History Boltzmann's entropy formula

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boltzmann s grave in zentralfriedhof, vienna, bust , entropy formula.


the equation formulated ludwig boltzmann between 1872 , 1875, later put current form max planck in 1900. quote planck, logarithmic connection between entropy , probability first stated l. boltzmann in kinetic theory of gases .


the value of w intended proportional wahrscheinlichkeit (the german word probability) of macroscopic state probability distribution of possible microstates—the collection of (unobservable) ways (observable) thermodynamic state of system can realized assigning different positions(x) , momenta(p) various molecules. interpreted in way, boltzmann s formula general formula thermodynamic entropy. however, boltzmann s paradigm ideal gas of n identical particles, of




n

i




{\displaystyle n_{i}}

in i-th microscopic condition (range) of position , momentum. case, probability of each microstate of system equal, equivalent boltzmann calculate number of microstates associated macrostate. w historically misinterpreted literally meaning number of microstates, , means today. w can counted using formula permutations











where ranges on possible molecular conditions , ! denotes factorial. correction in denominator due fact identical particles in same condition indistinguishable. w called thermodynamic probability since integer greater one, while mathematical probabilities numbers between 0 , one.








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