Non-equilibrium steady states: fluctuations and large deviations of the density and of the current
By Bernard Derrida. 2007
171 citations recorded by the source corpus.
These lecture notes give a short review of methods such as the matrix ansatz, the additivity principle or the macroscopic fluctuation theory, developed recently in the theory of non-equilibrium phenomena. They show how these methods allow us to calculate the fluctuations and large deviations of the density and the current in non-equilibrium steady states of systems like exclusion processes. The properties of these fluctuations and large deviation functions in non-equilibrium steady states (for example, non-Gaussian fluctuations of density or non-convexity of the large deviation function which generalizes the notion of free energy) are compared with those of systems at equilibrium.
Subfields: Condensed Matter Physics, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/3b7a0c750ed388ae7878e5a7ef05bdcc23722da5
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Condensed Matter Physics
- Giovanni Jona-Lasinio
- Salvatore Torquato
- Hugo Touchette
- Lorenzo Bertini
- C. Landim
- A. Sole
- D. Gabrielli
In Mathematical Physics
- Hugo Touchette
- Giovanni Jona-Lasinio
- Salvatore Torquato
- Lorenzo Bertini
- C. Landim
- A. Sole
- D. Gabrielli
- I. Losev
In Statistical and Nonlinear Physics
- Hugo Touchette
- Lorenzo Bertini
- D. Gabrielli
- Giovanni Jona-Lasinio
- A. Sole
- Salvatore Torquato
- C. Landim
- B. Doyon
Citations in the corpus
- Non-equilibrium statistical mechanics: from a paradigmatic model to biological transport (2011, unknown): “Thus, determining exact expressions for these large deviation functions 1203 for interacting particle processes, either analytically or numerically, is a major 1204 challenge in the field [77].”
- Macroscopic fluctuation theory (2014, methodology): “Here we just show, in a specific example, how the basic principles of the MFT need to be modified to cover these processes.”
- The large deviation approach to statistical mechanics (2008, background): “Two excellent review papers [113,215] have appeared recently on interacting particle models and their large deviations, so we will not review this subject in detail here.”
- Hyperuniform states of matter (2018, background): “It is well-established that many-particle systems far from equilibrium typically possess long-range correlations; see, for example, [287–291].”
- Dissipation Bounds All Steady-State Current Fluctuations. (2015, unknown): “[16,26–28]).”