Population biology is built on a strong mathematical foundation developed during the Modern Synthesis and encapsulated by the fields of theoretical population genetics, evolutionary game theory, and quantitative genetics. Historically, these formalisms have often worked with infinite populations, ignoring the effects of demographic stochasticity. Finite population models in population genetics usually assume a fixed population size and are of limited applicability in the real world, where population sizes routinely fluctuate. In this talk, I will outline how ideas from statistical physics can be used to analytically describe evolving populations from biological first principles. Starting from a density-dependent ‘birth-death process’ describing an arbitrary closed population of individuals with discrete traits, I derive a set of stochastic differential equations (SDEs) for how trait frequencies change over time. Along with recovering the effects of the standard evolutionary forces of selection, mutation, and drift, these SDEs also reveal a new directional evolutionary force, ‘noise-induced selection’, that is particular to finite populations and has been largely overlooked in standard mathematical formulations of evolution. Noise-induced selection can reverse the direction of evolution predicted by infinite-population frameworks, with implications for simulation studies and real world populations. Our equations also recover well-known results such as the replicator-mutator equation and Fisher’s fundamental theorem in the infinite population limit. I will try to stick to intuitive arguments and keep formal mathematics to a bare minimum in the talk.