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In statistical mechanics, a microstate is a specific configuration of a system that describes the precise positions and momenta of all the individual particles or components that make up the system. Each microstate has a certain probability of occurring during the course of the system's thermal fluctuations .
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For example, nested tables (tables inside tables) should be separated into distinct tables when possible. Here is a more advanced example, showing some more options available for making up tables. Users can play with these settings in their own table to see what effect they have.
It is assumed that each microstate is equally likely, so that the probability of a given microstate is p i = 1/W. When these probabilities are substituted into the above expression for the Gibbs entropy (or equivalently k B times the Shannon entropy), Boltzmann's equation results. In information theoretic terms, the information entropy of a ...
Boltzmann's equation—carved on his gravestone. [1]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:
A microstate or ministate is a sovereign state having a very small population or land area, usually both. However, the meanings of "state" and "very small" are not well-defined in international law. [ 1 ]
which is recognized as the probability of some microstate given a prescribed macrostate using the Gibbs rotational ensemble. [ 1 ] [ 3 ] [ 2 ] The term E i − ω → ⋅ J → i {\displaystyle E_{i}-{\vec {\omega }}\cdot {\vec {J}}_{i}} can be recognized as the effective Hamiltonian H {\displaystyle {\mathcal {H}}} for the system, which then ...
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.