Related papers: Ergodicity of the Nos\'e-Hoover method
Gibbs' thermodynamic entropy is given by the logarithm of the phase volume, which itself responds to heat transfer to and from thermal reservoirs. We compare the thermodynamic dissipation described by phase-volume loss with heat-transfer…
Nos\'e's pioneering 1984 work inspired a variety of time-reversible deterministic thermostats. Though several groups have developed successful doubly-thermostated models, single-thermostat models have failed to generate Gibbs' canonical…
Recent laboratory experiments suggest an intrinsic asymmetry between heating and cooling, with heating occurring more efficiently. Two decades earlier, molecular dynamics (MD) simulations had examined a related setup - heating one side of a…
For a harmonic oscillator, Nos\'e's single-thermostat approach to simulating Gibbs' canonical ensemble with dynamics samples only a small fraction of the phase space. Nos\'e's approach has been improved in a series of three steps: [ 1 ]…
Nos\'e and Hoover's 1984 work showed that although Nos\'e and Nos\'e-Hoover dynamics were both consistent with Gibbs' canonical distribution neither dynamics, when applied to the harmonic oscillator, provided Gibbs' Gaussian distribution.…
In the 1960s and 1970s a large part of the theory of dynamical systems concerned the case of uniformly hyperbolic or Axiom A dynamical system and abstract ergodic theory of smooth dynamical systems. However since around 1980 an emphasize…
The Birkhoff Ergodic Theorem asserts under mild conditions that Birkhoff averages (i.e. time averages computed along a trajectory) converge to the space average. For sufficiently smooth systems, our small modification of numerical Birkhoff…
The concept of weak ergodicity breaking is defined and studied in the context of deterministic dynamics. We show that weak ergodicity breaking describes a weakly chaotic dynamical system: a nonlinear map which generates subdiffusion…
We study the existence and properties of the non-equilibrium steady state which arises by putting two copies of systems at different temperatures into a thermal contact. We solve the problem for the relativistic systems that are described…
We introduce a variant of the asymmetric random average process with continuous state variables where the maximal transport is restricted by a cutoff. For periodic boundary conditions, we show the existence of a phase transition between a…
We study the low-temperature thermodynamics of weakly-interacting uniform liquids in one-dimensional attractive Bose-Bose mixtures.~The Bogoliubov approach is used to simultaneously describe quantum and thermal fluctuations. First, we…
We consider stationary stochastic dynamical systems evolving on a compact metric space, by perturbing a deterministic dynamics with a random noise, added according to an arbitrary probabilistic distribution. We prove the maximal and…
The rate of quantum ergodicity is studied for three strongly chaotic (Anosov) systems. The quantal eigenfunctions on a compact Riemannian surface of genus g=2 and of two triangular billiards on a surface of constant negative curvature are…
Some paradoxical aspects of the Nos\'e and Nos\'e-Hoover dynamics of 1984 and Dettmann's dynamics of 1996 are elucidated. Phase-space descriptions of thermostated harmonic oscillator dynamics can be simultaneously expanding, incompressible,…
Chaotic dynamics can be quite heterogeneous in the sense that in some regions the dynamics are unstable in more directions than in other regions. When trajectories wander between these regions, the dynamics is complicated. We say a chaotic…
In the first part of the note we analyze the long time behaviour of a two dimensional stochastic Navier--Stokes equations system on a torus with a degenerate, one dimensional noise. In particular, for some initial data and noises we…
We investigate one-dimensional driven diffusive systems where particles may also be created and annihilated in the bulk with sufficiently small rate. In an open geometry, i.e., coupled to particle reservoirs at the two ends, these systems…
Usual approach to investigate the statistical properties of deterministically thermostated systems is to analyze the regime of the system motion. In this work the cumulant analysis is used to study the properties of the stationary…
We explore layered strongly correlated materials as a platform to identify and control unconventional heat transfer phenomena. We demonstrate that these systems can be tailored to sustain a wide spectrum of heat transport regimes, ranging…
Recently, a number of authors have investigated the conditions under which a stochastic perturbation acting on an infinite dimensional dynamical system, e.g. a partial differential equation, makes the system ergodic and mixing. In…