# Jarzynski恆等式

Jarzynski恆等式(JE)是一個在統計力學中敘述平衡態非平衡態之間自由能差異的等式。它是以物理學家Christopher Jarzynski的名字命名的，他在1997年發現了此一恆等式。

$\Delta F \leq W$,

$\exp( -\Delta F / k T) = \overline{ \exp( -W/kT ) }.$

$\Delta F \leq \overline{W},$

## 參考文獻

• C. Jarzynski, Nonequilibrium equality for free energy differences, Phys. Rev. Lett. 78, 2690 (1997)
• C. Jarzynski, Equilibrium free-energy differences from nonequilibrium measurements: A master-equation approach, Phys. Rev. E 56, 5018 (1997)
• G. E. Crooks, Nonequilibrium measurements of free energy differences for microscopically reversible Markovian systems, J. Stat. Phys. 90, 1481 (1998)
• G. Hummer, A. Szabo, Free energy reconstruction from nonequilibrium single-molecule pulling experiments, Proc. Nat. Acad. Sci. 98, 3658 (2001)
• J. Liphardt et al., Equilibrium information from nonequilibrium measurements in an experimental test of Jarzynski's equality, Science 296, 1832 (2002)
• D. J. Evans, A non-equilibrium free energy theorem for deterministic systems, Mol. Phys. 101, 1551 (2003)
• A. B. Adib, Entropy and density of states from isoenergetic nonequilibrium processes, Phys. Rev. E 71, 056128 (2005)
• F. Douarche, S. Ciliberto, A. Petrosyan, I. Rabbiosi, An experimental test of the Jarzynski equality in a mechanical experiment, Europhys. Lett. 70 (5), 593（2005, see also cond-mat/0502395）非平衡程過的統計計算的早期結果，請見：
• G. N. Bochkov and Yu. E. Kuzovlev, Zh. Eksp. Teor. Fiz. 72, 238 (1977); op. cit. 76, 1071 (1979)
• G. N. Bochkov and Yu. E. Kuzovlev, Physica 106A, 443 (1981); op. cit. 106A, 480 (1981)