What is the Boltzmann distribution related to?

The Boltzmann distribution describes the distribution of particle energies in a system at thermal equilibrium, specifically relating to how the kinetic energy of particles varies with temperature. At any given temperature, the distribution shows that not all molecules in a gas have the same energy; instead, some have low kinetic energy while others have high kinetic energy.

As temperature increases, a greater proportion of particles gain sufficient energy to overcome potential barriers or engage in reactions. This relationship highlights how temperature influences the average kinetic energy of molecules, reflecting the kinetic theory of gases. The Boltzmann distribution is mathematically expressed through the formula ( n(E) \propto e^{-E/kT} ), where ( n(E) ) is the number of particles with energy ( E ), ( k ) is the Boltzmann constant, and ( T ) is the absolute temperature. Thus, it is directly connected to the kinetic energy of particles and their dependence on temperature, making this choice the most accurate representation of the Boltzmann distribution.