112 tT. W. Gibbs — Equilibrium of Heterogeneous Substances. 



doubt whether the case falls within or witliout the limit, will a moi'e 

 accurate knowledge of these resistances be necessary. 



To establisli the validity of the criterion of equilibrium, we will 

 consider first the sufficiency, and afterwards the necessity, of the con- 

 dition as expressed in either of the two equivalent forms. 



In the first place, if the system is in a state in which its entropy is 

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

 equilibrium, as any change of state must involve either a decrease of 

 entropy or an increase ot energy, which are alike impossible for an iso- 

 lated 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 any external bodies) can produce a finite 

 change of state, as this Avould involve a finite decrease of entropy or 

 increase of energy. 



We will next suppose that the system has the greatest entropy 

 consistent with its energy, and therefore the least energy consistent 

 with its entropy, but that there are other states of the same energy 

 and entropy as its actual state. In this case, 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. (But we cannot apply this reasoning J,o 

 the motion within any mass of its different components in different 

 directions, as in diffiision, when the momenta of the components 

 balance one another.) Nor, in the case supposed, can any conduction 

 of heat take place, for this involves an increase of entropy, as heat is 

 only conducted from bodies of higher to those of lower temperature. 

 It is equally impossible that any changes should be produced by the 

 transfer of heat by radiation. The condition which we have sup- 

 posed is therefore sufficient for equilibrium, so far as the motion of 

 masses and the transfer of heat are concerned, but to show that the 

 same is true in regard to the motions of diffusion and chemical or 

 molecular changes, when these can occur without being accompanied 

 or followed by the motions of masses or the transfer of heat, we must 

 have recourse to considerations of a more general nature. The fol- 

 lowing considerations seem to justify the belief that the condition is 

 sufficient for equilibrium in every respect. 



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

 that a system may have the greatest entropy consistent with its 

 energy without being in equilibrium. In such a case, changes in the 



