  We follow the Boltzmann-Clausius-Maxwell (BCM) proposal to solve a
long-standing problem of identifying the underlying cause of the second law
(SL) of spontaneous irreversibility, a stochastic universal principle, as the
mechanical equilibrium (stable or unstable) principle (Mec-EQ-P) of analytical
mechanics of an isolated nonequilibrium system of any size. The principle leads
to nonnegative system intrinsic (SI) microwork and SI-average macrowork dW
during any spontaneous process. In conjuction with the first law, Mec-EQ-P
leads to a generalized second law (GSL) dQ=dW>0, where dQ=TdS is the purely
stochastic SI-macroheat that corresponds to dS>0 for T>0 and dS<0 for T<0,
where T is the temperature. The GSL supercedes the conventional SL formulation
that is valid only for a macroscopic system for positive temperatures
temperatures, but reformulates it to dS<0 for negative temperatures. It is
quite surprising that GSL is not only a direct consequence of intertwined
mechanical and stochastic macroquantities through the first law but also
remains valid for any arbitrary irreversible process in a system of any size as
an identity for positive and negative temperatures. It also becomes a no-go
theorem for GSL-violation unless we abandon Mec-EQ-P of analytical mechanics
used in the BCM proposal, which will be catastrophic for theoretical physics.
In addition, Mec-EQ-P also provides new insights into the roles of spontaneity,
nonspontaneity, negative temperatures, instability, and the significance of
dS<0 due to nonspontaneity and inserting internal constraints.
