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          • The First Light Has Fluctuations
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        • Structure in the Genesis Narrative >
          • Examples of Parallelism
          • Parallel Structure in the Creation Narrative
        • Day Four >
          • Not All Stars Formed on the Fourth Day
          • When Did the Stars and Sun Start to Shine?
          • Signs for Animals and People
      • What Is the Origin of the Universe?
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Prigogine’s Explanation of His Method
Now let’s follow Prigogine’s method for accounting for entropy production.

The second principle of thermodynamics postulates the existence of a function of state, called entropy (from the Greek εν τρωπη meaning “evolution”) which possesses the following properties:[i]

Prigogine says that entropy is an “extensive” property. This means that the entropy in a given region is grows as the size of the region is extended.

a)  The entropy of the system is an extensive property. If a system consists of several parts, therefore the total entropy is equal to the sum of the entropies of each part.
b) The change of entropy dS can be split into two parts. Denoting by dₑS the flow of entropy due to interactions with the exterior, and by dᵢS the contribution due to changes inside the system, we have dS = dₑS + dᵢS. The entropy increase dᵢS due to changes inside the system is never negative. It is zero when the system undergoes reversible changes only, but it is positive if the system is subject to irreversible processes as well.
dᵢS = 0 (reversible processes)
dᵢS > 0 (irreversible processes)
In this chapter we shall calculate explicit expressions for the entropy production of some important irreversible processes and also the entropy flow related to exchanges of matter and energy with the external environment.[ii]

The analysis and measurement of the dynamics of properties like state variables is the domain of physics, the most precise of the natural sciences. When we call a science precise, we mean that its theoretical predictions agree precisely with experimental measurements. The Second Law of Thermodynamics says that in all processes without exception, the total amount of entropy or disorder never decreases. We can calculate amounts of entropy theoretically and compare the amounts accurately with measurements in controlled physical and chemical experiments.
Returning to Prigogine’s exposition, we note that he speaks loosely of the “flow of entropy.” What he means by a flow of entropy is a change of entropy inside a region enclosed within an imaginary bubble due to influences from the external region. These influences may be the movement of material or the flow of energy into or out of the region inside the bubble.
Prigogine says that, in the case of isolated systems, there is no such thing as “flow of entropy” into or out of the internal region. That is the meaning of saying that a system is isolated.

For isolated systems, there is no flow of entropy so that dS = dₑS + dᵢS and dᵢS ≥ 0 reduce to dS = dᵢS ≥ 0 (isolated system)[iii]

Next, Prigogine uses the production of an increase of entropy as the definition of an irreversible process.

For isolated systems, this relation is equivalent to the classical statement that entropy can never decrease, so that in this case the behavior of the entropy function provides a criterion that enables us to detect the presence of irreversible processes…. The only general criterion of irreversibility is given by the entropy production according to dᵢS = 0 (reversible processes) and dᵢS > 0 (irreversible processes).[iv]

Prigogine then sets up equations for two systems, one inside the other.
The boundary Prigogine draws may be all around the Earth, separating it from the Sun and outer space, or it may be just outside the skin of a living organism, separating it from the exterior world. In either of these two cases, what Prigogine calls “the global system containing both” is the rest of the universe. Using the definition of “the universe” as “everything physical that there is,” Prigogine says that the universe is isolated, meaning that the universe does not have the flow of energy or the transport of material into or out of it.

Suppose we enclose a system which we shall denote by I, inside a larger system II, so that the global system containing both I and II is isolated. In both parts, I and II, some irreversible processes may take place. The classical statement of the Second Law of Thermodynamics would be dS = dSᴵ + dSᴵᴵ ≥ 0. Applying now dᵢS = 0 (reversible processes) and dᵢS > 0 (irreversible processes) to each part separately, we shall postulate here that dᵢSᴵ ≥ 0, dᵢSᴵᴵ ≥ 0.[v]

Prigogine then denies that there can be any “physical situation” (a place where thermodynamic processes are operating) in which the entropy of any region enclosed within an imaginary boundary can decrease because of a sufficiently large increase of entropy outside the region.

A physical situation such that dᵢSᴵ > 0, dᵢSᴵᴵ < 0 with d (Sᴵ + Sᴵᴵ) > 0 is excluded. We can therefore say that “absorption” of entropy in one part, compensated by a sufficient “production” in another part of the system is prohibited.[vi]

Notice that there is no such thing as “‘absorption’ of entropy in one part, compensated by a sufficient ‘production’ in another part of the system.” Prigogine specifically states that a sufficiently large increase in entropy in the Sun and the rest of the universe cannot compensate for an entropy reduction on Earth. The entropy produced on the Earth cannot flow back to the Sun.

