Unilateral perturbations

We distinguish between two kinds of perturbation those in which can have only one sign unilateral perturbations) and those in which can be either positive or negative bilateral perturbations). An example of a unilateral perturbation is the appearance of a very small amount of solid phase in a system which was initially completely liquid. The importance of these conditions of stability, which we shall consider in... 

These conditions of stability with respect to unilateral perturbations may also be expressed in terms of the thermodynamic potentials U, H, F, G. For example, in terms of U we have from (4.30) and (15.12)... 

We now have to distinguish between two cases. If n is odd, then the criterion of stability (15.9) can only be satisfied for unilateral perturbations, since (8 ) will change sign with S. The phase will be stable with respect to unilateral perturbations (8 >0) provided that... 

These workers have since gone on [73,74] to conduct phase-coexistence calculations in pores using these ideas. These recent studies have many notable features, including the use of free-energy perturbation formulas in lieu of thermodynamic integration to maintain the chemical potential equality, and the introduction of a restraining field to eliminate unilateral or bilateral phase changes. 

Chmielewski TL, Hurd WJ, Rudolph KS, Axe MJ, Snyder-Mackler L (2005) Perturbation training improves knee kinematics and reduces muscle co-contraction after complete unilateral anterior raudate ligamcmt rupture. Phys Ther 85(8) 740-754... 

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