78 THE RUNNING-DOWN OF THE UNIVERSE 



scientific name for a fortuitous concourse of atoms is 

 "thermodynamical equilibrium". 



Thermodynamical equilibrium is the other case 

 which we promised to consider in which no increase in 

 the random element can occur, namely, that in which the 

 shuffling is already as thorough as possible. We must 

 isolate a region of the universe, arranging that no 

 energy can enter or leave it, or at least that any bound- 

 ary effects are precisely compensated. The conditions 

 are ideal, but they can be reproduced with sufficient 

 approximation to make the ideal problem relevant to 

 practical experiment. A region in the deep interior of 

 a star is an almost perfect example of thermodynamical 

 equilibrium. Under these isolated conditions the energy 

 will be shuffled as it is bandied from matter to aether 

 and back again, and very soon the shuffling will be 

 complete. 



The possibility of the shuffling becoming complete 

 is significant. If after shuffling the pack you tear each 

 card in two, a further shuffling of the half-cards becomes 

 possible. Tear the cards again and again; each time 

 there is further scope for the random element to 

 increase. With infinite divisibility there can be no end 

 to the shuffling. The experimental fact that a definite 

 state of equilibrium is rapidly reached indicates that 

 energy is not infinitely divisible, or at least that it is not 

 infinitely divided in the natural processes of shuffling. 

 Historically this is the result from which the quantum 

 theory first arose. We shall return to it in a later 

 chapter. 



In such a region we lose time's arrow. You remember 

 that the arrow points in the direction of increase of 

 the random element. When the random element has 

 reached its limit and become steady the arrow does not 



