
246 Friction-Induced Vibration and Self-Organization
8.5.2 Criterion for Self-Organization
The stability condition for the thermodynamic system is given in the varia-
tional form by
SXJ
1
2
0
kk
2
∑
δδ
(8.62)
where
2
is the second variation of entropy production rate (Nosonovsky
and Bhushan 2009) and k is the number of the generalized forces and ows.
Equation (8.62) states that the energy dissipation per unit time at the steady
state should be at its minimum, or the variations of the ow and the force
should be of the same sign. When Equation (8.62) is not satised, the sys-
tem is driven away from equilibrium, which creates the possibility for ...