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S = kBlnW
- The Boltzmann definition of entropy relates the entropy as the natural logarithm of the number of microstates, W: S = kBlnW where kB is a constant of proportionality known as Boltzmann’s constant: kB = 1.380658 × 10 − 23 J K − 1
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In statistical mechanics, Boltzmann's equation (also known as the Boltzmann–Planck equation) is a probability equation relating the entropy, also written as , of an ideal gas to the multiplicity (commonly denoted as or ), the number of real microstates corresponding to the gas's macrostate:
Aug 10, 2023 · In this chapter we introduce the statistical definition of entropy as formulated by Boltzmann. This allows us to consider entropy from the perspective of the probabilities of different configurations of the constituent interacting particles in an ensemble.
May 27, 2024 · His formula, \( S = k \log W \), where \( S \) is entropy, \( k \) is the Boltzmann constant, and \( W \) represents the number of microstates (distinct ways in which a system can be arranged while still having the same energy), bridged the gap between the macroscopic and microscopic worlds.
Boltzmann formulated a simple relationship between entropy and the number of possible microstates of a system, which is denoted by the symbol Ω. The entropy S is proportional to the natural logarithm of this number:
Boltzmann's entropy formula is a fundamental equation in statistical mechanics that relates the entropy of a system to the number of microscopic configurations (microstates) that correspond to a given macroscopic state.
Later on, people realize that Boltzmann's entropy formula is a special case of the entropy expression in Shannon's information theory. (7) This expression is called Shannon Entropy or Information Entropy. Unfortunately, in the information theory, the symbol for entropy is H and the constant kB is absent.
Mar 27, 2021 · The original formula for the entropy in terms of \(W\) includes the factor of \(N!\) in \(W\). This corresponds to an additional factor of \(N \log N − N\) in the formula from Equation \ref{7.2.24}.
