In establishing the existence of irreversibility, we can use one or both of the two general methods of approaching any physical problems (see Introduction, pp. [2], [3]) we can approach by way of the atomic theory or by considering the behavior of aggregates in Nature. Enough has already been said in this presentation of atomic behavior and arrangements to justify the statement that irreversibility is not inherent in the elementary procedures themselves but in their irregular arrangement. The motion of each atom is by itself reversible, but their combined mean effect is to produce something irreversible.[12]
This has been rigorously demonstrated by BOLTZMANN'S H-theorem for molecular physics, and when sufficiently general co-ordinates are substituted it is also available for the other domains of natural events. When we consider the behavior of aggregates we recognize at once a general, empirical law, which has also been called the one physical axiom, namely, that all natural processes are essentially irreversible. When we use this method of approach we confessedly rest entirely on experience, and then it does not make any logical difference whether we start with one particular fact or another, whether we start with a fact itself or its necessary consequence: For instance we may recognize that the universe is permanently different after a frictional event from what it was before, or we may start, as PLANCK does, by putting forward the following proposition:
"It is impossible to construct an engine which will work in a complete cycle,[13] and produce no effect except the raising of a weight and the cooling of a heat reservoir."[14]
Now up to this time no natural event has contradicted this theorem or its corollaries. The proof for it is cumulative, wholly experiential and therefore exactly like that for the law of conservation of energy.
Returning to irreversibility, the matter for immediate discussion, we premise that it will here clarify and simplify our ideas if we consider all the participating bodies as parts of the system experiencing the contemplated process. It is in this sense that we must understand the statement: Every natural event leaves the universe different from what it was before. Speaking very generally, we may say that in this difference lies what we call irreversibility.
Now irreversibility is what really does exist, everywhere in Nature, and our idea of reversibility is only a very convenient and fruitful fiction; our conception of reversibility must, therefore, ultimately be derived from that of irreversibility.
"A process which can in no way be completely reversed is termed irreversible, all other processes reversible. That a process may be irreversible, it is not sufficient that it cannot be directly reversed. This is the case with many mechanical processes which are not irreversible (See [p. 32]). The full requirement is, that it be impossible, even with the assistance of all agents in Nature, to restore everywhere the exact initial state when the process has once taken place."
Examples of irreversible processes, which involve only heat and mechanical phenomena, may be grouped in four classes:
(a) The body whose changes of state are considered is in contact with bodies whose temperature differs by a finite amount from its own. There is here flow of heat from the hotter to the colder body and the process is an irreversible one.
(b) The body experiences resistance from friction which develops heat; it is not possible to effect completely the opposite operation of restoring the whole system to its initial state.