Table Of ContentEntropy Principle for the Development
of Complex Biotic Systems
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Entropy Principle for the
Development of Complex
Biotic Systems
Organisms, Ecosystems, the Earth
Ichiro Aoki
(Formerly) Department of Systems Engineering
Faculty of Engineering
Shizuoka University
Japan
AMSTERDAM(cid:1)BOSTON(cid:1)HEIDELBERG(cid:1)LONDON(cid:1)NEWYORK(cid:1)OXFORD
PARIS(cid:1)SANDIEGO(cid:1)SANFRANCISCO(cid:1)SINGAPORE(cid:1)SYDNEY(cid:1)TOKYO
Elsevier
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Firstedition2012
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Contents
Preface ix
1 ThermodynamicsandLivingSystems 1
1.1 Thermodynamics 1
1.1.1 EntropyLaw 2
1.1.2 EntropyProduction:QuantifiabilityinLivingSystems 3
1.1.3 Maxwell’sDemon 5
2 PlantLeaves 7
2.1 BroadLeaves(Aoki,1987a) 7
2.1.1 EntropiesAssociatedwithShortwaveSolarRadiation 8
2.1.2 EntropiesAssociatedwithIRRadiation 10
2.1.3 EntropyAssociatedwithHeatFlowduetoEvaporation
ofWaterandConduction 12
2.1.4 EntropyFlowduetoMass-FlowAssociatedwith
Photosynthesis 12
2.1.5 NetEntropyFlowandEntropyProduction 13
2.1.6 OtherExamples 14
2.1.7 Discussion 15
2.2 ConiferBranches(Aoki,1989b) 16
2.2.1 SolarRadiationAbsorbedbyaBranchofPonderosaPine 16
2.2.2 IRRadiationEntropyAbsorbedbytheBranch 18
2.2.3 TemperatureoftheBranchandEntropyAssociatedwith
Transpiration 19
2.2.4 EntropyAssociatedwithFreeConvection 20
2.2.5 IRRadiationEntropyEmittedbytheBranch 20
2.2.6 NetEntropyFlowandEntropyProduction 21
2.2.7 OtherCases 22
2.3 EntropyProductionatNight 22
2.4 TheoremofOscillatingEntropyProduction 23
3 Animals 25
3.1 White-TailedDeer 25
3.2 Lizard 30
3.2.1 EntropyFlowduetoDirectSolarRadiation 30
3.2.2 EntropyFlowduetoDiffuseSolarRadiation 30
vi Contents
3.2.3 EntropyFlowduetoReflectedSolarRadiation 32
3.2.4 EntropyFlowduetoIRRadiationfromtheSky 34
3.2.5 EntropyFlowduetoIRRadiationfromtheGround 35
3.2.6 EntropyFlowduetoIRRadiationEmittedbythe
Organism 36
3.2.7 EntropyFlowduetoConvection 36
3.2.8 EntropyFlowduetotheEvaporationofWater 37
3.2.9 EntropyProductionduetoMetabolicHeatProduction 37
3.2.10 EntropyFlowduetoConduction 37
3.2.11 EntropyFlowduetoMass-FlowAssociatedwith
Respiration 38
3.2.12 TotalEntropyFlowandEntropyProduction 38
3.2.13 ComparisonwithWhite-TailedDeer 39
3.3 Pigs 40
3.3.1 NewbornPigs 40
3.3.2 MaturePigs 43
3.3.3 AgeDependence 44
3.3.4 Discussion 45
4 HumansI:DirectCalorimetry 47
4.1 DirectCalorimetry:OutlineandSignificance 47
4.2 CalculationofEntropyProduction 48
4.3 EntropyHomeostasis 52
4.4 NonbasalEffects 52
4.4.1 MildExercise 52
4.4.2 ViolentExercise 53
4.4.3 ChillsinColdEnvironments 53
4.4.4 Malarial Chill 54
5 HumansII:IndirectCalorimetry 55
5.1 BiologicalMeanings 55
5.2 PhysicalFormulation 56
5.2.1 DissipationFunction 56
5.2.2 EnergyMetabolisminOrganisms 57
5.2.3 Psiufunction 57
5.3 AgeDependenceI:PerSurfaceArea 58
5.4 AgeDependenceII:PerIndividual 58
5.4.1 TheAverageHumanIndividual:Extrapolation 59
5.4.2 APrincipleofOrganization 61
6 EcologicalCommunities 63
6.1 Respiration 63
6.2 TrophicDiversity 64
Contents vii
6.3 TrophicDiversityVersusRespiration 64
6.3.1 ThreeEstuariesintheUSA 64
6.3.2 ThreeJapaneseLakes 64
