dc.contributor.author |
Salagaram, Trisha
|
|
dc.contributor.author |
Chetty, Nithaya
|
|
dc.date.accessioned |
2012-06-06T11:32:00Z |
|
dc.date.available |
2012-06-06T11:32:00Z |
|
dc.date.issued |
2011-11 |
|
dc.description.abstract |
We devise a hierarchy of computational algorithms to enumerate the microstates of a system
comprising N independent, distinguishable particles. An important challenge is to cope with
integers that increase exponentially with system size, and which very quickly become too large to
be addressed by the computer. A related problem is that the computational time for the most
obvious brute-force method scales exponentially with the system size which makes it difficult to
study the system in the large N limit. Our methods address these issues in a systematic and
hierarchical manner. Our methods are very general and applicable to a wide class of problems
such as harmonic oscillators, free particles, spin J particles, etc. and a range of other models for
which there are no analytical solutions, for example, a system with single particle energy spectrum
given by ε(p, q) = ε0(p2 +q4), where p and q are non-negative integers and so on. Working within
the microcanonical ensemble, our methods enable one to directly monitor the approach to the
thermodynamic limit (N ! 1), and in so doing, the equivalence with the canonical ensemble is
made more manifest. Various thermodynamic quantities as a function of N may be computed using
our methods; in this paper, we focus on the entropy, the chemical potential and the temperature. |
en |
dc.description.librarian |
nf2012 |
en |
dc.description.uri |
http://ajp.aapt.org/ |
en_US |
dc.identifier.citation |
Salagaram, T & Chetty, N 2011, 'Enhancing the understanding of entropy through computation', American Journal of Physics, vol. 79, no. 11, pp. 1127-1132. |
en |
dc.identifier.issn |
0002-9505 (print) |
|
dc.identifier.other |
10.1119/1.3623416 |
|
dc.identifier.uri |
http://hdl.handle.net/2263/19126 |
|
dc.language.iso |
en |
en_US |
dc.publisher |
American Association of Physics Teachers |
en_US |
dc.rights |
© 2011 American Association of Physics Teachers |
en_US |
dc.subject |
Computation |
en |
dc.subject |
Heat bath |
en |
dc.subject |
Microstates |
en |
dc.subject |
Chemical potential |
en |
dc.subject |
Canonical ensemble |
en |
dc.subject.lcsh |
Entropy |
en |
dc.subject.lcsh |
Thermodynamics |
en |
dc.title |
Enhancing the understanding of entropy through computation |
en |
dc.type |
Postprint Article |
en |