Stability of a system with bilateral variations

The system will be subject to bilateral variations if the disturbance 5 can have any sign. Let us show tiiat such a system, if it is stable, is necessarily thermodynamically stable (.9 = 0). 

Indeed, suppose that it is otherwise, and that 0, for example. De Donder s inequality for the disturbed system, if we discount the variation of the affinity, gives us  

If we choose a positive value for 5, then the product is positive, 

In this case, the affinity of the disturbed system will be  

for a system with bilateral variations to be stable, it is necessary and sufficient that the following two conditions be fulfilled  

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