This formulation implies that in every macroscopic region of the system the entropy production due to the irreversible processes is positive. The term macroscopic region refers to any region containing a number of molecules sufficiently large for microscopic fluctuations to be negligible. Interference of irreversible processes is only possible when they occur in the same region of the system. Such a formulation may be called a “local” formulation of the second law in contrast to the “global” formulation of classical thermodynamics. Its value lies in the fact that it permits a much closer analysis of irreversible processes and, as such, it will constitute the central postulate on which this book is based. This postulate will have to be justified eventually by considerations based on statistical mechanics.
It is interesting to note that the splitting of the entropy change into two terms dᵢS and dₑS permits an easy discussion of the difference between closed and open systems as will be shown below. Clearly, this difference has to appear in the term dₑS that, for open systems, must contain terms due to the exchange of matter.[vii]


[i] Prigogine, Ilya, Introduction to Thermodynamics of Irreversible Processes (New York: John Wiley & Sons, 1967), p. 15

[ii] Prigogine, Ilya, op. cit., pp. 15–16.

[iii] Ibid. p. 16.

[iv] Ibid. pp. 16–17. Emphasis is Prigogine’s.

[v] Ibid. p. 17.

[vi] Ibid. p. 17.

[vii] Ibid. pp. 17–18.
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  • Home
  • Breaking News
  • The First Three Days of the Earth
    • Reconciling Science and the Bible >
      • Precise Science Confirms the Bible
      • Moses Foresaw Three Discoveries >
        • First Discovery >
          • Mass and Weight of Energy
          • Transformations and Materialization
          • Different Kinds of Rays and Materialization in Empty Space
          • Was Energy the Source of Material
        • Second Discovery
        • Third Discovery >
          • The First Light
          • Separating Light from Darkness
        • Early Ideas about the Beginning
        • An Up-to-Date Ancient Cosmology
        • The Confirmation
        • A Challenging Question
      • Cycles of Darkness and Light >
        • Teaching Children
        • The Idea the Word “Day” Expresses >
          • A Day Not The First Day
          • Not Literal 24-Hour Days
        • How Long Did the First Three Days Last?
        • Earth Rotation and the First Two Days
        • The Duration of the First Day
        • The First Three Cycles of Darkness and Light
      • Was There a Beginning? >
        • An Uncreated Unchanging Universe
        • Evidence for a Beginning >
          • Elements in the Stars
          • Natural Radiation from Space
          • Stars Consume Their Fuel
        • Cosmology and Relativity
        • Instability Determinism Uncertainty, Predestination >
          • Instability
          • Stability and Determinism
          • Predestination Indeterminacy Uncertainty
        • Einstein Science and Philosophy
        • Predestination versus Timely Intervention
    • Simple Elements and Morning Stars >
      • First Evening Energy and Particles >
        • The Energy of Different Kinds of Rays
        • The Most Energetic Rays
        • Natural Particle Production >
          • Simulating the Process
          • Particles from Darkness
        • Darkness in the Bible >
          • Why Darkness Comes First
          • Isaiah on Darkness and Light
      • First Morning-Simple Elements >
        • Doppler Shift Expansion and Cooling >
          • The Beginning of Nucleosynthesis
          • Four Forces
          • Forces Present in Empty Space
        • Nucleosynthesis >
          • The First Elements
          • The First Halt in Nuclei Production
          • Insufficient Complexity
        • The First Light Was Good >
          • The Immediate Cause of the First Light
          • Forming the Light
          • The Confirmation of Darkness and Light
    • Stars that Formed Complex Elements >
      • Second Evening-Expansion >
        • The Expanding Universe >
          • The Giant Atom that Exploded
          • Expansion Not a Big Bang Explosion
          • Expansion Preserves Order
        • Expanding Now But Later What? >
          • Expanding but Uncreated
          • Continuous Creation
          • The Cyclic Version of Continuous Creation
        • The Expanding Universe Prevails
      • Second Morning-Heavy Elements >
        • Heat and Light Make Heavy Elements >
          • Differences in Stellar Composition
          • Nuclear Binding Energy
        • Energy from Fusion and Fission >
          • The Proton-Proton Reaction
          • Nuclear Stability
        • Different Kinds of Fission
        • Burning Helium and Heavier Elements
    • Forming the Sun and Earth >