6.3.3 ECOPATHProject 65
6.4 Eutrophication 67
6.5 ArrowofTime 68
6.6 TheDissipationFunctionandEntropyProduction 69
6.7 Discussion 71
7 LakeEcosystems 73
7.1 MethodsofCalculation(Aoki1987b,1989a,1998) 73
7.1.1 DirectSolarRadiation 74
7.1.2 DiffuseSolarRadiation 75
7.1.3 DiffuselyReflectedSolarRadiation 76
7.1.4 IRRadiationEmittedbytheLakeSurface 78
7.1.5 IRRadiationIncidentontheLakeSurface 78
7.1.6 EvaporationofWaterandHeatConduction(cid:1)Convection 79
7.1.7 EntropyProduction 79
7.2 LakeBiwaandLakeMendota 80
7.2.1 LimnologicalMeanings 84
7.2.2 IncreasingEntropyProductionPrinciple 85
7.3 SenescentStages 85
7.4 Discussion 86
8 EntropyPrincipleinLivingSystems(Min(cid:1)MaxPrinciple) 87
9 TheEarth 89
9.1 PlanetsoftheSolarSystem 89
9.1.1 SolarEntropyFlow 89
9.1.2 EntropiesonthePlanetsoftheSolarSystem 90
9.2 Earth’sSurfaceandAtmosphere 92
Appendix:EnergyBudgetEquation:TheFirstLawofThermodynamics 97
A.1 FundamentalEquationofEnergyBudget 97
A.2 SpecialCases 99
References 101
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Preface
TheknellofthebellsattheGiontemple
Echoestheimpermanenceofallthings.
Thecolouroftheflowersonitsdouble-trunkedtree
Revealsthetruththattoflourishistofall.
Hewhoisproudisnotsoforlong,
Likeapassingdreamonanightinspring.
Hewhoisbraveisfinallydestroyed,
Tobenomorethandustbeforethewind.
TheHeikeStory1
Understanding the nature of the development of complex systems is a significant
subjectinrecentscienceandwillbeinthefuture.Althoughmanykindsofinvestiga-
tion on complexity—concepts of self-organization, self-adaptation, edge of chaos,
self-organized criticality, and so on—are going forward, these problems are tough,
andprogress(if)isslow.
However, this line of research is not the only one dealing with complexity, and
otherapproachesmaybepossible.Thenatureofcomplexsystemscanbeinvestigated
fromnonreductionistic,phenomenological,andholisticviewpoints.Apossibilityisto
use thermodynamics, specifically the concept of entropy production (a measure of
activity),tostudymacroscopicbiologicalobjects.Suchstudiesarepresentedhere.The
resultsareconcise,solid,anddefinitivewithclassicalbeauty,incontrasttosomeother
reductionisticnonlinearanalysesofcomplexsystems.
The properties of complex macroscopic systems with a biological function are
examined here. However, the natures of abiotic and biotic complexity may be dif-
ferent, and the properties of microscopic and macroscopic complexity may also
differ.
The time-course of entropy production for biotic systems, from their beginning
to their end, whether individual organisms or ecological systems, turns out here to
be of a gross diphase nature (with fluctuations): an initial rapid increase and a later
slow decrease. This tendency may be universally applied to any system with defi-
nitestructureandfunction.
Consequently, it can be proposed in more detail that natural living systems
evolve rapidly in the initial stage of their lives to an ordered and solid state, and
then they age gradually to a final state of death (chaos). This proposal is different
1Japaneseclassicinthirteenthcentury,theauthor(s)is/arenotspecified.Thestoryinthecontextofthe
Buddhismphilosophyofimpermanence(translatedbyP.G.O’Neill).
