Nonequilibrium partition identity
by gowtham[ Edit ] 2010-02-16 19:36:01
Another remarkably simple and elegant consequence of the FT is the so-called "nonequilibrium partition identity" (NPI):
\left\langle {\exp [ - \overline \Sigma_t \; t ]} \right\rangle = 1,\quad \forall t
see Carberry et al. J Chem Phys 121, 8179(2004). Thus in spite of the Second Law Inequality which might lead you to expect that the average would decay exponentially with time, the exponential probability ratio given by the FT exactly cancels the negative exponential in the average above leading to an average which is unity for all time!
There are many important implications from the FT. One is that small machines (such as nanomachines or even mitochondria in a cell) will spend part of their time actually running in "reverse". By "reverse", it is meant that they function so as to run in a way opposite to that for which they were presumably designed. As an example, consider a jet engine. If a jet engine were to run in "reverse" in this context, it would take in ambient heat and exhaust fumes to generate kerosene and oxygen.
