“A theory is the more impressive the greater the simplicity of its premises, the more different kinds of things it relates, and the more extended its area of applicability. Therefore the deep impression that classical thermodynamics made upon me. It is the only physical theory of universal content which I am convinced will never be overthrown, within the framework of applicability of its basic concepts.”— Albert Einstein

In the previous article I laid out general philosophical and psychological ideas about time. Here, I will deal with what science has to say, focusing on the thermodynamic measure of time, entropy — “the arrow of time”— and the Second Law of Thermodynamics. (I hope this doesn’t scare you, the reader! I’ll avoid math and illustrate concepts with simple, real examples.)

Einstein’s above quote about thermodynamics indicates that it is a fundamental explanation of how things work. Necessarily our story here will be brief, so let’s start off with a concise explanation of entropy, a key thermodynamic concept. One can think of entropy as a measure of order, or alternatively, a measure of information. (The two ideas are related: if a system is orderly — a closet with clothes neatly hung up, pants separated from shirts, etc. — we know where particular clothing items are located.) The greater the disorder of the system or the lesser our information about it, the greater its entropy. Thus, the messy closet has a greater entropy than the neat one.

The Second Law of Thermodynamics deals with how entropy (denoted by S) changes: A concise statement (rephrased for the layman) is that in an isolated system (no interactions with the environment) entropy changes will never decrease, but either remain constant (a system at equilibrium) or increase (a spontaneous change). Thus a disordered closet will never get more orderly on its own. You accidentally drop an egg on the floor and the yolk and white get mixed up. The egg will never spontaneously reassemble. Natural processes generally proceed from order to disorder in a sequence, so this increase of entropy defines a direction, whence calling entropy “The Arrow of Time.” (This felicitous name was given by the English physicist Sir Arthur Eddington.) Moreover, if we recall the Aristotelian/Thomistic definition of time as “the number of motion with respect to before and after” (remembering motion is equivalent to change) then the designation of entropy as an arrow is particularly appropriate.

THE SECOND LAW AND BOLTZMANN

Ludwig Boltzmann attempted to show that the Second Law could be derived from fundamental equations of physics. These equations are reversible, that is, give the same answers for prediction (forward in time) and retrodiction (backward in time). So Boltzmann would have derived irreversibility (The Second Law) from reversibility. Loschmidt pointed out the contradiction in this: If the velocities are reversed, then the system goes backward in time and entropy increases in the past. Thus Boltzmann’s theory can predict both a decrease and increase of entropy. Boltzmann modified his interpretation after this objection was raised and gave it a probability cast. Although decreasing entropy of an isolated system is possible, it is extremely unlikely in this universe. This change has important implications: it means that the Second Law is not a fundamental feature of how the world works, but is a consequence of initial conditions.

As the eminent English mathematical physicist Roger Penrose notes, the universe starts off in a very improbable, highly ordered state which necessarily from statistical considerations becomes more disordered. On the contrary, Prigogine asserts: Irreversibility is a fundamental feature of how the universe works. I’ll explore this notion in the next section.

PRIGOGINE: IRREVERSIBILITY AS FUNDAMENTAL

In 1977 Ilya Prigogine won the Nobel prize for his work on irreversible thermodynamics. His guiding principle, stated briefly, is that irreversibility is fundamental in how the universe works, not derivable from other fundamental laws. In short, “Entropy as the arrow of time” should be a basis for science, not symmetry in time.

“Irreversibility is either true on all levels or on none. It cannot emerge as if by a miracle, by going from one level to another.” — Ilya Prigogine, Order Out of Chaos

Prigogine argued that in the real world equilibrium — reversibility — is rarely achieved, and no system is ever truly isolated except for the universe itself. Further, he proposed that systems far from equilibrium could achieve order from disorder by getting energy in and sending entropy out. That is, the entropy of the system would decrease, even though it was far from equilibrium, but the entropy it would export (as heat or disordered products) would be sufficiently large that the total change of entropy of the universe would increase. He designated such systems as dissipative structures. Unlike equilibrium structures (crystals, for instance), which are ordered because they’ve reached minimum energy, dissipative structures are ordered only while energy flows through them — they are dynamic, self-organizing patterns sustained by irreversible thermodynamic processes. Cease the flow, and the structure collapses. Order here is not a resting state but an ongoing achievement. And the Second Law is not violated by such systems even though the order of the system increases, since total entropy (universe plus system) increases.

Dissipative structures are found in molecular biology: for example, a living cell’s metabolic network. The cell maintains membrane gradients, ATP production, and organized reactions by constantly taking in nutrients and releasing heat and waste. If energy flow stops, the organized state breaks down. A more specific example is the glycolytic oscillator: glycolysis breaks down sugar molecules as a step in forming ATP, the energy source of metabolism. The mathematics of the equations governing the reaction can yield, far from equilibrium, changes in concentration that oscillate — increasing and decreasing in a regular rhythm. (See this YouTube video.)

Where is the arrow of time in these irreversible processes? The cell, while in a state of active metabolism, is in a steady state — its motion (change) is in particular chemical reactions and these do not necessarily proceed to states of increased entropy. It seems evident then, that the arrow is an arrow for the universe and not necessarily for minute parts of the universe. If then entropy is an arrow of time for the universe, what problems might arise when we do so, taking time as a measure of change for the universe as a whole? This question we will introduce in the next section.

CONCLUSION

What does this say about God and time? One obvious conclusion is that if God created creatures and gave them free will, it is a necessary condition that there be change, for different events to occur, and choice be possible. It should also be evident that such change not be reversible, that there be a direction of time if consequences are to follow from acts. So we get time in one direction, and to enable biological activity — and ultimately, man — there is a mechanism to enable order to arise out of disorder — Prigogine’s dissipative structures. It is Prigogine’s new concepts that have given thermodynamics additional explanatory power.

In the next article in this series we’ll see what problems might arise when we take time as a measure of change for the universe as a whole — the Block Universe Controversy, for which relativity seems to deny the relevance of an arrow of time. If the reader finds sections of Part 3 too challenging, please skim those sections but be sure to read the final paragraphs offering my opinion against the block universe theory. Then in Part 4 I will draw these articles together into a context of what faith and revelation tell us about time and creation.

[A link to part 1 is here.]