10 THE PHYSICAL SIGNIFICANCE OF ENTROPY 



it may then possess whirls and eddies; it may have different 

 densities and temperatures in its different parts and then it will 

 be difficult or impossible to measure these external physical 

 features of its state as a whole. All this implies ever-varying 

 atomic locations and velocities, but does not indicate any such 

 special far-reaching regularities between adjacent and inter- 

 acting particles as would vitiate at any stage our hypothesis of 

 " elementary disorder " (elementar ungeordnet) or " molecular 

 chaos." 



Before going into more detail concerning this particular chaotic 

 condition of the particles we will give PLANCK'S somewhat fuller 

 statement of what constitutes the " state " of a physical system 

 at a particular time and under given external conditions. It is, 

 " the conception as a whole of all those mutually independent 

 magnitudes which determine the sequence of events occurring 

 in the system so far as they are accessible to measurement; the 

 knowledge of the state is therefore equivalent to a knowledge 

 of the initial conditions. For example, in a gas composed of 

 invariable molecules the state is determined by the law of their 

 space and velocity distribution, i.e., by the statement of the 

 number of molecules, of their co-ordinates and velocity compo- 

 nents which lie within each single small region. The number 

 of molecules in any one of these different regions is in general 

 entirely independent of the number in any other region, for the 

 state need not be a stationary one nor one of equilibrium; these 

 numbers should therefore all be separately known if the state 

 of the gas is to Be considered as given in the absolute mechanical 

 sense. On the other hand, for the characterization of the state 

 in the statistical sense, it is not necessary to go into closer detail 

 concerning the molecules present in each elementary space; 

 for here the necessary supplement is supplied by the hypothesis 

 of molecular chaos, " which in spite of its mechanically indeter- 

 minate character guarantees the unambiguous sequence of the 

 physical events." 



