Ergodicity of One-dimensional Oscillators with a Signum Thermostat

J. C. Sprott
Department of Physics
University of Wisconsin-Madison,

Madison, Wisconsin 53706, USA

Received 29 August 2018; accepted: 25 September 2018; published online: 28 September 2018


Gibbs' canonical ensemble describes the exponential equilibrium distribution f(q,p,T)e-H(q,p)/kTf(q, p, T) \propto e^{-H(q,p)/kT} for an ergodic Hamiltonian system interacting with a 'heat bath' at temperature T. The simplest deterministic heat bath can be represented by a single 'thermostat variable' ζ\zeta. Ideally, this thermostat controls the kinetic energy so as to give the canonical distribution of the coordinates and momenta {q, p}. The most elegant thermostats are time-reversible and include the extra variable(s) needed to extract or inject energy. This paper describes a single-variable 'signum thermostat.' It is a limiting case of a recently proposed 'logistic thermostat.' It has a single adjustable parameter and can access all of Gibbs' microstates for a wide variety of one-dimensional oscillators.

Ref: J. C. Sprott, Computational Methods in Science and Technology  24, 169-176 (2018)

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