To derive a generalized entropy balanced equation, we start with the general balance equation for the change in any extensive quantity θ θ in a thermodynamic system, a quantity that may be either conserved, such as energy, or non-conserved, such as entropy. The basic generic balance expression states that d θ θ / d t , i.e. the rate of change of θ θ in the system, equals the rate at which θ θ enters the system at the boundaries, minus the rate at which θ θ leaves the system across the system boundaries, plus the rate at which θ θ is generated within the system. For an open thermodynamic system in which heat and work are transferred by paths separate from the paths for transfer of matter, using this generic balance equation, with respect to the rate of change with time t of the extensive quantity entropy S , the entropy balance equation is: d S d t = ∑ ∑ k = 1 K M ˙ ˙ k S ^ ^ k + Q ˙ ˙ T + S ˙ ˙ g e n where ∑ ∑ k = 1 K M ˙ ˙ k S ^ ^ k is the net rate of entropy flow due to the flows of mass M ˙ ˙ k into and out of the system with entropy per unit mass S ^ ^ k , Q ˙ ˙ / T is the rate of entropy flow due to the flow of heat across the system boundary and S ˙ ˙ g e n is the rate of entropy generation within the system, e.g. by chemical reactions, phase transitions, internal heat transfer or frictional effects such as viscosity.