch and Anastasia Svirejeva-Hopkins for their help in the preparation and editing of our manuscript Finally, we are... virtual particle to penetrate from the environment into the system it has to overcome these barriers For this, it has to perform certain work moving 20 Towards a Thermodynamic Theory for Ecological Systems Table 2.1 Different forms of energy and their intensive and extensive variables (potential and kinetic energies are denoted as mechanical energy) Energy form Extensive variable Intensive variable Heat... is formulated in everyday language as “do not cry over spilt milk” This may be called the “arrow of time” 22 Towards a Thermodynamic Theory for Ecological Systems † All real processes are irreversible † All real processes result in a partial transfer of one of the other energy forms to heat, that unfortunately cannot be fully utilised to do work because of the difficulties in providing a reservoir at... Svirezhev is a passionate mathematician, who has used his mathematics during almost his entire career on biological – ecological problems He has been able to present many of Sven Erik Jørgensen’s previously published ideas with the right mathematical elegance, but there are also a lot of new ideas that are a result of the teamwork and the brain storming meetings In turn, many concepts of mathematical ecology... necessary that dA ¼ 2dA0 and dQ ¼ 2dQ0 : Therefore, the infinitesimal change in internal energy is the full differential but the changes in heat and work are not the full differentials In other words, U is a state variable but A and Q are not the same, and the system energy cannot be split into heat energy and, for instance, mechanical or chemical energy The work done and the capability to do work are... solved by use of an approach Fig 1.1 The theoretical network of physics consists of a few fundamental laws, for instance the thermodynamic laws, from which other laws can be derived All (or almost all) observations can be explained by a fundamental law or a derived law Thermodynamics as a Method 11 based on energy and exergy, these concepts should be applied, but when the processes and reactions concern . Maciej Zalewski, Nikolai Zavalishin and J. Zhang. We are also grateful to Valentina Krysanova, Valery Pomaz, Alison Schlums, Stephen Sitch and Anastasia. Information and evolutionary paradigm: selection of information . . . . . 87 4.9 Genetic information contained in an organism: hierarchy of information and