Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Energy-pressure relation for low-dimensional gases   A particularly simple relation of proportionality between internal energy and
pressure holds for scale invariant thermodynamic systems, including classical
and quantum Bose and Fermi ideal gases. One can quantify the deviation from
such a relation by introducing the internal energy shift as the difference
between the internal energy of the system and the corresponding value for scale
invariant gases. We discuss general thermodynamic properties associated to the
scale invariance, provide criteria for which the internal energy shift density
is a bounded function of temperature. We then study the internal energy shift
and deviations from the energy-pressure proportionality in low dimensional
models of gases interpolating between the ideal Bose and the ideal Fermi gases,
focusing on the Lieb-Liniger model in 1d and on the anyonic gas in 2d. In 1d
the internal energy shift is determined from the thermodynamic Bethe ansatz
integral equations and an explicit relation for it is given at high
temperature. Our results show that the internal energy shift is positive, it
vanishes in the two limits of zero and infinite coupling (respectively the
ideal Bose and the Tonks Girardeau gas) and it has a maximum at a finite,
temperature depending, value of the coupling. Remarkably, at fixed coupling the
energy shift density saturates to a finite value for infinite temperature. In
2d we consider systems of Abelian anyons and non Abelian Chern-Simons
particles: as it can be seen also directly from a study of the virial
coefficients, in the usually considered hard-core limit the internal energy
shift vanishes and the energy is just proportional to the pressure, with the
proportionality constant being simply the area of the system. Soft-core
boundary conditions at coincident points for the two-body wavefunction
introduce a length scale, and induce a non-vanishing internal energy shift.

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The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
2
The categories of this paper are: math
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The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: nlin