This chapter requires some familiarity with the rudiments of physics and mathematics. Readers lacking this familiarity may skip it and proceed to "B_Morphogenesis" on condition, however, to accept:
-the physical foundations of Informatics as granted and
-a loose definition of the concept of order.

In physics, the customary way to express the probability of a given heat distribution is the ENTROPY E defined by the BOLTZMANN expression

(1): E = k ln(S)

where k is the Boltzmanns gas constant and S is the number of microscopic states in which the macroscopic state E may be realized. The concept of entropy may be generalized by extending the expression over all forms of energy. Setting in the generalized expression k = 1/ln(2) we get:

(2): E = ln(S) / ln(2) = log2(S) (where log2 means log base 2).

(2) allows to express the entropy of the system as the number of digits of a binary string capable to address all possible system's states. Each digit of this string determines a degree of freedom of the system.

Entropy represents the part of energy of a system unfit for doing mechanical work.

Replacing entropy E with information I we may say that the complete set of system's states may be addressed with help of I binary bits:

(3): I = log2(S)

(2) and (3) express the analogy between entropy and information.

The second law of thermodynamics, the "LAW OF ENTROPY" which may be generalized over all practical energetic systems states that any change of the system state increases its entropy. In the limit, for the purely theoretical reversible system, entropy stays constant. It never decreases. NOTE: This holds for closed systems. As we shall see in "B_Morphogenesis" entropy may decrease in local open systems. Such systems may get ordered and their ordering is foundation of the cosmos, of life and of human reason.

Analogically, as result of a communication some of the I bits necessary to describe the S possible system states may get corrupted in which case the amount of useful information contained in I decreases. For each corrupted bit half of the possible system states S is excluded from the information I. This is the customary way of representing the analogy between entropy and information.

Another way of presenting the analogy, which we find more appropriate for the present study is to consider not the information, but the information carrier as analogous and say that for each corrupted bit a new must be added in order to describe all S possible states of the system. In this context the analogy becomes strictly isomorphic and we may refer to I as to the ENTROPY OF INFORMATION, or shortly ENTROPY, when no misunderstanding about the nature of the involved system is possible.

Entropy may be considered as the measure of disorder and its inverse as measure of order. In information systems entropy represents the degree of uncertainty of a message.

NOTE: We shall further use the term Chaos as synonym of Disorder which differs from the definition used in certain Chaos Theories, where "Chaos" points to some "hidden order" concealed by apparent disorder. "Disorder" contains a suggestion of having necessarily emerged from some preliminary Order by its destruction. "Chaos", on the contrary, is, like "Order", just a system's state not prejudging any direction of emerging. We shall see in B_Morphogenesis that Order may under certain circumstances emerge from Chaos, which sounds better than talking about Order emerging from Disorder. For instance discussing the Big Bang we shall admit Chaos as the original state of this Cosmos Model while the negative term "Disorder" could hardly pertain to this context.

Based upon the notion of entropy we define the ORDER of an information system:

(4): O = I1 / I

where I is systems entropy in a given situation and I1 = log2(S) is the minimum possible entropy of the system. Consequently, the highest possible order is 1. When entropy increases order decreases. Its value range is between 1 and 0.

After introduction of the concept of order the law of entropy extended over information systems may be called DISORDERING PRINCIPLE and formulated: any spontaneous change of a system decreases its order. In the limit case of an ideal "reversible system", the order stays constant. It never increases. (With exception of local open systems which we mentioned above. We shall discuss them in the next chapter "B_Morphogenesis".)

With respect to entropy and order Informatics is analogous to Physics. By virtue of this analogy we shall consider Informatics as a domain which may be investigated, ordered and processed with help of rigorous scientific methods.