Spontaneous changes in an isolated system

An isolated system is one that exchanges no matter or energy with its surroundings. Any change of state of an isolated system that actually occms is spontaneous, and arises solely from conditions within the system, uninfluenced by changes in the surroundings— the process occurs by itself, of its own accord. The initial state and the intermediate states of the process must be nonequilibrium states, because by definition an equilibrium state would not change over time in the isolated system. 

Thermodynamics and Chemistry, second edition, version 3 2011 by Howard DeVoe. Latest version Hww.chem.rjmd.edu/themobook 

Unless the spontaneous change is purely mechanical, it is irreversible. According to the second law, during an infinitesimal change that is irreversible and adiabatic, the entropy increases. For the isolated system, we can therefore write 

In later chapters, the inequality of Eq. 4.6.6 will turn out to be one of the most useful for deriving conditions for spontaneity and equilibrium in chemical systems The entropy of an isolated system continuously increases during a spontaneous, irreversible process until it reaches a maximum value at equilibrium. 

If we treat the universe as an isolated system (although cosmology provides no assurance that this is a valid concept), we can say that as spontaneous changes occur in the universe, its entropy continuously increases. Clausius summarized the first and second laws in a famous statement Die Energie der Welt ist constant die Entropie der Welt strebt einem Maximum zu (the energy of the universe is constant the entropy of the universe strives toward a maximum). 

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An isolated system is one that exchanges neither matter nor energy with the surroundings. What is the entropy criterion for spontaneous change in an isolated system Give an example of a spontaneous process in an isolated system. 

All natural spontaneous changes in an isolated system involve an increase in its entropy. 

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