Related papers: Large deviation approach to nonequilibrium systems
Fluctuation theorems are a generalization of thermodynamics on small scales and provide the tools to characterize the fluctuations of thermodynamic quantities in non-equilibrium nanoscale systems. They are particularly important for…
We apply the large-deviation method to study trajectories in dissipative quantum systems. We show that in the long time limit the statistics of quantum jumps can be understood from thermodynamic arguments by exploiting the analogy between…
Boltzmann-Sanov and Cramer-Chernoff's theorems provide large deviation probabilities, entropy, and rate functions for the spatial distribution of systems and the total internal energy of an ensemble respectively. By the method of Lagrange's…
Lack of knowledge about the detailed many-particle motion on the microscopic scale is a key issue in any theoretical description of a macroscopic experiment. For systems at or close to thermal equilibrium, statistical mechanics provides a…
This paper focuses on systems of nonlinear second-order stochastic differential equations with multi-scales. The motivation for our study stems from mathematical physics and statistical mechanics, for examples, Langevin dynamics and…
Equilibrium is a rather ideal situation, the exception rather than the rule in Nature. Whenever the external or internal parameters of a physical system are varied its subsequent relaxation to equilibrium may be either impossible or take…
There has been substantial progress in recent years in the quantitative understanding of the nonequilibrium time evolution of quantum fields. Important topical applications, in particular in high energy particle physics and cosmology,…
An overview is given of recent advances in nonequilibrium statistical mechanics about the statistics of random paths and current fluctuations. Although statistics is carried out in space for equilibrium statistical mechanics, statistics is…
The theory of large deviations constitutes a mathematical cornerstone in the foundations of Boltzmann-Gibbs statistical mechanics, based on the additive entropy $S_{BG}=- k_B\sum_{i=1}^W p_i \ln p_i$. Its optimization under appropriate…
Living systems operate far from thermodynamic equilibrium. Enzymatic activity can induce broken detailed balance at the molecular scale. This molecular scale breaking of detailed balance is crucial to achieve biological functions such as…
Current fluctuations in boundary-driven diffusive systems are, in many cases, studied using hydrodynamic theories. Their predictions are then expected to be valid for currents which scale inversely with the system size. To study this…
Nonequilibrium complex systems are often effectively described by the mixture of different dynamics on different time scales. Superstatistics, which is "statistics of statistics" with two largely separated time scales, offers a consistent…
For non-equilibrium systems described by finite Markov processes, we consider the number of times that a system traverses a cyclic sequence of states (a cycle). The joint distribution of the number of forward and backward instances of any…
We give a new proof of the large deviation principle from the hydrodynamic limit for the Ginzberg-Landau model studied in Donsker and Varadhan (1989) using techniques from the theory of stochastic control and weak convergence methods. The…
These notes are based on the lectures that one of us (HT) gave at the Summer School on the "Theory of Large Deviations and Applications", held in July 2024 at Les Houches in France. They present the basic definitions and mathematical…
In these notes we present a pedagogical account of the population dynamics methods recently introduced to simulate large deviation functions of dynamical observables in and out of equilibrium. After a brief introduction on large deviation…
We consider a general class of statistical mechanical models of coherent structures in turbulence, which includes models of two-dimensional fluid motion, quasi-geostrophic flows, and dispersive waves. First, large deviation principles are…
Finding equilibrium points in continuous minmax games has become a key problem within machine learning, in part due to its connection to the training of generative adversarial networks and reinforcement learning. Because of existence and…
Disordered many-body systems exhibit a wide range of emergent phenomena across different scales. These complex behaviors can be utilized for various information processing tasks such as error correction, learning, and optimization. Despite…
Particle approximations for certain nonlinear and nonlocal reaction-diffusion equations are studied using a system of Brownian motions with killing. The system is described by a collection of i.i.d. Brownian particles where each particle is…