Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Statistical Foundation of Entropy in Extended Irreversible
  Thermodynamics   In the theory of extended irreversible thermodynamics (EIT), the
flux-dependent entropy function plays a key role and has a fundamental
distinction from the usual flux-independent entropy function adopted by
classical irreversible thermodynamics (CIT). However, its existence, as a
prerequisite for EIT, and its statistical origin have never been justified. In
this work, by studying the macroscopic limit of an \epsilon-dependent Langevin
dynamics, which admits a large deviations (LD) principle, we show that the
stationary LD rate functions of probability density p_{\epsilon}(x; t) and
joint probability density p_{\epsilon}(x; \dot{x}; t) actually turn out to be
the desired fluxindependent entropy function in CIT and flux-dependent entropy
function in EIT respectively. The difference of the two entropy functions is
determined by the time resolution for Brownian motions times a Lagrangian, the
latter arises from the LD Hamilton-Jacobi equation and can be used for
constructing conserved Lagrangian/Hamiltonian dynamics.

10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex