Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An introduction to nanothermodynamics: Thermal equilibrium for
  heterogeneous and finite-sized systems   The theory of small-system thermodynamics was originally developed to extend
the laws of thermodynamics to length scales of nanometers. Here we review this
"nanothermodynamics," and stress how it also applies to large systems that
subdivide into a heterogeneous distribution of internal subsystems that we call
"regions." We emphasize that the true thermal equilibrium of most systems often
requires that these regions are in the fully-open generalized ensemble, with a
distribution of region sizes that is not externally constrained, which we call
the "nanocanonical" ensemble. We focus on how nanothermodynamics impacts the
statistical mechanics of specific models. One example is an ideal gas of
indistinguishable atoms in a large volume that subdivides into an ensemble of
small regions of variable volume, with separate regions containing atoms that
are distinguishable from those in other regions. Combining such subdivided
regions yields the correct entropy of mixing, avoiding Gibbs paradox without
resorting to macroscopic quantum symmetry for semi-classical particles. Other
models are based on Ising-like spins (binary degrees of freedom), which are
solved analytically in one-dimension, making them suitable examples for
introductory courses in statistical physics. A key result is to quantify the
net increase in entropy when large systems subdivide into small regions of
variable size. Another result is to show similarity in the equilibrium
properties of a two-state model in the nanocanonical ensemble and a three-state
model in the canonical ensemble. Thus, emergent phenomena may alter the thermal
behavior of microscopic models, and the correct ensemble is necessary for
accurate predictions.

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The categories of this paper are: q-bio
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The categories of this paper are: econ
1
The categories of this paper are: cs
2
The categories of this paper are: math
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex