Nonequilibrium statistical mechanics

By Michel Le Bellac. Physics Subject Headings (PhySH), 2007

2,262 citations recorded by the source corpus.

In part I of these lecture notes, I introduce the basic tools of non equilibrium statistical mechanics: linear response, Brownian motion, Langevin equation, (Pauli) master equation. Part II is devoted to a derivation of quantum master equations from the Schrodinger equation, and to some of their applications to quantum optics and to Brownian motion. Finally, in part III, I examine more recent developments: the Crooks and Jarzynski equalities and the Gallavotti-Cohen fluctuation theorem.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/304f6d530b9f16297228602bfb6fab4952be770d

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In Atomic and Molecular Physics, and Optics

In Statistical and Nonlinear Physics

Citations in the corpus

Lecture notes on Generalised Hydrodynamics (2019, background): “Non-equilibrium phenomena, often defined as those where time-reversal invariance is broken or where entropy is produced, constitute one of the most active and high profile areas of studies in modern science [3, 4].”
Glass Transition Thermodynamics and Kinetics (2013, methodology): “This approach is based on the MoriZwanzig formalism (37, 38) to describe the time dependence of density fluctuations at the atomic or molecular level.”
Effective Theory for the Measurement-Induced Phase Transition of Dirac Fermions (2021, methodology): “[51] It is also possible to perturbatively incorporate correlations between the center-of-mass and the relative degrees of freedom beyond a product state assumption by applying time-dependent perturbation theory in the Mori-Zwanzig formalism [79].”
Quantum master equation for electron transport through quantum dots and single molecules (2006, background): “Note that a similar derivation can be done in Liouville space [15, 45] by defining the Liouville space projection operator Cn, CnρT = ρρB.”
Supervised parallel-in-time algorithm for long-time Lagrangian simulations of stochastic dynamics: Application to hydrodynamics (2019, methodology): “agator corrects the prediction iteratively. For demonstration, we employ DPD to model the stochastic microscopic dynamics and the Navier-Stokes equations to obtain mean-ﬁeld behavior in the continuum [30, 31]. It is worth noting that SPASD is a scalable and stable parallel-in-time algorithm applicab”
The free energy principle for action and perception: A mathematical review (2017, background): “(21), but rather a Langevin-type equation (Zwanzig, 2001) dμ dt = f (μ) + w (33)”
Numerical implementation of dynamical mean field theory for disordered systems: application to the Lotka–Volterra model of ecosystems (2019, methodology): “[18] Robert Zwanzig.”
Mathematical and physical ideas for climate science (2013, methodology): “As described by Zwanzig (2001), a generalized Langevin equation can then be derived based on Dyson’s formula for operator exponentials etL = etQL + ∫ t 0 e(t−s)LPLesQLds (91) We write the Liouville equation for an observable A as dA(t) dt = LA(t) = etLLA = etLPLA+ etLQLA The factor exp(tL) in the…”
Scalable molecular dynamics on CPU and GPU architectures with NAMD. (2020, background): “Studies of complex conformational transitions occurring on long timescales often proceed by identifying a geometric transformation associated with a general-extent parameter, 116 ξ ( x ) , often referred to as the reaction-coordinate model 117 and formed by collective variables.”