## A Proposed Fifth Law of Thermodynamics

Entropy is what is probable in general systems theory, but existence is not what is probable, it is what is possible, it is what is left after that which would be lost, is lost.
Jim Whitescarver

#### Abstract

The missing link in thermodynamics as taught in schools today seems to be a concise explanation of why order and structures abound in a universe purported to be driven by a Second Law that states that disorder increases, always and everywhere. This short note is provided in order to stimulate discussion around a possible Fifth Law which predicts what we observe, which is that order and structures should actually predominate in the world in which we live.

#### Introduction

Thermodynamics has become a stable body of knowledge based on four laws, along with an occassionally quoted Law #5. Thermodynamicists preferring to begin counting at zero have named Law #5, "The Fourth Law leading us to entitle this article "A Proposed Fifth Law of ..."

The five commonly quoted laws are:

0th Law: "If two thermodynamic systems are in thermal equilibrium with a third, they are also in thermal equilibrium with each other."
1st Law: "The increase in the internal energy of a thermodynamic system is equal to the amount of heat energy added to the system minus the work done by the system on the surroundings."
2nd Law: "The entropy of an isolated system not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium."
3rd Law: "As a system approaches absolute zero of temperature, all processes cease and the entropy of the system approaches a minimum value."
4th Law: Onsager reciprocal relations.

The most widely quoted of these laws is the 2nd Law. It has been interpreted as saying that entropy, a measure of disorder, always increases, or at best stays the same over increasing time. In fact, the 2nd Law is one of the few laws of physics which is asymmetric in time. Some discussions assert that it is "the law" which actually defines the direction of time within our universe.

The "elephant in the room" is the fact that, in the face of the 2nd Law, which implies that our rooms should become messier over time; our rooms do occasionally become tidy, and life has somehow evolved from crude one celled creatures into the complex set of organisms and ecosystems that inhabit our planet today.

The answer to this puzzle lies in the fact that, in order to create order within one location, we need to create compensating disorder in another location. So even though our room is now tidy, the garbage container has absorbed the missing disorder and then some! So in order to be valid the Second Law must be calculated based the summation of the effect of all the changes taking place within a closed system. So if some parts of the system become more organized, then other parts must become less so, in compensation.

So this explains HOW life could evolve, and how it could be that we occassionally clean up our room, but it certainly doesn't really explain WHY life evolved! or even why we clean our room for that matter.

So for a model of "WHY" this happens, I point to chemistry where we see reactions that involve intermediate compounds. Compounds that usually exist only briefly in order to provide the intermediate step between the chemical reactants we started with and the chemical products which we end up with.

I will argue here that life and the other beautiful structures within our universe, can similarly be seen as intermediary structures which exist in order to speed certain irreversible physical, chemical and nuclear processes that would otherwise be delayed in their occurrence. Processes which in total move our universe forward more quickly towards its final state of total equilibrum.

As an example of this, consider how chlorophyly intercepts visible light, uses that energy to help combine carbon dioxide and water into sugars, and how these sugars are later consumed in order to release lower frequency (higher entropy) heat radiation along with the carbon dioxide and water that we started with. Other structures such as our sun convert hydrogen and helium into heavier elements of all kinds. Unlike the analogous short lived chemical intermediaries, highly ordered structures such as life, stars and galaxies, can be very complex and very long lived.

Barring divine intervention, there is clearly almost no possibility that complex structures such as these could have sprung spontaneously into existence as a result of a single molecular collision. Instead each of these incredibly complex structures must have evolved from only slightly less, incredibly complex structures, and going back some billions of years in tiny steps we find the seed reactions that led to this ultimate chain of processes. A chain which terminates in the present, with the existence of structures of such sophistication and beauty that it would seem that they could only have been the handiwork of some supreme creative intelligence.

Not everyone will subscribe to the above explanation of the origin and function of structures within our universe, but for those who do, I am unaware of any law of thermodynamics that could be seen to govern or describe this model of formation.

It is the purpose of this note to propose just such a law and a mechanism which could be used to explain the functioning of that law.

#### A Model for the Creation of Structure within Our Universe

Consider an open system in contact with a non-equilibriated environment which is effectively constant in temperature, pressure and composition. This open system is capable of taking material from and giving material back to its environment, but in quantities sufficiently small as to not immediately effect the properties of its environment.

