Mechanical Foundations of the Generalized Second Law and the Irreversibility Principle - Purushottam Das Gujrati (Foundations)
We follow the Boltzmann-Clausius-Maxwell (BCM) proposal to establish the generalized second law (GSL) that is applicable to a system of any size, including a single particle system as our example establishes, and that supercedes the celebrated second law (SL) of increase of entropy of an isolated system. It is merely a consequence of the mechanical equilibrium (stable or unstable) principle (Mec-EQ-P) of analytical mechanics and the first law. We justify an irreversibility priciple that covers all processes, spontaneous or not, and having both positive and negative nonequilibrium temperatures temperatures T defined by <semantics>(dQ/dS)E</semantics>. Our novel approach to establish GSL/SL is the inverse of the one used in classical thermodynamics and clarifies the concept of spontaneous processes so that <semantics>dS≥0</semantics> for <semantics>T>0</semantics> and <semantics>dS<0</semantics> for <semantics>T<0</semantics>. Nonspontaneous processes such as creation of internal constraints are not covered by GSL/SL. Our demonstration establishes that Mec-EQ-P controls spontaneous processes, and that temperature (positive and negative) must be considered an integral part of dissipation.