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Boltzmann constant: The Boltzmann constant, k, is one of seven fixed constants defining the International System of Units, the SI, with k = 1.380 649 x 10 −23 J K −1. The Boltzmann constant is a proportionality constant between the quantities temperature (with unit kelvin) and energy (with unit joule).
Boltzmann's entropy formula—carved on his gravestone. [1]In statistical mechanics, Boltzmann's entropy formula (also known as the Boltzmann–Planck equation, not to be confused with the more general Boltzmann equation, which is a partial differential equation) is a probability equation relating the entropy, also written as , of an ideal gas to the multiplicity (commonly denoted as or ), the ...
The proportionality constant k B is one of the fundamental constants of physics and is named the Boltzmann constant in honor of its discoverer. Boltzmann's entropy describes the system when all the accessible microstates are equally likely. It is the configuration corresponding to the maximum of entropy at equilibrium.
The constant of proportionality is the Boltzmann constant. The Boltzmann constant, and therefore entropy, have dimensions of energy divided by temperature, which has a unit of joules per kelvin (J⋅K −1) in the International System of Units (or kg⋅m 2 ⋅s −2 ⋅K −1 in terms of base units).
is the thermodynamic beta, defined as where is the Boltzmann constant; E i {\displaystyle E_{i}} is the total energy of the system in the respective microstate . The exponential factor e − β E i {\displaystyle e^{-\beta E_{i}}} is otherwise known as the Boltzmann factor .
Despite the foregoing, there is a difference between the two quantities. The information entropy Η can be calculated for any probability distribution (if the "message" is taken to be that the event i which had probability p i occurred, out of the space of the events possible), while the thermodynamic entropy S refers to thermodynamic probabilities p i specifically.
As the minuteness of the Boltzmann constant k B indicates, the changes in S / k B for even tiny amounts of substances in chemical and physical processes represent amounts of entropy that are extremely large compared to anything in data compression or signal processing. In classical thermodynamics, entropy is defined in terms of macroscopic ...
In 1877 he provided the current definition of entropy, = , where Ω is the number of microstates whose energy equals the system's energy, interpreted as a measure of the statistical disorder of a system. [3] Max Planck named the constant k B the Boltzmann constant. [4]