Wednesday, March 28, 2012

Muscular Thermodynamics

Muscles are pretty efficient at turning energy into motion. Apparently efficiencies as high as 70% can be achieved. To the naive former student of thermodynamics this may be a bit of a puzzle. Don't we recall that the ideal efficiency of a heat engine is given by Kelvin’s formula for the efficiency of a reversible Carnot engine: e =1-T/T’

If we apply that rule to muscles, where temperatures are nearly uniform, it would seem to imply that thermodynamic efficiency must be near zero, which is a lot less than 70%. It might appear that our biological systems are troubling the second law of thermodynamics.

Of course, physicists know that the second law always wins, so clearly our analysis has a flaw.

That flaw is that muscles are not heat engines, and they don’t exactly extract heat from one heat reservoir and transfer it to another. Instead, they extract energy from excited molecules (ATP) and transfer it to less excited molecules. E. T. Jaynes pointed out that Gibbs seems to have understood this point in 1887, when he argued that the salient fact is the energy per degree of freedom of the respective molecules e = 1 –W/W’

In effect, the excited ATP molecule serves as an effective micro heat reservoir of temperature Teff = 2W/k, where W is the energy stored in its chemical bonds per degree of freedom. Those effective temperatures, says Jaynes, can be 20 times ambient temperatures, accounting for the high efficiencies of actual muscles. Thus our problem has been transformed back into a heat engine problem of a sort.

Of course modern chemical thermodynamics can doubtless handle this sort of problem more elegantly and comprehensively, but I always like simple pictures.

Yet another example of how meta-stable systems far from equilibrium are key to most of the interesting structure in our universe.