Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Renyi Thermostatistics and Self-Organization   Taking into account extremum of a Helmholtz free energy in the equilibrium
state of a thermodynamic system the Renyi entropy is derived from the Boltzmann
entropy by the same way as the Helmholtz free energy from the Hamiltonian. The
application of maximum entropy principle to the Renyi entropy gives rise to the
Renyi distribution. The $q$-dependent Renyi thermodynamic entropy is defined as
the Renyi entropy for Renyi distribution. A temperature and free energy are got
for a Renyi thermostatistics. Transfer from the Gibbs to Renyi thermostatistics
is found to be a phase transition at zero value of an order parameter
$\eta=1-q$. It is shown that at least for a particular case of the power-law
Hamiltonian $H=C\sum_i x_i^\kappa$ this entropy increases with $\eta$.
Therefore in the new entropic phase at $\eta>0$ the system tends to develop
into the most ordered state at $\eta=\eta_{max}=\kappa/(1+\kappa)$. The Renyi
distribution at $\eta_{max}$ becomes a pure power-law distribution.

14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
2
The categories of this paper are: math
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas