Generalized Second Law of Thermodynamics and Its Applications in Social Science

The arrow-of-time phenomena are everywhere in the physical world, biological systems, and human society. Despite its great importance in physics, the second law of thermodynamics can only successfully explain small percentages of these arrow-of-time phenomena in the physical world, and generally not applicable in biology and human society. For example, the powerful second law of thermodynamics can neither explain arrow-of-time phenomena like Darwin’s evolution in biological systems, nor the globalization processes in human society. Most physicists regard the Darwinian evolution and human society as physical systems far away from thermodynamic equilibrium, which is a physics terminology means that the concept of entropy cannot be precisely defined and the second law of thermodynamics is not useful for studying the Darwinian evolution and human society. While the concept of equilibrium is one of the most important concepts in economics, the concept of equilibrium in economics and physics are two completely different concepts. This paper generalizes the second law of thermodynamics into a universal law of physics called law of equilibrium, which is universally applicable in any system governed by quantum mechanics including physical systems, biological systems, and human society. The concept of entropy in statistical physics is generalized using the concept of relative entropy or Kullback-Leibler divergence from the information theory. Law of equilibrium is one of five physics laws of social science, which is based on a new interpretation of quantum mechanics. In the framework of physics laws of social science, economics and other fields of social science become subfields of quantum physics. The concept of equilibrium and relative entropy are generalized to be equally applicable for all subfields of physics including biology and social science. Law of equilibrium provides a rock solid physics foundation to expand the traditional equilibrium analysis in economics and game theory into a universal mathematical framework useful to study social phenomena. This paper resolves two outstanding problems in modern physics: how to generalize the second law of thermodynamics to non-equilibrium physics, and the nature of arrow of time. This paper concludes that the irreversible processes and arrow of time phenomena in the physical world, biological systems, and human society are fundamentally the same quantum phenomena due to indeterministic nature of quantum events including human choices.