Thermodynamics provides a successful theoretical framework to describe the equilibrium properties of substances and near-equilibrium processes within the linear response regime. However, our daily-life experiences, industrial processes, and almost all aspects of biology are ubiquitously far away from thermal equilibrium. First, we will briefly review the modern theory of non-equilibrium statistical mechanics and stochastic thermodynamics. Then, this framework is applied to resolve a 2000-year-old myth named the Mpemba effect. This counter-intuitive effect claimed that hot water can freeze faster than cold water. Finally, inspired by the Mpemba effect, we will briefly demonstrate the non-equilibrium design principle behind life-like intelligent materials with surprising information and energy controllability.