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Ludwig Eduard Boltzmann (/ ˈ b ɒ l t s m ə n /, [2] US: / ˈ b oʊ l-, ˈ b ɔː l-/; [2] [3] German: [ˈluːtvɪk ˈbɔltsman]; 20 February 1844 – 5 September 1906) was an Austrian physicist and philosopher. His greatest achievements were the development of statistical mechanics and the statistical explanation of the second law of ...
The Boltzmann constant (k B or k) is the proportionality factor that relates the average relative thermal energy of particles in a gas with the thermodynamic temperature of the gas. [2] It occurs in the definitions of the kelvin (K) and the gas constant , in Planck's law of black-body radiation and Boltzmann's entropy formula , and is used in ...
The Boltzmann equation can be used to determine how physical quantities change, such as heat energy and momentum, when a fluid is in transport. One may also derive other properties characteristic to fluids such as viscosity , thermal conductivity , and electrical conductivity (by treating the charge carriers in a material as a gas). [ 2 ]
Boltzmann's distribution is an exponential distribution. Boltzmann factor (vertical axis) as a function of temperature T for several energy differences ε i − ε j.. In statistical mechanics and mathematics, a Boltzmann distribution (also called Gibbs distribution [1]) is a probability distribution or probability measure that gives the probability that a system will be in a certain ...
kT (also written as k B T) is the product of the Boltzmann constant, k (or k B), and the temperature, T.This product is used in physics as a scale factor for energy values in molecular-scale systems (sometimes it is used as a unit of energy), as the rates and frequencies of many processes and phenomena depend not on their energy alone, but on the ratio of that energy and kT, that is, on E ...
Boltzmann in his original publication writes the symbol E (as in entropy) for its statistical function. [1] Years later, Samuel Hawksley Burbury, one of the critics of the theorem, [7] wrote the function with the symbol H, [8] a notation that was subsequently adopted by Boltzmann when referring to his "H-theorem". [9]
Ludwig Boltzmann, after whom Boltzmann brains are named. The Boltzmann brain thought experiment suggests that it might be more likely for a brain to spontaneously form in space, complete with a memory of having existed in our universe, rather than for the entire universe to come about in the manner cosmologists think it actually did.
A Boltzmann machine, like a Sherrington–Kirkpatrick model, is a network of units with a total "energy" (Hamiltonian) defined for the overall network. Its units produce binary results. Boltzmann machine weights are stochastic. The global energy in a Boltzmann machine is identical in form to that of Hopfield networks and Ising models: