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are irreversible; they proceed in one direction only. Examples of such laws are the law of entropy (see the appendix), the chemical principle of Le Chatelier (Henry-Louis Le Chatelier, French chemist, 1850–1936; see Q20 p. 128–130), and the law of mass action.
    Impossibility theorems: Most laws of nature can be expressed in the form: "It is impossible that…." The energy law for example, can be stated as follows: "It is impossible that energy can come into existence by itself." R. Clausius formulated the second law of thermodynamics as an impossibility: "Heat cannot of itself pass from a colder to a hotter body" The impossibility theorems are very useful, because they effectively distinguish between possible and impossible events. This type of scientific formulation will be encountered frequently when we come to the information theorems.
    Geometrical impossibilities can also be devised. Three different geometric representations appear in Figure 6, but such bodies are just as impossible to construct as it is to expect results that are precluded by laws of nature.
    Figure 6: Geometrically impossible bodies.
     
    Laws which describe processes: If the future (prognosis) or the past (retrognosis) states of a system can be described when the values of the relevant variables are known for at least one moment in time, such a formulation is known as a process law. A typical physical example is the description of radioactive decay.
    Co-existence laws: These describe the simultaneous existence of the properties of a system. The formula describing the state changes of an ideal gas, p x v = R x T, is a typical physical co-existence law. The values of the three quantities, pressure p, specific volume v, and absolute temperature T, comprise a complete description of the "state" of an ideal gas. This means that it does not depend on the previous history of the gas, and neither does it depend on the way the present pressure or the present volume has been obtained. Quantities of this type are known as state variables.
    Limit theorems: Limit theorems describe boundaries that cannot be overstepped. In 1927, the German physicist Werner Heisenberg (1901–1976) published such a theorem, namely the so-called uncertainty principle of Heisenberg. According to this principle, it is impossible to determine both the position and the velocity of a particle exactly at a prescribed moment. The product of the two uncertainties is always greater than a specific natural constant, which would have been impossible if the uncertainties were vanishingly small. It follows, for example, that certain measurements can never be absolutely exact. This finding resulted in the collapse of the structure of the then current 19th century deterministic philosophy. The affirmations of the laws of nature are so powerful that viewpoints which were held up to the time they are formulated, may be rapidly discarded.
    Information theorems: In conclusion, we mention that there is a series of theorems which should also be regarded as laws of nature, although they are not of a physical or a chemical nature. These laws will be discussed fully in this book, and all the previously mentioned criteria, N1 to N9, as well as the relevance statements R1 to R6, are also valid in their case.
    2.6 Possible and Impossible Events
     
    The totality of all imaginable events and processes can be divided into two groups as in Figure 7, namely,
a) possible events
b) impossible events.
    Possible events occur under the "supervision" of the laws of nature, but it is in general not possible to describe all of them completely. On the other hand, impossible events could be identified by means of the so-called impossibility theorems.
    Impossible events can be divided into two groups, those which are "fundamentally impossible," and those which are "statistically impossible." Events which contradict, for example, the energy law, are impossible in principle, because this theorem even holds for individual