Gibbs considered several such kinds of ensembles relevant here is the canonical one. Instead one must consider the ensemble of states of the system as a whole, called by Boltzmann a holode, rather than single particle states. \displaystyle leads to increasingly wrong predictions of entropies and physical behaviours, by ignoring the interactions and correlations between different molecules. W can be counted using the formula for permutations W was historically misinterpreted as literally meaning the number of microstates, and that is what it usually means today. For this case, the probability of each microstate of the system is equal, so it was equivalent for Boltzmann to calculate the number of microstates associated with a macrostate. Boltzmann's paradigm was an ideal gas of N identical particles, of which N i are in the i-th microscopic condition (range) of position and momentum. Interpreted in this way, Boltzmann's formula is the most basic formula for the thermodynamic entropy. Subsequently, Gibbs called it a microcanonical ensemble, and this name is widely used today, perhaps partly because Bohr was more interested in the writings of Gibbs than of Boltzmann. For single particle instantaneous microstates, Boltzmann called the collection an ergode. For a given macrostate, he called the collection of all possible instantaneous microstates of a certain kind by the name monode, for which Gibbs' term ensemble is used nowadays. Boltzmann considered collections of such microstates. There are many instantaneous microstates that apply to a given macrostate. The value of W was originally intended to be proportional to the Wahrscheinlichkeit (the German word for probability) of a macroscopic state for some probability distribution of possible microstates-the collection of (unobservable microscopic single particle) "ways" in which the (observable macroscopic) thermodynamic state of a system can be realized by assigning different positions and momenta to the respective molecules. The present account concerns instantaneous microstates. In experimental practice, such are scarcely observable. A microstate can be instantaneous, or can be a trajectory composed of a temporal progression of instantaneous microstates. A macrostate is experimentally observable, with at least a finite extent in spacetime. Ī 'microstate' is a state specified in terms of the constituent particles of a body of matter or radiation that has been specified as a macrostate in terms of such variables as internal energy and pressure. Boltzmann in his kinetic theory of gases". To quote Planck, "the logarithmic connection between entropy and probability was first stated by L. The equation was originally formulated by Ludwig Boltzmann between 18, but later put into its current form by Max Planck in about 1900. Boltzmann's grave in the Zentralfriedhof, Vienna, with bust and entropy formula.
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