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.

Keywords: entropy production, nonequilibrium thermodynamics, nonequilibrium phase transitions, evolution PACS: 01.65.+g, 05.65.+b, 05.70.Ln, 87.23.−n (all) DOI: 10.3367/UFNe.2020.08.038819 URL: https://ufn.ru/en/articles/2021/6/b/ 000691293300002 2-s2.0-85114964331 2021PhyU...64..558M Citation: Martyushev L M "Мaximum entropy production principle: history and current status" Phys. Usp. 64 558–583 (2021) BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks Received: 24th, April 2020, revised: 13th, August 2020, accepted: 13th, August 2020 Оригинал: Мартюшев Л М «Принцип максимума производства энтропии: история возникновения и современное состояние» УФН 191 586–613 (2021); DOI: 10.3367/UFNr.2020.08.038819