What is the name of the principle that states that the equilibrium state of a closed system is the one with maximum entropy?

The principle stating that an equilibrium state has maximum entropy is the maximum entropy principle. In thermodynamics, it identifies the equilibrium macrostate as the one compatible with the constraints that has the greatest entropy.

The strict thermodynamic version applies most directly to an isolated system, or to a closed system whose total internal energy and other relevant extensive quantities are fixed. A closed system cannot exchange matter but may exchange energy, so simply calling every closed-system equilibrium a maximum-entropy state can be an oversimplification. Under fixed entropy and external parameters, the equivalent description is the principle of minimum energy.

Entropy measures the number of microscopic arrangements compatible with the observed macroscopic state. A gas spreading uniformly through a container, for example, has vastly more available arrangements than the same gas confined to one corner. Random molecular motion therefore drives the system toward the overwhelmingly most probable macrostate.

The idea also influenced information theory. In 1957, physicist Edwin Jaynes developed the maximum-entropy method for selecting the least-assumptive probability distribution consistent with known constraints. This informational use is related to, but not identical with, thermodynamic entropy.