136.

If now the assumed system of oscillators is in a space traversed by heat rays, the energy of vibration, $U$, of an oscillator will not in general remain constant, but will be always changing by absorption and emission of energy. Without, for the present, considering in detail the laws to which these processes are subject, let us consider any one arbitrarily given thermodynamic state of the oscillators and calculate its entropy, irrespective of the surrounding field of radiation. In doing this we proceed entirely according to the principle advanced in the two preceding chapters, allowing, however, at every stage for the conditions caused by the peculiarities of the case in question.

The first question is: What determines the thermodynamic state of the system considered? For this purpose, according to

[sect:124.] Sec. 124, the numbers $N_1$, $N_2$, $N_3,\dots$ of the oscillators, which lie in the region elements $1$, $2$, $3,\dots$ of the "state space" must be given. The state space of an oscillator contains those coordinates which determine the microscopic state of an oscillator. In the case in question these are only two in number, namely, the moment $f$ and the rate at which it varies, $\dot{f}$, or instead of the latter the quantity $\psi =L\dot{f},\mathrm{\backslash Label}[eqn](209)\text{upshape (209)}$ which is of the dimensions of an impulse. The region element of the state plane is, according to the hypothesis of quanta ([sect:126.] Sec. 126), the double integral $\iint dfd\psi =h.\mathrm{\backslash Label}[eqn](210)\text{upshape (210)}$ The quantity $h$ is the same for all region elements. A priori, it might, however, depend also on the nature of the system considered, for example, on the frequency of the oscillators. The following simple consideration, however, leads to the assumption that $h$ is a universal constant. We know from the generalized displacement law of Wien (equation [eqn:(119)] (119)) that in the universal function, which gives the entropy radiation as dependent on the energy radiation, there must appear a universal constant of the dimension ${\displaystyle \frac{c^3𝗎}{{\nu }^3}}$ and this is of the dimension of a quantity of actionThe quantity from which the principle of least action takes its name. (Tr.) ($\text{erg}\text{sec}.$). Now, according to [eqn:(210)] (210), the quantity $h$ has precisely this dimension, on which account we may denote it as "element of action" or "quantity element of action." Hence, unless a second constant also enters, $h$ cannot depend on any other physical quantities.