SECTION EEQUIVALENTS OF CHANGE OF ENTROPY IN MORE OR LESS GENERAL PHYSICAL TERMSHere we are really considering the Second Law, for change of entropy is the kernel of this law, in fact is identical with it. It will be profitable, however, to view this law in all its many physical aspects. To be sure, in times past it has been accounted a reproach to the Second Law that it should be stated in so many different forms,[18]but now that we know precisely that it stands for the growth in the number of complexions we can more easily trace the connection between any of these rather vague statements and the present precise definition. As we have in the main reserved physical interpretations to a later section we need here only bear in mind certain general principles of comparison:Any complete summary of the premises necessary for establishing the inevitable growth of the number of complexions of a system is a valid statement of the second law.Any general corollary from said growth is a valid statement of the second law.When instituting any comparison we must keep in mind also the two principal points of view of regarding any physical problem, namely, the view of it in the aggregate and that which sees it in its constituent parts.While we cannot here sharply separate these two points of view, we have on the whole sought to present first those statements which are based on experience and next those based on the atomic theory.(1) Growth of entropy is a passage from more to less available energy. By available is here meant energy which we can direct into any required channel. With the growth in the number of complexions we can readily see there is greater inability, on the part of the molecules, for that concerted and co-operative action which is necessary for the putting forth of the energy of a system.(2) Growth of entropy is a passage from a concentrated to a distributed condition of energy. Energy originally concentrated variously in the system is finally scattered uniformly in said system. In this aggregateaspect it is a passage from variety to uniformity.(3) Net growth of entropy in all bodies participating in an occurrence means that the system as a whole has experienced an irreversible change of state. This change is of course in harmony with the first law of energy, but this growth gives additional information as it indicates thedirectionin which a natural process occurs.(4) Growth of entropy is from less probable to more probable states.Growth of entropy is passage to a state more greatly preferred by nature.Growth of entropy is what obtains whenever a natural process occurs "spontaneously."Growth of entropy is a passage fromto moreconditions.All these statements are conspicuously based on the theory of probabilities.(5) Growth of entropy is a passage from a somewhat regulated to a less regulated state. It represents, in a certain sense, Nature's escape from thralldom.Growth of entropy is a passage from a somewhat ordered to a less ordered molecular arrangement.Growth of entropy is an increase in the disorder of a system of mass points.Growth of entropy corresponds to an increase in the number of molecular complexions.(6) Finally we give a mathematical concept which covers the whole domain of physics: "Any function whose time variation always has the same sign until a certain state is reached and is then zero, may be called an entropy function."[18]This need cause no surprise, for it is only very recently that the conviction is gaining ground that the Second Law has no independent significance, but that its full content will only be grasped when its roots are sought in the Theorems of the Calculus of Probabilities.
EQUIVALENTS OF CHANGE OF ENTROPY IN MORE OR LESS GENERAL PHYSICAL TERMS
Here we are really considering the Second Law, for change of entropy is the kernel of this law, in fact is identical with it. It will be profitable, however, to view this law in all its many physical aspects. To be sure, in times past it has been accounted a reproach to the Second Law that it should be stated in so many different forms,[18]but now that we know precisely that it stands for the growth in the number of complexions we can more easily trace the connection between any of these rather vague statements and the present precise definition. As we have in the main reserved physical interpretations to a later section we need here only bear in mind certain general principles of comparison:
Any complete summary of the premises necessary for establishing the inevitable growth of the number of complexions of a system is a valid statement of the second law.
Any general corollary from said growth is a valid statement of the second law.
When instituting any comparison we must keep in mind also the two principal points of view of regarding any physical problem, namely, the view of it in the aggregate and that which sees it in its constituent parts.
While we cannot here sharply separate these two points of view, we have on the whole sought to present first those statements which are based on experience and next those based on the atomic theory.
(1) Growth of entropy is a passage from more to less available energy. By available is here meant energy which we can direct into any required channel. With the growth in the number of complexions we can readily see there is greater inability, on the part of the molecules, for that concerted and co-operative action which is necessary for the putting forth of the energy of a system.
(2) Growth of entropy is a passage from a concentrated to a distributed condition of energy. Energy originally concentrated variously in the system is finally scattered uniformly in said system. In this aggregateaspect it is a passage from variety to uniformity.
(3) Net growth of entropy in all bodies participating in an occurrence means that the system as a whole has experienced an irreversible change of state. This change is of course in harmony with the first law of energy, but this growth gives additional information as it indicates thedirectionin which a natural process occurs.
(4) Growth of entropy is from less probable to more probable states.
Growth of entropy is passage to a state more greatly preferred by nature.
Growth of entropy is what obtains whenever a natural process occurs "spontaneously."
Growth of entropy is a passage fromto moreconditions.
All these statements are conspicuously based on the theory of probabilities.
(5) Growth of entropy is a passage from a somewhat regulated to a less regulated state. It represents, in a certain sense, Nature's escape from thralldom.
Growth of entropy is a passage from a somewhat ordered to a less ordered molecular arrangement.
Growth of entropy is an increase in the disorder of a system of mass points.
Growth of entropy corresponds to an increase in the number of molecular complexions.
(6) Finally we give a mathematical concept which covers the whole domain of physics: "Any function whose time variation always has the same sign until a certain state is reached and is then zero, may be called an entropy function."
[18]This need cause no surprise, for it is only very recently that the conviction is gaining ground that the Second Law has no independent significance, but that its full content will only be grasped when its roots are sought in the Theorems of the Calculus of Probabilities.
[18]This need cause no surprise, for it is only very recently that the conviction is gaining ground that the Second Law has no independent significance, but that its full content will only be grasped when its roots are sought in the Theorems of the Calculus of Probabilities.