Temperature as an Emergent Property of Non-Equilibrium Systems

Depicted by P. W. Anderson as "more is different", an emergent phenomenon occurs when a large number of identical objects behaves differently than its original constituents. This situation lays at the core of our understanding of strongly correlated materials, such as insulators and superconductors. However, present theories are often limited to equilibrium systems that can be described by a thermal ensemble at a fixed temperature. How can we extend these ideas to non-equilibrium environments? I will describe a recent approach to the problem, where the temperature is represented as an emergent phenomenon. Although the microscopic degrees of freedom are externally driven and do not equilibrate, the macroscopic properties of the system often display a thermal behavior. Starting from specific case studies, I will present successes and failures of this approach. In my last slide, I will discuss possible relations with the philosophical concept of the messianic era as an emergent property of the universe.