We devise a hierarchy of computational algorithms to enumerate themicrostates of a system comprising N independent, distinguishable particles. Animportant challenge is to cope with integers that increase exponentially withsystem size, and which very quickly become too large to be addressed by thecomputer. A related problem is that the computational time for the most obviousbrute-force method scales exponentially with the system size which makes itdifficult to study the system in the large N limit. Our methods address theseissues in a systematic and hierarchical manner. Our methods are very generaland applicable to a wide class of problems such as harmonic oscillators, freeparticles, spin J particles, etc. and a range of other models for which thereare no analytical solutions, for example, a system with single particle energyspectrum given by {\epsilon}(p,q) = {\epsilon}0 (p^2 + q^4), where p and q arenon-negative integers and so on. Working within the microcanonical ensemble,our methods enable one to directly monitor the approach to the thermodynamiclimit (N \rightarrow \infty), and in so doing, the equivalence with thecanonical ensemble is made more manifest. Various thermodynamic quantities as afunction of N may be computed using our methods; in this paper, we focus on theentropy, the chemical potential and the temperature.
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