Boltzmann distribution in mechanics
Description
In statistical mechanics and mathematics, a Boltzmann distribution (also called Gibbs distribution) is a probability distribution, probability measure, or frequency distribution of particles in a system over various possible states. In statistical mechanics, the Boltzmann distribution is a probability distribution 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 Boltzmann distribution is a probability distribution that gives the probability of a certain state as a function of that state’s energy and temperature of the system to which the distribution is applied. It is given as shown.
Related formulasVariables
M | number of the state (dimensionless) |
n | energy of state n (dimensionless) |
ϵn | energy of state n (J) |
k | Boltzmann constant |
T | temperature of the system (K) |
e | e |
ϵi | energy of state i (J) |
pi | probability of state i (dimensionless) |