# Projection Operators and Memory Function Formalism

### Books
* Zwanzig-Nonequilibrium Statistical Mechanics
* Memory Functions, Projection Operators, and the Defect Technique (Lecture Notes in Physics)
* (Advances in Chemical Physics) - Memory Function Approahes to Stochastic Problems in Condensed Matter, Volume 62(1985).
* Boon, Yip - Molecular Hydrodynamics (Chapter 1, 2)
* Projection Operator Techniques in the theory of fluctuations by Bruce Berne in Modern Theoretical Chemistry. v.5 Statistical Mechanics, Part B Time-dependent processes
* Dieter Forster.-Hydrodynamic fluctuations, broken symmetry, and correlation functions
* Chapter 11 in Bruce J. Berne, Robert Pecora - Dynamic Light Scattering

### Papers
* [Ottinger - General projection operator formalism for the dynamics and thermodynamics of complex fluids](https://journals.aps.org/pre/abstract/10.1103/PhysRevE.57.1416)
* [Multi-level Dynamical Systems: Connecting the Ruelle Response Theory and the Mori-Zwanzig Approach_2013](https://doi.org/10.1007/s10955-013-0726-8)
* [Derivation of Transport Equations Using the Time-Dependent Projection Operator Method_2002](https://doi.org/10.1143/PTP.107.525)
* [Mode-Coupling Theory of the Glass Transition: A Primer_2018](https://doi.org/10.3389/fphy.2018.00097)
* [Transport coefficients of non-Newtonian fluid and causal dissipative hydrodynamics_2008](https://doi.org/10.1103/PhysRevE.78.051107)
* [A mode coupling theory for Brownian particles in homogeneous steady shear flow_2009](https://sor.scitation.org/doi/10.1122/1.3119084)
* [Mori–Zwanzig formalism as a practical computational tool_2009](https://doi.org/10.1039/D1SM00521A)
* [Many chain correlated dynamics in polymer fluids_1999](https://doi.org/10.1063/1.478660)
* [On the non-stationary generalized Langevin equation_2017](https://doi.org/10.1063/1.5006980)
* [The modified Langevin description for probes in a nonlinear medium_2016](https://doi.org/10.1088/1361-648X/29/6/064004)
* [Equation of motion for coarse-grained simulation based on microscopic description_2007](https://doi.org/10.1103/PhysRevE.75.051109)
* [Microscopic derivation of particle-based coarse-grained dynamics_2013](https://doi.org/10.1063/1.4795091)
* [Extracting macroscopic dynamics: model problems and algorithms_2004](https://doi.org/10.1088/0951-7715/17/6/R01)
* [Mori-Zwanzig theory for dissipative forces in coarse-grained dynamics in the Markov limit_2017](https://doi.org/10.1103/PhysRevE.95.013303)
* [Microscopic derivation of particle-based coarse-grained dynamics: Exact expression for memory function_2017](https://doi.org/10.1063/1.4978572)
* [Microscopic derivation of coarse-grained, energy-conserving generalized Langevin dynamics_2019](https://doi.org/10.1063/1.5096655)
* [Systematic derivation of hybrid coarse-grained models_2019](https://doi.org/10.1103/PhysRevE.99.013303)
* [Bottom-up approach to represent dynamic properties in coarse-grained molecular simulations_2018](https://doi.org/10.1063/1.5064369)
* [The multi-dimensional generalized Langevin equation for conformational motion of proteins_2019](https://doi.org/10.1063/1.5055573)
* [Construction of dissipative particle dynamics models for complex fluids via the Mori–Zwanzig formulation_2014](https://doi.org/10.1039/C4SM01387E)
* [Perspective: Dissipative particle dynamics_2017](https://doi.org/10.1063/1.4979514)
* [Hybrid description of complex molecules_2009](https://doi.org/10.1209/0295-5075/88/40008)
* [Contraction of State Variables in Non-Equilibrium Open Systems. I_1980](https://doi.org/10.1143/PTP.63.1865)
* [Generalized Langevin equation for nonequilibrium systems_2001](https://doi.org/10.1016/S0378-4371(01)00328-4)
* [Mori-Zwanzig projection operator formalism for far-from-equilibrium systems with time-dependent Hamiltonians_2019](https://doi.org/10.1103/PhysRevE.99.062118)
* [Fluctuation–dissipation relations far from equilibrium: a case study_2021](https://doi.org/10.1039/D1SM00521A)
* [Application of the projection operator formalism to non-Hamiltonian dynamics_2011](https://doi.org/10.1063/1.3530071)
* [Computing generalized Langevin equations and generalized Fokker–Planck equations_2009](https://doi.org/10.1073/pnas.0902633106)
* [Generalized Langevin Equation: An Introductory Review for Biophysicists](https://doi.org/10.1142/S1793048019300019)
* [Mode-coupling theory](https://doi.org/10.1088/1742-5468/2005/05/P05013)
* [Phys. Rev. E 104, 024121 (2021) - Mori-Zwanzig projection operator formalism: Particle-based coarse-grained dynamics of open classical systems far from equilibrium (aps.org)](https://journals.aps.org/pre/abstract/10.1103/PhysRevE.104.024121)