Jarzynski’s Equality, Fluctuation Theorems, and Variance Reduction: Mathematical Analysis and Numerical Algorithms

  • Carsten Hartmann
  • Christof Schütte
  • Wei ZhangEmail author


In this paper, we study Jarzynski’s equality and fluctuation theorems for diffusion processes. While some of the results considered in the current work are known in the (mainly physics) literature, we review and generalize these nonequilibrium theorems using mathematical arguments, therefore enabling further investigations in the mathematical community. On the numerical side, variance reduction approaches such as importance sampling method are studied in order to compute free energy differences based on Jarzynski’s equality.


Jarzynski’s equality Fluctuation theorem Nonequilibrium dynamics Free energy difference Variance reduction Reaction coordinate 



The authors acknowledge financial support by the Einstein Center of Mathematics (ECMath) through project CH21, and the DFG-CRC 1114 “Scaling Cascades in Complex Systems” through project A05 “Probing scales in equilibrated systems by optimal nonequilibrium forcing” and B05 “Origin of the scaling cascades in protein dynamics”. Part of the work was done while CS and WZ were attending the program “Complex High-Dimensional Energy Landscapes” at IPAM (UCLA), 2017. The authors thank the institute for hospitality and support.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Carsten Hartmann
    • 1
  • Christof Schütte
    • 2
    • 3
  • Wei Zhang
    • 3
    Email author
  1. 1.Institut für MathematikBrandenburgische Technische Universität Cottbus-SenftenbergCottbusGermany
  2. 2.Institut für MathematikFreie Universität BerlinBerlinGermany
  3. 3.Zuse Institute BerlinBerlinGermany

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