A Kac system interacting with two heat reservoirs

2025/08/18 by Bonetto, Federico, Loss, Michael, Powell, Matthew
#FOS: Physical sciences #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.2508.13122

Abstract

We study a system formed by M particles moving in 3 dimension and interacting with 2 heat reservoirs with N>>M particles each. The system and the reservoirs evolve and interact via random collision described by a Kac-type master equation. The initial state of the reservoirs is given by 2 Maxwellian distributions at temperature T₊ and T_-. We show that, for times much shorter than √(N) the interaction with the reservoirs is well approximated by the interaction with 2 Maxwellian thermostats, that is, heat reservoirs with N=∞. As a byproduct, if T₊=T_- we extend the results in \citeBLTV to particles in 3 dimension.

Citations

• Spectral Gaps for Reversible Markov Processes with Chaotic Invariant\n Measures: The Kac Process with Hard Sphere Collisions in Three Dimensions
• Approach to the steady state in kinetic models with thermal reservoirs\n at different temperatures
• On the Mixing Time of Kac's Walk and Other High-Dimensional Gibbs\n Samplers with Constraints
• Exponential approach to, and properties of, a non-equilibrium steady state in a dilute gas
• Kac's Program in Kinetic Theory
• On Villani's Conjecture Concerning Entropy Production for the Kac Master\n Equation

Related

• Improved Approximation of Infinite Thermostat by Finite Reservoir Using the 3D Kac Model
• Dynamics of the Kac Ring Model with switching scatterers
• Decay of Entropy and Information for multidimensional Kac models
• Kac's Program in Kinetic Theory
• A N-uniform quantitative Tanaka's theorem for the conservative Kac's N-particle system with Maxwell molecules