Entropy Changes in an Open System

In an open system, the entropy may change due to either increases caused by spontaneous thermodynamically irreversible internal processes in the system, djS, or exchanges between the system and the surrounding, dgS. In chemically reactive systems, djS may change as a result, for example, of spontaneous reactions inside the system, while dgS may change as a result of supply or extraction of heat and/or some reactants. 

The terms d,S and dgS are postulated in thermodynamics of irreversible processes as independent, and a total of the entropy change, dS, in the open system is expressed as the sum  

When only thermodynamically reversible changes occur inside the system, they are not followed by the entropy increase and diS = 0. Other wise, in the case of existence of irreversible processes diS 0. Obviously, in the isolated systems dgS = 0, and the equation is reduced to 

This equation matches the classical formulation of the Second Law of thermodynamics for isolated systems. 

In a general case of an open system, at a given point with space coordi nate r a set of different irreversible processes can occur simultaneously with a total of entropy increment density dis(r, t) 0. In this situation, the overall entropy increment due to internal processes in the entire system is expressed by integral 

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