      • Third Evening-A Dusty Yellow Star >
        • Supernovas Begin the Third Evening
        • Extraterrestrial Water
        • Lighting the Sun
        • The Carbon to Oxygen Reaction
        • The Darkness of the Third Evening
      • Third Morning-The Earth Forms >
        • The Search for a Planet Suitable for Life
    • How Does God Create? >
      • Conditions at the Very Beginning >
        • Creation from Nothing
        • Can We Create Energy? >
          • God Works to Create Energy
          • The Work Necessary to Create the Universe
        • Denial of Creation
        • The Simplest Explanation
        • Creation in a Singularity >
          • Can We Investigate the Instant of Creation?
          • The First Light Has Fluctuations
      • The Next Three Days >
        • Structure in the Genesis Narrative >
          • Examples of Parallelism
          • Parallel Structure in the Creation Narrative
        • Day Four >
          • Not All Stars Formed on the Fourth Day
          • When Did the Stars and Sun Start to Shine?
          • Signs for Animals and People
      • What Is the Origin of the Universe?
    • Appendices >
      • Appendix A
      • Appendix B
  • Design or Luck?
    • Creative Design >
      • Darwin and Adaptive Variation >
        • Finches and Form Adaptation
        • Adaptive Behavior and Structure
        • Intelligence and Autonomy
      • Biological Structure and Reproduction
      • Adaptive Form
      • Darwin and Darwinism >
        • The Development of the Sciences
        • Contrasting Darwinism and Thermodynamics
        • Darwinism Today
      • The Limits of Automatic Design
    • Why Are Not All Darwinists Rich? >
      • Automatic Design: Artificial and Natural >
        • The Automatic Lens-Design Program
        • Company Top Secret
        • Comparing Evolution and Lens Design
        • My Colleagues Reacted
      • Conclusion-Darwinism Does Not Work >
        • Can Design Be Automatic?
        • Darwinism and Automatic Design
      • How Far Can Small Steps Take Us? >
        • Small Improvements Are Merely Engineering
        • The Vastness of Hyperspace
        • Primordial Alphabet Soup >
          • Wide Coding Overcomes Noise
          • DNA is a Natural Language
          • Common Ancestry
          • Accepted Words Span the Space
        • Is Creative Design Consistent with Darwinism? >
          • Engineering Design
          • A Challenge for Darwinists
    • Thermodynamics >
      • Thermodynamics Information and Creation >
        • The First Law of Thermodynamics
        • Physical Law Keeps Life from Starting by Itself
        • Spontaneous-assembly-by-random-action >
          • Random action cannot produce living beings
        • Prigogine’s Explanation of His Method
        • Reasons for Not Applying Thermodynamics
        • Does Crystallization Defeat the Second Law?
        • Does Gravity Organize Things?
        • The Second Law of Thermodynamics >
          • Entropy
          • Perpetual Motion
        • Information and Order >
          • Entropy Probability and Information
          • Multiplying Probability and Adding Entropy
          • Probability and Information
        • Structure Design Intelligence and Creativity >
          • Structure and Breakdown--Death and Decay
          • Perfection and Beauty
      • Earth-Sun Thermodynamics >
        • A Simple Example of a Thermodynamic Process
        • The Example Applied to the Sun and Earth
      • Another Error about Thermodynamics >
        • A Darwinist Argument about Thermodynamics
        • Sunlight and Earth Temperature
        • What Makes Sunlight Suitable?
      • The Night Sky Is Dark >
        • Olbers and his Paradox
        • A Black Forest and the Stars >
          • Seeing to the Far Limit of the Universe
          • The Limit of the Known Universe
          • Ordinary Darkness
      • A Planet Suitable for Life
      • The Thermodynamics of Life >
        • Living Organisms and Heat Engines >
          • The Thermodynamics of Life without Sunlight
        • Entropy Thermodynamics and Prigogine >
          • Darwinism and Thermodynamics
      • Thermodynamics and the Universe >
        • Formless and Dark but Energetic and Orderly >
          • Entropy and Penrose
        • Creative Agencies and Their Characteristics
    • Complex Order-Life-Intelligence >
      • Random Action and Complexity
      • Does Matter Organize Itself?
      • Complexity Can Be Specified
      • Information and Physical Laws
      • Did Our Life Begin Elsewhere?
      • Discovering Alien Life Will Change Nothing
      • Creative Design Suits the Universe for Life
    • The Quest Continues
  • Creationism that Scientists Can Accept
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  • DVD
  • Booklet