Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mathematical Formalism of Nonequilibrium Thermodynamics for Nonlinear
  Chemical Reaction Systems with General Rate Law   This paper studies a mathematical formalism of nonequilibrium thermodynamics
for chemical reaction models with $N$ species, $M$ reactions, and general rate
law. We establish a mathematical basis for J. W. Gibbs' macroscopic chemical
thermodynamics under G. N. Lewis' kinetic law of entire equilibrium (detailed
balance in nonlinear chemistry kinetics). In doing so, the equilibrium
thermodynamics is then naturally generalized to nonequilibrium settings without
detailed balance. The kinetic models are represented by a Markovian jumping
process. A generalized macroscopic chemical free energy function and its
associated balance equation with nonnegative source and sink are the major
discoveries. The proof is based on the large deviation principle of this type
of Markov processes. A general fluctuation dissipation theorem for stochastic
reaction kinetics is also proved. The mathematical theory illustrates how a
novel macroscopic dynamic law can emerges from the mesoscopic kinetics in a
multi-scale system.

11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph