Equilibrium free-energy differences from nonequilibrium measurements: A master-equation approach

By Christopher Jarzynski. 1997

It has recently been shown that the Helmholtz free energy difference between two equilibrium configurations of a system may be obtained from an ensemble of finite-time (nonequilibrium) measurements of the work performed in switching an external parameter of the system. Here this result is established, as an identity, within the master equation formalism. Examples are discussed and numerical illustrations provided.

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Deep Unsupervised Learning using Nonequilibrium Thermodynamics (2015, methodology): “We compare experimentally against adversarial networks and MCGSMs. Related ideas from physics include the Jarzynski equality [16] (known in machine learning as annealed importance sampling [30]), which uses a Markov chain which converts one distribution into another to compute the ratio of…”
Accurate and conservative estimates of MRF log-likelihood using reverse annealing (2014, background): “Importantly, unbiasedness is not an asymptotic property, but holds for any K (Neal, 2001; Jarzynski, 1997).”
Diffusion Probabilistic Models for 3D Point Cloud Generation (2021, background): “This process is termed the diffusion process that converts the initial distribution of the particles to a simple noise distribution by adding noise at each time step [12, 20].”
A Variational Perspective on Diffusion-Based Generative Models and Score Matching (2021, methodology): “When used as an EBM, sampling from the conditional score model can be achieved by running the annealed Langevin diffusion (Neal, 2001), which is connected to free-energy estimaton in physics (Jarzynski, 1997), wherein the path integral is essentially a Feynman Kac representation.”
Fluctuation Relations for Diffusion Processes (2007, methodology): “In this section we shall derive an identity that generalizes the celebrated Jarzynski equality [48, 49] and shall prepare the ground for obtaining more refined fluctuation relations following the ideas of [31], [63] and [19].”
Steered molecular dynamics and mechanical functions of proteins. (2001, background): “Jarzynski C: Nonequilibrium equality for free energy differences.”
Hamiltonian Annealed Importance Sampling for partition function estimation (2012, background): “The proposal and target distributions q (x) and p (x) are extended to corresponding distributions q∪ (y) and p∪ (y) 2 There is a direct mapping between annealed importance sampling and the Jarzynski equality in non-equilibrium thermodynamics - see Jarzynski (1997).”
Enhanced Sampling Methods for Molecular Dynamics Simulations [Article v1.0] (2022, background): “In intermediate cases, the free energy difference can be estimated [82] by weighting the non-equilibrium trajectories.”
Score-Based Generative Modeling with Critically-Damped Langevin Diffusion (2021, methodology): “Learning a mapping between a simple, tractable and a complex distribution as in SGMs is inspired by annealed importance sampling (Neal, 2001) and the Jarzynski equality from non-equilibrium statistical mechanics (Jarzynski, 1997a;b; 2011).”
Experiments in Stochastic Thermodynamics: Short History and Perspectives (2017, background): “The Jarzynski equality states that [13,14]”
Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems (2008, methodology): “In this section, we show that the FT (58) can be used to derive the Crooks [42, 43, 94] and the Jarzynski relations [95, 96, 97] in either isolated or closed driven quantum systems as well as a FT for for heat and particles exchange between two finite systems.”