Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equivalence and nonequivalence of ensembles: Thermodynamic, macrostate,
  and measure levels   We present general and rigorous results showing that the microcanonical and
canonical ensembles are equivalent at all three levels of description
considered in statistical mechanics - namely, thermodynamics, equilibrium
macrostates, and microstate measures - whenever the microcanonical entropy is
concave as a function of the energy density in the thermodynamic limit. This is
proved for any classical many-particle systems for which thermodynamic
functions and equilibrium macrostates exist and are defined via large deviation
principles, generalizing many previous results obtained for specific classes of
systems and observables. Similar results hold for other dual ensembles, such as
the canonical and grand-canonical ensembles, in addition to path ensembles used
for describing nonequilibrium systems driven in steady states.

8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
2
The categories of this paper are: math
11
The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas