History
A question has been raised about who gave the earliest statement of the Jarzynski equality. For example in 1977 the Russian physicists G.N. Bochkov and Yu. E. Kuzovlev (see Bibliography) proposed a generalized version of the Fluctuation-Dissipation relations which holds in the presence of arbitrary external time-dependent forces. Despite its close similarity to the JE, the Bochkov-Kuzovlev result does not relate free energy differences to work measurements, as discussed by Jarzynski himself in 2007 (see references below).
Another similar statement to the Jarzynski equality is the nonequilibrium partition identity, which can be traced back to Yamada and Kawasaki. (The Nonequilibrium Partition Identity is the Jarzynski equality applied to two systems whose free energy difference is zero - like straining a fluid.) However, these early statements are very limited in their application. Both Bochkov and Kuzovlev as well as Yamada and Kawasaki consider a deterministic time reversible Hamiltonian system. As Kawasaki himself noted this precludes any treatment of nonequilibrium steady states. The fact that these nonequilibrium systems heat up forever because of the lack of any thermostatting mechanism leads to divergent integrals etc. No purely Hamiltonian description is capable of treating the experiments carried out to verify the Crooks fluctuation theorem, Jarzynski equality and the Fluctuation theorem. These experiments involve thermostated systems in contact with heat baths.
Read more about this topic: Jarzynski Equality
Famous quotes containing the word history:
“The history of progress is written in the blood of men and women who have dared to espouse an unpopular cause, as, for instance, the black man’s right to his body, or woman’s right to her soul.”
—Emma Goldman (1869–1940)
“History has neither the venerableness of antiquity, nor the freshness of the modern. It does as if it would go to the beginning of things, which natural history might with reason assume to do; but consider the Universal History, and then tell us,—when did burdock and plantain sprout first?”
—Henry David Thoreau (1817–1862)
“In history as in human life, regret does not bring back a lost moment and a thousand years will not recover something lost in a single hour.”
—Stefan Zweig (18811942)