A thermostat algorithm generating target ensembles

Abstract

We present a deterministic algorithm called contact density dynamics that generates any prescribed target distribution in the physical phase space. Akin to the famous model of Nosé-Hoover, our algorithm is based on a non-Hamiltonian system in an extended phase space. However the equations of motion in our case follow from contact geometry and we show that in general they have a similar form to those of the so-called density dynamics algorithm. As a prototypical example, we apply our algorithm to produce Gibbs canonical distribution for a one-dimensional harmonic oscillator.

6 pages, improved version, numerical results added

References in corpus (4)

• Liouville's Theorem and the canonical measure for nonconservative systems from contact geometry
• Completely Integrable Contact Hamiltonian Systems and Toric Contact Structures on $S^2\times S^3$
• Legendre submanifolds in contact manifolds as attractors and geometric nonequilibrium thermodynamics
• Para-Sasakian geometry in thermodynamic fluctuation theory

Cited by in corpus (18)

• Contact Hamiltonian Mechanics
• Contact Hamiltonian Systems
• Thermodynamic geometry for charged Gauss-Bonnet black holes in AdS spacetimes
• Singular Lagrangians and precontact Hamiltonian Systems
• Contact variational integrators
• Contact geometry and thermodynamics of black holes in AdS spacetimes
• Invariant measures for contact Hamiltonian systems: symplectic sandwiches with contact bread
• A review on contact Hamiltonian and Lagrangian systems
• On the Kaniadakis distributions applied in statistical physics and natural sciences
• Geometric integrator for simulations in the canonical ensemble
• Exact Baker-Campbell-Hausdorff formula for the contact Heisenberg algebra
• Application of Herglotz's Variational Principle to Electromagnetic Systems with Dissipation
• Stochastic sampling of the isothermal-isobaric ensemble: phase diagram of crystalline solids from molecular dynamics simulation
• Generalized virial theorem for contact Hamiltonian systems
• Contact geometry and quantum thermodynamics of nanoscale steady states
• Invariant measures for some dissipative systems from the Jacobi last multiplier
• New directions for contact integrators
• Geometric numerical integration of Liénard systems via a contact Hamiltonian approach