Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonequilibrium Thermodynamics. Symmetric and Unique Formulation of the
  First Law, Statistical Definition of Heat and Work, Adiabatic Theorem and the
  Fate of the Clausius Inequality: A Microscopic View   The status of heat and work in nonequilibrium thermodynamics is quite
confusing and non-unique at present with conflicting interpretations even after
a long history of the first law in terms of exchange heat and work, and is far
from settled. Moreover, the exchange quantities lack certain symmetry. By
generalizing the traditional concept to also include their time-dependent
irreversible components allows us to express the first law in a symmetric form
dE(t)= dQ(t)-dW(t) in which dQ(t) and work dW(t) appear on an equal footing and
possess the symmetry. We prove that irreversible work turns into irreversible
heat. Statistical analysis in terms of microstate probabilities p_{i}(t)
uniquely identifies dW(t) as isentropic and dQ(t) as isometric (see text)
change in dE(t); such a clear separation does not occur for exchange
quantities. Hence, our new formulation of the first law provides tremendous
advantages and results in an extremely useful formulation of non-equilibrium
thermodynamics, as we have shown recently. We prove that an adiabatic process
does not alter p_{i}. All these results remain valid no matter how far the
system is out of equilibrium. When the system is in internal equilibrium,
dQ(t)\equivT(t)dS(t) in terms of the instantaneous temperature T(t) of the
system, which is reminiscent of equilibrium. We demonstrate that p_{i}(t) has a
form very different from that in equilibrium. The first and second laws are no
longer independent so that we need only one law, which is again reminiscent of
equilibrium. The traditional formulas like the Clausius inequality
{\oint}d_{e}Q(t)/T_{0}<0, etc. become equalities {\oint}dQ(t)/T(t)\equiv0, etc,
a quite remarkable but unexpected result in view of irreversibility. We
determine the irreversible components in two simple cases to show the
usefulness of our approach; here, the traditional formulation is of no use.

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The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin