|American chemical engineer and cosmologist Richard Tolman and German-born American physicist Albert Einstein at CalTech in 1932 discussing what seems to be maximum entropy as a final state (possibly of the universe), radiation as an irreversible process, among other topics.|
In statistical thermodynamics, maximum entropy is the state of an isolated ideal gas phase system in which the entropy can no longer increase.  In other words, entropy reaches its “maximum” possible value when the system finally reaches its dominant macrostate; when that happens, the system has reached the equilibrium state. This state is defined as the thermodynamic system in its largest macrostate. The translation of this term and its description into non-gas phase system, has often led to gross misapplication and misinterpretation.
In 1944, for living systems, Austrian physicist physicist Erwin Schrödinger incorrectly equated the state of maximum entropy with death. 
In more complex systems, i.e. ones that are not composed of ideal gas phase particles, namely any material system, one must study both the entropy and the energy of the system to determine the criteria of stability and equilibrium. 
In 1990, American sociologist Kenneth Bailey stated that maximum entropy in a social system is a “state of complete system disintegration or social disorganization”, of no use to social theorists. 
1. Lee, Jooh, C. (2002). Thermal Physics - Entropy and Free Energies. (pg. 18). London: World Scientific.
2. Schrödinger, Erwin. (1944). What is Life? (ch. 6 “Order, Disorder, and Entropy). pgs. 67-75 Cambridge: Cambridge University Press.
3. Gibbs, Willard. (1876). "On the Equilibrium of Heterogeneous Substances", Transactions of the Connecticut Academy, III. pp. 108-248, Oct., 1875-May, 1876, and pp. 343-524, may, 1877-July, 1878.
4. Bailey, Kenneth D. (1990). Social Entropy Theory (pg. 64). New York: State University of New York Press.