THERMODYNAMICAL SYSTEM OF GIBBS 75 



than in any other state of the same energy, it is evidently in 

 equinbrium, as any change of state must involve either a de- 

 crease of entropy or an increase of energy, which are alike 

 impossible for an isolated system. We may add that this is a 

 case of stable equilibrium, as no infinitely small cause (whether 

 relating to a variation of the initial state or to the action of 

 external bodies) can produce a finite change of state, as this 

 would involve a finite decrease of entropy or increase of energy." 



(b) "The system has the greatest entropy consistent with its 

 energy, and therefore the least energy consistent with its 

 entropy but there are other states of the same energy and 

 entropy as its actual state." 



Gibbs first shows by special arguments that in this case the 

 criteria are sufficient for equilibrium in two respects. In the 

 first place, "it is impossible that any motion of masses should 

 take place; for if any of the energy of the system should come to 

 consist of vis viva (of sensible motions), a state of the system 

 identical in other respects but without the motion would have 

 less energy and not less entropy, which would be contrary to 

 the supposition." It is evident that if this last state is im- 

 possible, a similar state in which the parts of the system are in 

 motion is equally impossible, since the motion of appreciable 

 parts of the system does not change their nature. 



Secondly, the passage of heat from one part of the system 

 to another, either by conduction or radiation, cannot take place, 

 as heat only passes from bodies of higher to those of lower 

 temperature, and this involves an increase of entropy. 



The criteria are therefore sufficient for equilibrium, so far as 

 the motion of the masses and the transfer of heat are concerned. 

 In order to justify the belief that the condition is sufficient for 

 equilibrium in every respect, Gibbs makes use of the following 

 considerations. 



"Let us suppose, in order to test the tenability of such a 

 hypothesis, that a system may have the greatest entropy con- 

 sistent with its energy without being in equihbrium. In such a 

 case, changes in the state of the system must take place, but 

 these will necessarily be such that the energy and entropy 

 remain unchanged and the system will continue to satisfy the 



