The discussion focuses on the derivation of the Boltzmann distribution, particularly addressing the transition from discrete to continuous variables in statistical mechanics. Participants highlight the importance of large particle numbers, which allows the use of Stirling's approximation for simplifying calculations. The conversation emphasizes that while individual states (n1, n2, etc.) are discrete, the large quantity of particles enables the application of derivatives in this context. This transition is crucial for understanding the behavior of systems at thermodynamic limits.
PREREQUISITESStudents and professionals in physics, particularly those specializing in statistical mechanics, thermodynamics, and anyone interested in the mathematical foundations of the Boltzmann distribution.
Correct. But between 5:16 and 5:20 the transition from discrete to continuous is being made. The reason this can be done is that n is always large (and Stirling's formula is a good approximation)kidsasd987 said:However its a finite discrete number. as far as I know, derivative is defined on continuous(complete) functions