Challenges to the 2nd Law

The book Challenges to the Second Law of Thermodynamics by Capek and Sheenan starts out describing the status of this most fundamental law of physics as of 2005:

• For more than a century this field has lain fallow and beyond the pale of legitimate scientific inquiry due both to a dearth of scientific results and to a surfeit of peer pressure against such inquiry. 
• It is remarkable that 20th century physics, which embraced several radical paradigm shifts, was unwilling to wrestle with this remnant of 19th century physics, whose foundations were admittedly suspect and largely unmodified by the discoveries of the succeeding century. 
• This failure is due in part to the many strong imprimaturs placed on it by prominent scientists like Planck, Eddington, and Einstein. There grew around the second law a nearly inpenetrable mystique which only now is being pierced.

The book then continues to present 21 formulations of the 2nd Law followed by 20 versions of entropy and then proceeds to a large collection of challenges, which are all refuted, starting with this background:

• The 2nd Law has no general theoretical proof.
• Except perhaps for a dilute gas (Boltzmann's statistical mechanics), its absolute status rests squarely on empirical evidence.  

We learn that modern physics when confronted with the main unresolved problem of classical physics reacted by denial and oppression as cover up of a failure of monumental dimension. The roots of the present crisis of modern physics may hide here. 

Computational Thermodynamics seeks to demystify the 2nd Law as a result of finite precise computation  meeting systems developing increasing complexity like turbulence in slightly viscous flow.  

Physicists confronted with proving the 2nd Law.