А.О. Шишанин
6
Hardy—Ramanujan formula and
thermodynamics of quantum string
© A.O. Shishanin
Bauman Moscow State Technical University, Moscow 105005, Russia
For partitions of natural numbers, there is an asymptotic formula of the Hardy-
Ramanujan. In this paper we propose to compare this formula with the number of mi-
crostates, using entropy calculation of the quantum string by means of Euler–Maclaurin
formula. The work briefly touches upon a different approach, using counting the number
of states through the inverse Laplace transformation of the partition function.
Keywords:
partition of the number, the generating function, Hardy–Ramanujan formula,
quantum string, partition function, free energy, entropy, Euler–Maclaurin formula.
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Shishanin A.O.
(b. 1980) graduated from Lomonosov Moscow State University.
Ph.D.,
Assoc. Professor of the Physics Department at Bauman Moscow State Technical Univer-
sity. He is the author of about 20 publications. Scientific interests include mathematical
physics. е-mail:
