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We study a system of $N$ particles interacting through the Kac collision, with $m$ of them interacting, in addition, with a Maxwellian thermostat at temperature $frac{1}{beta}$. We use two indicators to understand the approach to the equilibrium Gaussian state. We prove that i) the spectral gap of the evolution operator behaves as $frac{m}{N}$ for large $N$ ii) the relative entropy approaches its equilibrium value (at least) at an eventually exponential rate $sim frac{m}{N^2}$ for large $N$. The question of having non-zero entropy production at time $0$ remains open. A relationship between the Maxwellian thermostat and the thermostat used in Bonetto, Loss, Vaidyanathan (J. Stat. Phys. 156(4):647-667, 2014) is established through a van Hove limit.
We introduce a global thermostat on Kacs 1D model for the velocities of particles in a space-homogeneous gas subjected to binary collisions, also interacting with a (local) Maxwellian thermostat. The global thermostat rescales the velocities of all t
In this paper we study a model of randomly colliding particles interacting with a thermal bath. Collisions between particles are modeled via the Kac master equation while the thermostat is seen as an infinite gas at thermal equilibrium at inverse tem
We consider Kacs 1D N-particle system coupled to an ideal thermostat at temperature T, introduced by Bonetto, Loss, and Vaidyanathan in 2014. We obtain a propagation of chaos result for this system, with explicit and uniform-in-time rates of order N^
We review the exact results on the various critical regimes of the antiferromagnetic $Q$-state Potts model. We focus on the Bethe Ansatz approach for generic $Q$, and describe in each case the effective degrees of freedom appearing in the continuum limit.
Kinetic energy equipartition is a premise for many deterministic and stochastic molecular dynamics methods that aim at sampling a canonical ensemble. While this is expected for real systems, discretization errors introduced by the numerical integrati