Why does the second law of thermodynamics prevent heat from flowing spontaneously from cold to hot?

The second law of thermodynamics states that a cyclic process whose only final result is to transfer heat from a colder body to a hotter body is impossible.12

This principle is rooted in the concept of entropy, which measures the disorder of a system. When heat flows from a hotter reservoir to a colder one, the net entropy of the system increases. Conversely, a spontaneous flow from cold to hot would result in a net decrease in entropy, which violates the second law.1

While individual molecular collisions are time-reversible, the second law is statistical in nature. In a system containing a vast number of molecules, the probability of cold molecules spontaneously clustering to transfer heat to a hotter region is so infinitesimally small that it is never observed in practice. Thus, the law is essentially exact for macroscopic systems, ensuring that heat naturally moves toward equilibrium rather than away from it.13