Renaud Raquépas

Renaud Raquépas
New York University | NYU · Courant Institute of Mathematical Sciences

Ph D

About

17
Publications
506
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67
Citations
Introduction
Renaud Raquépas studies mathematical physics, with emphasis on time-dependent aspects of statistical mechanics and entropy production, in both quantum and classical systems.
Education
September 2017 - December 2020
McGill University and Université Grenoble Alpes
Field of study
  • Mathematics

Publications

Publications (17)
Preprint
Full-text available
The universal typical-signal estimators of entropy and cross entropy based on the asymptotics of recurrence and waiting times play an important role in information theory. Building on their construction, we introduce and study universal typical-signal estimators of entropy production in the context of nonequilibrium statistical mechanics of one-sid...
Preprint
Full-text available
The universal typical-signal estimators of entropy and cross entropy based on the asymptotics of recurrence and waiting times play an important role in information theory. Building on their construction, we introduce and study universal typical-signal estimators of entropy production in the context of nonequilibrium statistical mechanics of one-sid...
Preprint
Full-text available
We introduce conditions of lower decoupling to the study of waiting-time estimations of the cross entropy between two mutually independent stationary stochastic processes. Although similar decoupling conditions have been used in the literature on large deviations and statistical mechanics , they appear largely unexplored in information theory. Buil...
Article
Full-text available
We consider a discrete-time non-Hamiltonian dynamics of a quantum system consisting of a finite sample locally coupled to several bi-infinite reservoirs of fermions with a translation symmetry. In this setup, we compute the asymptotic state, mean fluxes of fermions into the different reservoirs, as well as the mean entropy production rate of the dy...
Article
We prove existence and uniqueness of the invariant measure and exponential mixing in the total-variation norm for a class of stochastic differential equations driven by degenerate compound Poisson processes. In addition to mild assumptions on the distribution of the jumps for the driving process, the hypotheses for our main result are that the corr...
Thesis
This thesis consists mainly of a collection of papers on the study of the large-time asymptotics of entropy production and associated mixing problems. After having introduced the central notions, we present, in order: a study of the vanishing-noise limit for the large deviations of entropy production functionals in nondegenerate diffusions; an expo...
Preprint
Full-text available
We consider a discrete-time non-Hamiltonian dynamics of a quantum system consisting of a finite sample locally coupled to several bi-infinite reservoirs of fermions with a translation symmetry. In this setup, we compute the asymptotic state, mean fluxes of fermions into the different reservoirs, as well as the mean entropy production rate of the dy...
Preprint
Full-text available
We investigate the behaviour of a family of entropy production functionals associated to stochastic differential equations of the form $\mathrm{d} X_s = -\nabla V(X_s) \, \mathrm{d} s + b(X_s) \, \mathrm{d} s + \sqrt{2\epsilon} \, \mathrm{d} W_s $, where $b$ is a globally Lipschitz nonconservative vector field keeping the system out of equilibrium,...
Article
Full-text available
We study the large-time behaviour of a sample \(\mathcal {S}\) consisting of an ensemble of fermionic walkers on a graph interacting with a structured infinite reservoir of fermions \(\mathcal {E}\) through an exchange of particles in preferred states. We describe the asymptotic state of \(\mathcal {S}\) in terms the initial state of \(\mathcal {E}...
Preprint
Full-text available
We prove existence and uniqueness of the invariant measure and exponential mixing in the total-variation norm for a class of stochastic differential equations driven by degenerate compound Poisson processes. In addition to mild assumptions on the distribution of the jumps for the driving process, the hypotheses for our main result are that the corr...
Preprint
Full-text available
We study the large-time behaviour of a sample $\mathcal{S}$ consisting of an ensemble of fermionic walkers on a graph interacting with a structured infinite reservoir of fermions $\mathcal{E}$ through an exchange of particles in preferred states. We describe the asymptotic state of $\mathcal{S}$ in terms the initial state of $\mathcal{E}$, with esp...
Article
We show that elements of control theory, together with an application of Harris’ ergodic theorem, provide an alternate method for showing exponential convergence to a unique stationary measure for certain classes of networks of quasi-harmonic classical oscillators coupled to heat baths. With the system of oscillators expressed in the form dXt=AXtdt...
Article
Full-text available
We study heat fluctuations in the two-time measurement framework. For bounded perturbations, we give sufficient ultraviolet regularity conditions on the perturbation for the moments of the heat variation to be uniformly bounded in time, and for the Fourier transform of the heat variation distribution to be analytic and uniformly bounded in time in...
Preprint
Full-text available
We study heat fluctuations in the two-time measurement framework. For bounded perturbations, we give sufficient ultraviolet regularity conditions on the perturbation for the moments of the heat variation to be uniformly bounded in time, and for the Fourier transform of the heat variation distribution to be analytic and uniformly bounded in time in...
Preprint
Full-text available
We show that elements of control theory, together with an application of Harris' ergodic theorem, provide an alternate method for showing exponential convergence to a unique stationary measure for certain classes of perturbed networks of classical oscillators. With the system of oscillators expressed in the form $\mathrm{d} X_t = A X_t \,\mathrm{d}...
Article
We analyze Landauer's principle for repeated interaction systems consisting of a reference quantum system $\mathcal{S}$ in contact with a environment $\mathcal{E}$ consisting of a chain of independent quantum probes. The system $\mathcal{S}$ interacts with each probe sequentially, for a given duration, and the Landauer principle relates the energy...
Article
Full-text available
We study Landauer's Principle for Repeated Interaction Systems (RIS) consisting of a reference quantum system $\mathcal S$ in contact with a structured environment $\mathcal E$ made of a chain of independent quantum probes; $\mathcal S$ interacts with each probe, for a fixed duration, in sequence. We first adapt Landauer's lower bound, which relate...

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