Let us assume as well that the open system is made up of a large number (N) of atomatons where the atomotons fall into n distinct catagories. We will require that N»n so that the system's operation can be described as the sum of the statistical average of the operating characteristics of its component automotons.

This open system may, or may not, provide unique pathways for the conversion of environmental reactants into higher entropy products. However these products, if produced, would be returned to the environment from which the reactants were taken.

In the event that this open system does provide conversion pathways for the transformation of environmental reactants into lower grade products; these pathways must necessarily fall into one of three categories.
1. Pathways which become used up and close with use;
2. Pathways which remain open after use;
3. Pathways which expand with use.
Pathways of type 1 are of little interest since they will eventually cease being pathways and at that point stop having any effect on the system.

Pathways of type 2 will in all likelihood eventually change into either type 1 or type 3 pathways.

This leaves us with type 3 pathways, which grow continuously over time until they either become converted into type 1 or 2 pathways, or if they remain of type 3 they must ultimately become large enough, or numerous enough, to create macroscopic features observeable within the open system in question.

I would argue that these "macroscopic features" are in fact the structures of the universe, structures such as planets, stars, galaxies, lakes, rivers, frost on a window, bubbles in a soft drink and of course, life itself.

However before stating this I would note that there is a huge distance between the creation of simple and sustainable chemical or nuclear pathways and the creation of life. I offer the following model to explain why we should expect that at least some simple pathways would evolve into more complex pathways which could eventually lead to structures as complex as life.

Consider that having created macroscopic features within the open system, the pathways in question can vary over time due to random effects. Variations within an individual pathway which degrade or destroy the ability of that pathway to function will lead to the creation of a new kind of pathway of type 1 or 2, which in time will necessarily evolve out of existence. Variations which enhance the ability of the pathway to function, could create a new, more effective kind of type 3 pathway one with the potential to grow, to compete with, and eventually possibly to replace, the original variety of type 3 pathway. The probability of a random variation in an existing type 3 pathway producing a more viable replacement pathway may be miniscule. however as long as the probability is not zero, it is, over a long enough period of time, likely to arise, and when it does, it is likely to persist.

#### A Proposed Fifth Law of Thermodynamics

Based on the above model and obervations the proposed 5th Law would be:

5th Law: "An open system containing a large mixture of similar automatons, placed in contact with a non-equilibriated environment, has a finite probability of supporting the spontaneous generation and growth of self constructing machines of unlimited complexity."

An "open system" is one that can exchange energy and matter with its environment.

An "automaton" is a particle or physical object or machine, capable of interacting with other particles, objects or machines.

A "machine" is a mechanism capable of extracting work from the the conversion of high energy reactants,into low grade waste products plus heat.

A "non-equilibriated environment" is an environment which contains materials capable of reacting together in order to release energy plus waste products.

By "unlimited complexity" we imply that within the constraints imposed by available energy, materials, possible pathways, and time, that the system could evolve indefinitely to become a more and more effective mechanism for the conversion of the materials found within the environment into waste products, waste energy and machine structure.

#### Discussion

The implications of the 5th Law are as wide ranging as they are intuitively obvious. Any system containing a large number of similar elements is potentially capable of self organizing, using energy and matter taken from its environment.

An extremely simple example would be the a bed of sand which forms ripples on its surface in response to having either wind or water flow over it.

More complex examples would be the stock market, the Amazon rain forest, the North American economy or even the dynamic which leads to you clean up your room.

An alternative but less explicit statement of the 5th Law could be that:

"Wherever possible systems adapt to bring dS/dt to a maximum over some variably sized window of visibility."

The peculiar aspect of this statement of the law is the mention of a "window of visibility." Observation of the world around us will show you that different people will maximize their spending strategies in different ways. Whereas one person will "blow their pay cheque on beer" every payday, another person will save pennies for years in order to create a nest egg for their retirement. Both individuals have the goal of maximizing their consumption, (i.e. entropy maximization) but different people use different "windows of visibility" over which to carry out their maximization strategy. The same is true in physical and life processes, however in the interests of brevity I will pursue this topic at another time and in another place, or perhaps simply leave it for other better minds than mine.

#### Acknowledgement

I would like to thank Jim Whitescarver for sharing his flash of brilliance when the stated that:
"Existence is not what is probable, it is what is possible, it is what is left after that which would be lost, is lost"
thus explaining in a phrase why our world is not dominated by the randomness that the 2nd Law would seem to predict.

Philip Carr
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