Nano statistical thermodynamics, a term, which has been recently introduced in the literature, is an extension of usual statistical thermodynamics, which deals with the systems consisting of finite number of particles / molecules. In other words, the study of sufficiently small systems consisting of limited assembly of molecules requires a modification of ordinary statistical thermodynamics.
For the study of small systems or nanostructures, one needs detailed information about the geometry and arrangement of particles in these nanostructures. In this presentation, a number of mathematical concepts have been introduced using geometrical number theory in order to derive working equations for statistical thermodynamics of small systems. Application of these new mathematical concepts has allowed us to derive analytic expressions for the distribution functions equation in a three-dimensional space.
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