Nonequilibrium partition identity
Encyclopedia
The nonequilibrium partition identity (NPI) is a remarkably simple and elegant consequence of the Fluctuation Theorem
previously known as the Kawasaki Identity:
(Carberry et al. 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!
The first derivation of the NonEquilibrium Partition Identity for Hamiltonian systems was by Yamada and Kawaski in 1967. For thermostatted deterministic systems the first derivation was by Morriss and Evans in 1985.
Fluctuation theorem
The fluctuation theorem , which originated from statistical mechanics, deals with the relative probability that the entropy of a system which is currently away from thermodynamic equilibrium will increase or decrease over a given amount of time...
previously known as the Kawasaki Identity:
(Carberry et al. 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!
The first derivation of the NonEquilibrium Partition Identity for Hamiltonian systems was by Yamada and Kawaski in 1967. For thermostatted deterministic systems the first derivation was by Morriss and Evans in 1985.
See also
- Fluctuation theoremFluctuation theoremThe fluctuation theorem , which originated from statistical mechanics, deals with the relative probability that the entropy of a system which is currently away from thermodynamic equilibrium will increase or decrease over a given amount of time...
- Provides an equality that quantifies fluctuations in time averaged entropy production in a wide variety of nonequilibrium systems. - Crooks fluctuation theoremCrooks Fluctuation TheoremThe Crooks equation is an equation in statistical mechanics that relatesthe work done on a system during a non-equilibrium transformation to thefree energy difference between the final and the initial state of the...
-Provides a Fluctuation TheoremFluctuation theoremThe fluctuation theorem , which originated from statistical mechanics, deals with the relative probability that the entropy of a system which is currently away from thermodynamic equilibrium will increase or decrease over a given amount of time...
between two equilibrium states. ImpliesJarzynski equalityJarzynski equalityThe Jarzynski equality is an equation in statistical mechanics that relates free energy differences between two equilibrium states and non-equilibrium processes...
. - Jarzynski Equality on arxiv.org
- "Fluctuation-Dissipation: Response Theory in Statistical Physics" by Umberto Marini Bettolo Marconi, Andrea Puglisi, Lamberto Rondoni, Angelo Vulpiani, http://arxiv.org/abs/0803.0719