Boltzmann distribution

Uncommon card · No. 130311

In statistical mechanics and mathematics, a Boltzmann distribution (also called Gibbs distribution) is a probability distribution or probability measure that gives the probability that a system will be in a certain state as a function of that state's energy and the temperature of the system. The distribution is expressed in the form pi∝exp⁡(−εikBT), where pi is the probability of the system being in state i, exp is the exponential function, εi is the energy of that state, and a constant kBT of the distribution is the product of the Boltzmann constant kB and thermodynamic temperature T. The symbol ∝ denotes proportionality (see § The distribution for the proportionality constant). The term system here has a wide meaning; it can range from a collection of "sufficient number" of atoms or a single atom to a macroscopic system such as a natural-gas storage tank. Therefore, the Boltzmann distribution can be used to solve a wide variety of problems. The distribution shows that states with lower...

Read on Wikipedia · Image sonium, CC BY-SA 4.0