Мaximum entropy production principle: history and current status

The maximum entropy production principle (MEPP) was repeatedly and independently proposed in the mid-20th century in various fields of physics and proved to be extremely effective in various nonequilibrium problems. We describe the main areas of research that laid the foundations for this principle and discuss its modern form and limitations. We give special attention to a discussion of nonequilibrium phase transitions based on the MEPP and to the relation between the MEPP and other known assertions about the behavior of entropy. We discuss the role of this principle in the analysis of various modern problems in both physics and biology, including the laws of evolution and the definition of life.