Entropy - An Expanded Explanation.
The over-unity generator,
Many scientists as well as laymen, seem confused concerning the issues surrounding what the Second Law of Thermodynamics allows and specifically disallows as a spontaneous process.  This is especially true in the realm of inverted population thermodynamics.  Yet a firm grasp of concepts surrounding the Second Law of Thermodynamics as it applies to inverted populations, is critical to understanding how systems such as the Tesla Generator, the Hendershot machine, or the myriad other alternative energy over-unity generation devices reported in the literature actually function.  All in apparent violation of the First and Second Laws.  When the researcher or scientist truly understands what is allowed within the scope of the Second Law, he/she will quickly realize that Tesla, Hendershot, et al, were accurately reporting the phenomena they observed, AND these phenomena are FULLY consistent with BOTH the First and Second Laws of Thermodynamics.

In this paper, I seek to lay the ground work for that understanding...

Entropy defined:
What is entropy?  Simply stated, it is a measure of the disorder within a system or collection objects, usually (but not always) molecules or atoms.  In numerical terms, it is assigned the variable "S", and has units of Joules per Degree (Kelvin), as shown in Eq. 1.

[Eq. 1]    

 = Entropy (disorder).
 = Energy (in joules).
 = Temperature (in degrees Kelvin).

Notice that entropy is related to both energy AND temperature.  In other words, the entropy of a system is the RATIO of energy to temperature.

Many systems have unlimited freedom in terms of vibration and/or movement.  A good example is a container full of water molecules.  The unlimited freedom of water molecules means there is no upper limit to entropy, since there will always be another vibration mode, or velocity at which these molecules can move, if we add more energy (heat).

Consider what happens when we add energy (heat) to a container full of water molecules.

Lets add enough energy (heat) to raise the temperature of the water by exactly 1 degree, from 270 degrees (Kelvin) to 271 degrees (Kelvin).  This takes 1 calorie of energy (per gram of water) to accomplish.  Lets do it again, and raise the temperature from 271 degrees, to 272 degrees.

Notice the change in entropy "S" is LESS for the second addition of energy, than it was for the first addition of energy.  This is true because every time we add another calorie of heat, it raises the temperature of the water, and therefore in Eq. 1 we are dividing the energy "Q" by a larger "T".

In other words, adding or subtracting energy (heat) in a system at low temperature changes the entropy of that system by a greater amount, than adding or subtracting the same quantity of energy (heat) to a system at some higher temperature.  This is VERY important!  Make sure you understand this concept and the mathematical reasoning behind it.

The second law:
The second law of thermodynamics states:  "In any natural process, the entropy of a system must either rise, or remain constant."

A natural process is a spontaneous process.  In other words, a process that happens without any outside intervention.

Now, lets take two objects at different temperatures, and bring them into thermal contact with each other.  What happens?  The hot object cools down, and the cold object heats up, until both objects are at the SAME temperature.

Why? (dramatic pause)

Most people answer by saying something like:  "Well, heat flows from the hot object to the cold object."

But this answer doesn't really clarify anything at all.  It just hides the question behind another layer of explanation.  Now we are left with the question:  "Why does heat flow from hot to cold?"

The "why" is a consequence of the second law of thermodynamics (as stated above), AND the observation in the last paragraph of 1.1.1 (above), regarding our definition of entropy (Eq. 1).

As the temperature of the cold object rises, it's entropy increases faster than the entropy of the hot declines as it's temperature falls.  Therefore the entropy of the TOTAL SYSTEM (both hot and cold objects) rise, as the temperatures of the two objects equalize.  This system is obeying the second law of thermodynamics.

Again, make very sure you understand this concept.  It is pivotal to understanding what will happen spontaneously, and what requires outside intervention to make it happen.  For instance, a conventional refrigerator requires outside intervention (a source of energy) because it is removing heat from a cold place, and moving that heat to a hotter place.  In other words, a refrigerator lowers the entropy inside, more than it raises the entropy outside, and therefore requires an external source of energy to perform this task.

Heat driven engines:
All conventional heat driven engines, be it a steam engine, a piston driven internal combustion engine, or a jet engine, operate on the difference in temperature between a hot source, and a cold sink.

In the case of a steam engine, we call the hot source a boiler, and the cold sink a condenser.  In the case of a piston driven internal combustion engine, the hot source is the ignited fuel/air mixture, and the cold sink is the lower temperature of the atmosphere surrounding the engine.  In other words, an internal combustion engine would NOT WORK, if the temperature of the surrounding atmosphere was equal to the ignited fuel/air mixture.  The same is true for a jet engine.

This need for a temperature differential between a hot source and cold sink is a direct consequence of The Second Law of Thermodynamics, as it applies to Eq. 1 (above).  In other words, if we want our heat driven engine to be a "spontaneous process", it MUST cause a rise in entropy as it operates.  And if we intend to use the ambient environment as the cold sink, we need fuel to create the hot source.

While the layman considers this condition to be the result of his "heat flow" definition, the REAL cause is the relative change in entropy created by extracting energy from a hot source, and dumping "waste energy" into the cold sink.

Limited freedom:
Everything we have discussed in sections 1.1.1, 1.1.2, and 1.1.3 (above) assumes the system (of molecules or atoms) has unlimited freedom of vibration and/or movement.  In the classical thermodynamics of steam engines or internal combustion engines, this assumption is valid.

However, not all systems behave as defined by classical thermodynamics.  Some systems have very limited freedom of vibration and/or movement, and these systems have radically different thermodynamic behavior.  It is perhaps best to consider an artificial system, before looking at real systems, therefore we shall consider a system composed of 20 identical coins.

Each coin has two sides (heads and tails).  Furthermore, our ideal coins are always oriented with either the heads or tails side facing up, never on their edge.  The individual objects (coins) in this system have exactly two degrees of freedom (heads or tails).  Lastly, we shall define tails as a lower energy state than heads.

Inverted Populations:
What is the entropy of our system when all 20 coins are oriented as tails facing up?  Since all 20 coins are in an identical state, the entropy must be zero.  In other words, there is no disorder in this system.

What is the entropy of our system when all 20 coins are oriented as heads facing up?  Since all 20 coins are in an identical state, again the entropy must be zero, because again there is no disorder in this system.  Furthermore, since we defined tails as the lower energy state, this system (heads facing up) is also at maximum energy, because it can not contain any more energy than 20 coins "oriented heads facing up".

Here is our first indication that systems with limited freedom behave differently than systems with unlimited freedom.  In systems with unlimited freedom, entropy and energy can rise without limit (1.1.1).  This is NOT TRUE for systems with limited freedom.

If 20 coins oriented tails facing up, and 20 coins oriented heads facing up, are both zero entropy, then what orientation of our 20 coin system equals maximum entropy?  Obviously 10 coins oriented tails facing up, and 10 coins oriented heads facing up represents the maximum entropy (disorder) this system can have.

Here is our second indication of strange behavior.  In systems of limited freedom, maximum entropy and maximum energy DO NOT coincide.  In particular, for a binary system (two degrees of freedom) such as our coins, maximum entropy is reached at 50% of maximum energy.  Entropy actually declines as we add more energy (beyond the 50% energy content point), becoming zero at maximum energy.

The system states beyond 50% energy content are collectively called an "Inverted Population" because energy and entropy have an inverted relationship to each other.

Now remember that removing heat from a normal hot source, lowers it's entropy, so we have to dump waste heat into a cold sink in order to meet the requirements of The Second Law of Thermodynamics (1.1.2 & 1.1.3 above).

Suppose we remove heat from an inverted population, what happens to the entropy of this system?  It rises...  Therefore the act of removing heat from an inverted population is sufficient, in and of it self, to meet the requirements of The Second Law of Thermodynamics.  NO COLD SINK IS REQUIRED!!!!!

Furthermore, if we can construct a boiler (hot source) that operates at ambient (atmospheric) temperature, our heat engine will be a perpetual motion machine of the second type (anti-entropic) because we do not need a cold sink.

This represents a loop hole in The Second Law of Thermodynamics as it traditionally applies to heat driven engines.

Real inverted populations:
Consider a gas such as helium.  The electrons orbit the nucleus in discreet shells (limited freedom).  Under normal conditions, the vast majority of the electrons occupy the inner most (lowest energy) shell.  Suppose we use intense light, or electrical energy to "push" a majority of these electrons into the second shell.  These electrons are now an inverted population (1.2.2), and we can spontaneously extract energy from them without any consideration as to the temperature of where that energy will end up going.

This is the principal behind the laser, and one of the reasons a laser beam is considered to be of infinite temperature.  In other words, the laser beam behaves as if it is hotter than any possible cold sink.

In contrast, a regular light bulb would not radiate light, if located inside the sun, for the same reason an internal combustion engine will not work if the temperature of the surrounding atmosphere was equal to the ignited fuel/air mixture.

Next, in the presence of a magnetic field, the rules of quantum electrodynamics require the un-paired electron spins of any paramagnetic material to be either aligned, or anti-aligned to the magnetic field vector (two degrees of freedom).  Therefore, un-paired electron spins in paramagnetic materials represent another material for constructing an inverted population system.

It is this last observation that forms the foundation of magneto-thermodynamics (Tesla, Hendershot, et al. over-unity generators), and it is the thermodynamic nature of inverted populations that allows these generators to operate as heat engines, driven from an ambient heat source, without the need for a colder sink.  In other words, these generators are NOT "over-unity", they are converting ambient heat directly into electrical energy.  They obey the First Law of Thermodynamics (conservation of energy), and thanks to our new found insight into inverted populations, we now see they also obey the Second Law of Thermodynamics as well.

To an electrical engineer or technician, it is enough to say these (magneto thermodynamic) generators convert ambient heat to electrical energy.  It is only the scientist, trained in thermodynamics that will object to such an explanation.  His objection will be based on the consequences of the Second law of Thermodynamics as it applies to heat driven engines.  However, the thermodynamics of inverted populations side step these objections.  And the nature of electron spins in paramagnetic materials is clearly that of a system with limited freedom, and therefore capable of supporting an inverted population.

It is obvious that neither Tesla or Hendershot ever knew the true source of energy in their inductive kickback generators.  Tesla's best hypothesis was "atmospheric electricity".  Yet every inductive kickback device from Tesla to Hendershot have the same basic characteristics.  i.e. A slow build up of electrical energy in an inductor, followed by a fast removal (kickback) of electrical energy from an inductor.  These two steps form a common thread throughout the recorded annals of electrical over unity devices.  And when viewed from a thermodynamic perspective, these two steps lead an inverted population condition within the electron spins of the paramagnetic material that comprise the core of an inductor.  See companion paper entitled:  "Magneto-Thermodynamics, the fine art of demonology part 1, part 2 and part 3".

Entropy - An Expanded Explanation