Here T = ∂ ∂ V / ∂ ∂ S is the temperature of the system, F i are the external forces, C i are the internal dissipative forces. It results in the mechanical and thermal balance equations: m i a i = − − ∂ ∂ V ∂ ∂ r i + C i + F i , i = 1 , . . . , N T S ˙ ˙ = − − ∑ ∑ i C i ⋅ ⋅ r ˙ ˙ i . Typical applications of the principle include thermo-mechanical systems, membrane transport, and chemical reactions.