Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Foundations of a Finite Non-Equilibrium Statistical Thermodynamics:
  Extrinsic Quantities   Statistical thermodynamics is valuable as a conceptual structure that shapes
our thinking about equilibrium thermodynamic states. A cloud of unresolved
questions surrounding the foundations of the theory could lead an impartial
observer to conclude that statistical thermodynamics is in a state of crisis
though. Indeed, the discussion about the microscopic origins of irreversibility
has continued in the scientific community for more than a hundred years. This
paper considers these questions while beginning to develop a statistical
thermodynamics for finite non-equilibrium systems. Definitions are proposed for
all of the extrinsic variables of the fundamental thermodynamic relation that
are consistent with existing results in the equilibrium thermodynamic limit.
The probability density function on the phase space is interpreted as a
subjective uncertainty about the microstate, and the Gibbs entropy formula is
modified to allow for entropy creation without introducing additional physics
or modifying the phase space dynamics. Resolutions are proposed to the mixing
paradox, Gibbs' paradox, Loschmidt's paradox, and Maxwell's demon thought
experiment. Finally, the extrinsic variables of the fundamental thermodynamic
relation are evaluated as functions of time and space for a diffusing ideal
gas, and the initial and final values are shown to coincide with the expected
equilibrium values when interpreted in a classical context.

9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int