Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Energy-exchange stochastic models for non-equilibrium   Non-equilibrium steady states are subject to intense investigations but still
poorly understood. For instance, the derivation of Fourier law in Hamiltonian
systems is a problem that still poses several obstacles. In order to
investigate non-equilibrium systems, stochastic models of energy-exchange have
been introduced and they have been used to identify universal properties of
non-equilibrium. In these notes, after a brief review of the problem of
anomalous transport in 1-dimensional Hamiltonian systems, some boundary-driven
interacting random systems are considered and the "duality approach" to their
rigorous mathematical treatment is reviewed. Duality theory, of which a brief
introduction is given, is a powerful technique to deal with Markov processes
and interacting particle systems. The content of these notes is mainly based on
the papers [10, 11, 12].

35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc