This web page is associated with a book called called Reverse Engineering the Universe.
The book can be bought at: https://play.google.com/store/books/details/Dr_Jerome_Heath_Reverse_Engineering_the_Universe?id=_OvqBQAAQBAJ
The book gives a more complete explanation of these issues and includes a number of related topic discussions. The combination develops the understanding of these concepts from a number of viewpoints.
Clausius definition of temperature does not require that temperature is the value we measured with a thermometer. This was to make sure the temperature was a thermodynamic quantity and not just a physical manifestation of that quantity. If energy is easily converted into other forms of energy then the normal thermodynamic concepts are true. But if the energy of a system is not readily converted to other forms of energy that system becomes isolated and the energy equations are only applicable within. Then the definition of temperature will be internal to that system. Such a temperature then can affect the outcome of entropy relationships.
Thermometer
Thermometer
When a system has a constraint on the maximum energy, particularly involving energy not easily and directly converted into heat energy, there is an upper limit on energy. Because of this upper limit there must be an inflection point in the entropy curve. Above this inflection point, particularly close to the maximum energy allowed, the inverse entropy slope creates feedback within the system which causes coordination. This coordination provides new properties that are of the system and not of the components.
There is another way of looking at this process to understand what is happening here. As a teen-ager I liked to tune the radio to one of those spots where there were four or five stations all at the same time. That was just to bug my friends. They took me off of radio duty. But the point is when we tune in a good station we have a limited number (one) of energy bands to deal with. Without the limit, the energy that is available just mushes together and is lost. But if we only have a very small number of possible energy states available (and the best such level is just one) the energy is tunable so it expresses something besides noise.
When we look at the Mandelbrot set we see visual patterns appear which are produced by a simple set of rules. This simple set of rule allows only a limited set of possible next processes. The results of this type of regulation are patterns but here the patterns are merely a trace on a computer screen. These are similar rules to those I am proposing, that is a limit on the possibilities, but with energy distributions under such a limit.
The rules of emergence are simple. For emergence to occur there must be limitations on the possibilities for the next step. These very limits help to create an out of equilibrium situation that characterizes emergence. But here the actual process steps that occur are energy states. Energy states show more attributes than mere dots on a computer screen. These energy states can render properties in themselves. In fact the most important properties are those that result from sets of specific groupings of energy state changes (which occurs in chemical bonding).
The energy we are talking about, here, is not from putting a beaker on a Bunsen burner. In emergent issues this energy is measured as the amount of information, or the amount of food, or the degree of motivation. That this form of energy can be limited to a maximum level is shown by facts, such as, in most cases a herd does not eat all the grass, or a lecture of more than an hour is too long.
Reverse Engineering the Universe
Jerome Heath