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The status of heat and work in nonequilibrium thermodynamics is quiteconfusing and non-unique at present with conflicting interpretations even aftera long history of the first law in terms of exchange heat and work, and is farfrom settled. Moreover, the exchange quantities lack certain symmetry. Bygeneralizing the traditional concept to also include their time-dependentirreversible components allows us to express the first law in a symmetric formdE(t)= dQ(t)-dW(t) in which dQ(t) and work dW(t) appear on an equal footing andpossess the symmetry. We prove that irreversible work turns into irreversibleheat. 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 exchangequantities. Hence, our new formulation of the first law provides tremendousadvantages and results in an extremely useful formulation of non-equilibriumthermodynamics, as we have shown recently. We prove that an adiabatic processdoes not alter p_{i}. All these results remain valid no matter how far thesystem 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 thesystem, which is reminiscent of equilibrium. We demonstrate that p_{i}(t) has aform very different from that in equilibrium. The first and second laws are nolonger independent so that we need only one law, which is again reminiscent ofequilibrium. 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. Wedetermine the irreversible components in two simple cases to show theusefulness of our approach; here, the traditional formulation is of no use.

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