相关论文: Work distribution and path integrals in general me…

We propose a generalization of classical statistical mechanics which describes the behavior of dissipative systems placed in contact with a heat bath. In contrast to conventional statistical mechanics, which assigns probabilities to the…

We consider closed quantum systems (into which baths may be integrated) that are driven, i.e., subject to time-dependent Hamiltonians. Our point of departure is the assumption that, if systems start in microcanonical states at some initial…

It has been shown recently that the Jarzynski equality is generalized under nonequilibrium feedback control [T. Sagawa and M. Ueda, Phys. Rev. Lett. {\bf 104}, 090602 (2010)]. The presence of feedback control in physical systems should…

The purpose of this work is to pose and solve the problem to guide a collection of weakly interacting dynamical systems (agents, particles, etc.) to a specified terminal distribution. The framework is that of mean-field and of cooperative…

We establish the path integral approach for the time-dependent heat exchange of an externally driven quantum system coupled to a thermal reservoir. We derive the relevant influence functional and present an exact formal expression for the…

The special trajectory ensemble average (TEA), denoted by a subscript 0, in the Jarzynski Equality (JE) results in the Jensen inequality <R>_0 GT-EQ delta(F) for the work R done on the system, and not the thermodynamic work inequality <R>…

Kinetic Ising models are powerful tools for studying the non-equilibrium dynamics of complex systems. As their behavior is not tractable for large networks, many mean-field methods have been proposed for their analysis, each based on unique…

The nonequilibrium work relation, or Jarzynski equality, establishes a statistical relationship between a series of nonequilibrium experiments on a system subjected to thermal fluctuations and a hypothetical experiment at thermodynamic…

A general framework of evolutionary dynamics under heterogeneous populations is presented. The framework allows continuously many types of heterogeneous agents, heterogeneity both in payoff functions and in revision protocols and the entire…

The paper describes and compares three approaches to modeling an epidemic spread. The first approach is a well-known system of SIR ordinary differential equations. The second is a mean-field model, in which an isolation strategy for each…

Genetic variation in a population can sometimes arise so fast as to modify ecosystem dynamics. Such phenomena have been observed in natural predator-prey systems, and characterized in the laboratory as showing unusual phase relationships in…

Empirically derived continuum models of collective behavior among large populations of dynamic agents are a subject of intense study in several fields, including biology, engineering and finance. We formulate and study a mean-field game…

The main difficulty that arises in the analysis of most machine learning algorithms is to handle, analytically and numerically, a large number of interacting random variables. In this Ph.D manuscript, we revisit an approach based on the…

An asymmetric exclusion process with $N$ particles on $L$ sites is considered where particles can move one or two sites per infinitesimal time-step. An exact analysis for N=2 and a mean-field theory in comparison with simulations show…

In this work, we formulate an abstract framework to study mean-field systems. In contrast to most approaches in the available literature which primarily rely on the analysis of SDEs, ours is based on optimal transport and semigroup theory.…

The paper concerns classical solution of path-dependent partial differential equations (PPDEs) with coefficients depending on both variables of path and path-valued measure, which are crucial to understanding large-scale mean-field…

A large class of classical dynamical systems with an external rapidly oscillating driving action is considered and the effective Hamiltonian-like equations for the mean motion are obtained. The respective Liouville equation for the…

In this work, we systematically investigate mean field games and mean field type control problems with multiple populations using a coupled system of forward-backward stochastic differential equations of McKean-Vlasov type stemming from…

In this paper, we discuss the joint value distribution of $L$-functions in a suitable class. We obtain joint large deviations results in the central limit theorem for these $L$-functions and some mean value theorems, which give evidence…

On contrary to the customary thought, the well-known ``lemma'' that the distribution function of a collisionless Boltzmann gas keeps invariant along a molecule's path represents not the strength but the weakness of the standard theory. One…