Prevailing dissipation mechanisms

Under those conditions P behaves as a Lagrangian in mechanics. Furthermore, as P is a nonnegative function for any positive value of the concentrations X,, by a theorem due to Lyapounov, the asymptotic stability of nonequilibrium steady states is ensured (theorem of minimum entropy production.1-23 These steady states are thus characterized by a minimum level of the dissipation in the linear domain of nonequilibrium thermodynamics the systems tend to states approaching equilibrium as much as their constraints permit. Although entropy may be lower than at equilibrium, the equilibrium type of order still prevails. The steady states belong to what has been called the thermodynamic branch, as it contains the equilibrium state as a particular case. 

Mechanisms of heat generation between the pin tool and the workpiece are also due to friction or plastic dissipation, depending on whether slide or stick conditions prevail at the interface. The amount of heat input from deformational heating around the pin tool has been estimated to range from 2% (Ref 5) to 20% (Ref 6). 

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