Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New universal Lyapunov functions for non-linear reaction networks   In 1961, R\'enyi discovered a rich family of non-classical Lyapunov functions
for kinetics of the Markov chains, or, what is the same, for the linear kinetic
equations. This family was parameterised by convex functions on the positive
semi-axis. After works of Csisz\'ar and Morimoto, these functions became widely
known as $f$-divergences or the Csisz\'ar--Morimoto divergences. These Lyapunov
functions are universal in the following sense: they depend only on the state
of equilibrium, not on the kinetic parameters themselves.
  Despite many years of research, no such wide family of universal Lyapunov
functions has been found for nonlinear reaction networks. For general
non-linear networks with detailed or complex balance, the classical
thermodynamics potentials remain the only universal Lyapunov functions.
  We constructed a rich family of new universal Lyapunov functions for {\em any
non-linear reaction network} with detailed or complex balance. These functions
are parameterised by compact subsets of the projective space. They are
universal in the same sense: they depend only on the state of equilibrium and
on the network structure, but not on the kinetic parameters themselves.
  The main elements and operations in the construction of the new Lyapunov
functions are partial equilibria of reactions and convex envelopes of families
of functions.

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The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph