The relation [eqn:(164)] (164) contains a general method for calculating the entropy by probability considerations.
This, however, is of no practical value, unless the thermodynamic probability of a system in a given state can be expressed numerically. The problem of finding the most general and most precise definition of this quantity is among the most important problems in the mechanical or electrodynamical theory of heat. It makes it necessary to discuss more fully what we mean by the "state" of a physical system.
By the state of a physical system at a certain time we mean the aggregate of all those mutually independent quantities, which determine uniquely the way in which the processes in the system take place in the course of time for given boundary conditions. Hence a knowledge of the state is precisely equivalent to a knowledge of the "initial conditions."
If we now take into account the considerations stated above in [sect:113.] Sec. 113, it is evident that we must distinguish in the theoretical treatment two entirely different kinds of states, which we may denote as "microscopic" and "macroscopic" states.
- The microscopic state is the state as described by a mechanical or electrodynamical observer; it contains the separate values of all coordinates, velocities, and field-strengths. The microscopic processes, according to the laws of mechanics and electrodynamics, take place in a perfectly unambiguous way; for them entropy and the second principle of thermodynamics have no significance.
- The macroscopic state, however, is the state as observed by a thermodynamic observer; any macroscopic state contains a large number of microscopic ones, which it unites in a mean value. Macroscopic processes take place in an unambiguous way in the sense of the second principle, when, and only when, the hypothesis of the elemental chaos ([sect:117.] Sec. 117) is satisfied.