In physics, specifically statistical mechanics, a population inversion occurs while a system (such as a group of atoms or molecules) exists in a state in which more members of the system are in higher, excited states than in lower, unexcited energy states. It is called an "inversion" because in many familiar and commonly encountered physical systems, this is not possible. This concept is of fundamental importance in laser science because the production of a population inversion is a necessary step in the workings of a standard laser. Boltzmann distributions and thermal equilibrium To understand the concept of a population inversion, it is necessary to understand some thermodynamics and the way that light interacts with matter. To do so, it is useful to consider a very simple assembly of atoms forming a laser medium. Assume there is a group of N atoms, each of which is capable of being in one of two energy states: either The ground state, with energy E1; or The excited state, with energy E2, with E2 > E1. The number of these atoms which are in the ground state is given by N1, and the number in the excited state N2. Since there are N atoms in total, The energy difference between the two states, given by determines the characteristic frequency of light which will interact with the atoms; This is given by the relation h being Planck's constant. If the group of atoms is in thermal equilibrium, it can be shown from Maxwell–Boltzmann statistics that the ratio of the number of atoms in each state is given by the ratio of two Boltzmann distributions, the Boltzmann factor: where T is the thermodynamic temperature of the group of atoms, and k is Boltzmann's constant. We may calculate the ratio of the populations of the two states at room temperature (T ≈ 300 K) for an energy difference ΔE that corresponds to light of a frequency corresponding to visible light (ν ≈ 5×1014 Hz). In this case ΔE = E2 - E1 ≈ 2.07 eV, and kT ≈ 0.026 eV. Since E2 - E1 ≫ kT, it follows that the argument of the exponential in the equation above is a large negative number, and as such N2/N1 is vanishingly small; i.e., there are almost no atoms in the excited state. When in thermal equilibrium, then, it is seen that the lower energy state is more populated than