Jarzynski equality

Jarzynski equality
Name	Jarzynski equality
Field	Statistical mechanics
Introduced	1997
Introduced by	Christopher Jarzynski
Key concepts	Nonequilibrium thermodynamics; Free energy differences; Fluctuation theorems

Contents

Jarzynski equality The Jarzynski equality is an exact relation in nonequilibrium statistical mechanics that links irreversible work performed during finite-time transformations to equilibrium free energy differences. It was introduced by Christopher Jarzynski and quickly influenced research programs at institutions such as Princeton University, Los Alamos National Laboratory, University of Chicago, and California Institute of Technology. The equality has been tested and applied in experimental platforms associated with groups at Harvard University, University of Oxford, Max Planck Society, and Imperial College London.

Introduction

The Jarzynski equality emerged amid contemporaneous developments including the Evans–Searles fluctuation theorem, the Crooks fluctuation theorem, and theoretical advances by researchers affiliated with University of California, Berkeley, Massachusetts Institute of Technology, Rutgers University, and University of Illinois Urbana–Champaign. Christopher Jarzynski derived the relation while at Los Alamos National Laboratory and it was rapidly cited by investigators at Cornell University, University of Geneva, University of Tokyo, and ETH Zurich. The equality relates a path-dependent observable measured under time-dependent driving to an equilibrium property central to work by scholars at Princeton University Press and organizations such as the National Science Foundation and European Research Council.

The formal derivation of the Jarzynski equality employs techniques from canonical ensemble theory, path integrals, and stochastic calculus developed at centers including Harvard University, Stanford University, University of Cambridge, and Columbia University. Starting from an initial equilibrium ensemble described by a Hamiltonian with control parameter protocols inspired by experimental setups at Bell Labs and IBM Research, one considers repeated realizations of nonequilibrium processes studied in laboratories like Brookhaven National Laboratory and Lawrence Berkeley National Laboratory. The equality states that the exponential average of the negative work over k_B T equals the exponential of the negative free energy difference, a relation that connects to derivations by authors at Yale University, Brown University, Duke University, and Johns Hopkins University. Rigorous proofs invoke measure-preserving dynamics and Liouville theorems familiar to mathematicians at Princeton University, Institute for Advanced Study, University of Michigan, and University of Toronto.

Physically, the Jarzynski equality implies that rare fluctuations in work during driven processes encode equilibrium information, a perspective advanced by researchers at University of Pennsylvania, University of California, San Diego, University of British Columbia, and University of Sydney. The implication impacts theoretical frameworks explored by groups at Los Alamos National Laboratory, Sandia National Laboratories, National Institutes of Health, and NIST and connects to entropy production studies pursued at University of Copenhagen, University of Helsinki, Weizmann Institute of Science, and Tel Aviv University. The equality complements the second law of thermodynamics as discussed in treatises associated with Cambridge University Press and reviews by scholars from Princeton University, Oxford University Press, and MIT Press.

Experimental validations were performed with single-molecule manipulation techniques developed in laboratories such as Harvard University, University of Oxford, University of Basel, and Max Planck Institute for Biophysical Chemistry. Early confirmations used optical tweezers and atomic force microscopy apparatuses from groups at University of Vienna, Ecole Normale Supérieure, Institute of Photonic Sciences, and University of Glasgow. Demonstrations in colloidal particles and electronic systems were realized by teams at École Polytechnique, University of Amsterdam, University of Geneva, and University of Twente. Implementations in quantum systems attracted attention at Imperial College London, Technion, University of Waterloo, and Purdue University where connections to quantum fluctuation relations and experiments in superconducting circuits and trapped ions were explored.

The Jarzynski equality sits among a family of fluctuation relations including the Crooks fluctuation theorem, the Evans–Searles fluctuation theorem, and extensions developed in collaborations involving Stanford University, ETH Zurich, University of Illinois, and Tel Aviv University. Generalizations address feedback control and information-theoretic corrections inspired by work at Google Quantum AI, Microsoft Research, IBM Research, and academic groups at University of California, Santa Barbara and University College London. Further extensions include steady-state versions, quantum generalizations, and relations incorporating measurement and feedback that have been formalized by theorists at Seoul National University, Tsinghua University, Indian Institute of Science, and Australian National University.

Applications of the Jarzynski equality span biomolecular free energy calculations, ligand binding studies, and reaction pathway sampling pursued by research teams at Scripps Research, European Molecular Biology Laboratory, Cold Spring Harbor Laboratory, and Riken. Computational implementations leverage alchemical transformations and nonequilibrium pulling protocols developed at Argonne National Laboratory, Lawrence Livermore National Laboratory, Oak Ridge National Laboratory, and Pacific Northwest National Laboratory. In chemical physics and materials science, the equality has informed work on folding landscapes, catalysis, and nanoscale engines by investigators at Max Planck Society, ETH Zurich, Columbia University, and University of California, Santa Barbara.