Thermostat algorithm for generating target ensembles

Bravetti, Alessandro; Tapias, Diego

doi:10.1103/physreve.93.022139

Cited by 39 publications

(51 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recently, in [38], another application of contact Hamiltonian dynamics has been proposed, namely in equilibrium statistical mechanics (SM). A major problem for the dynamical simulations of systems in an equilibrium ensemble different from the microcanonical one is that of finding equations of motion that generate the correct equilibrium distribution for the positions and momenta of the physical system (see, e.g., [39][40][41]).…”

Section: Equilibrium Statistical Mechanicsmentioning

confidence: 99%

“…Using the above-mentioned Liouville theorem, it follows that the invariant measure of the dynamics has the distribution ρ t (q a , p a , S) [38]. Therefore, one is free to choose ρ t from the onset to be any distribution in T SM .…”

Section: Equilibrium Statistical Mechanicsmentioning

confidence: 99%

“…For example, it has been shown both analytically and with numerical simulations that when ρ target and f (S) are a canonical and a logistic distribution, respectively, then Equations (47)- (49) correctly simulate the equilibrium properties of systems in the canonical ensemble (see [38,44,45]). …”

Section: Equilibrium Statistical Mechanicsmentioning

confidence: 99%

See 2 more Smart Citations

Contact Hamiltonian Dynamics: The Concept and Its Use

Bravetti

2017

Entropy

129

100

View full text Add to dashboard Cite

show abstract

Section: Equilibrium Statistical Mechanicsmentioning

confidence: 99%

Section: Equilibrium Statistical Mechanicsmentioning

confidence: 99%

See 1 more Smart Citation

Contact Hamiltonian Dynamics: The Concept and Its Use

Bravetti

2017

Entropy

129

100

View full text Add to dashboard Cite

show abstract

“…The DD method provides an algorithm for the generation of a set of equations in a (2n + 1)-dimensional space consistent with a prescribed probability distribution (n being the degrees of freedom of the physical system). For a general description of the method we refer to [13][14][15]. In this section we present its application to ST1DS.…”

Section: Density Dynamicsmentioning

confidence: 99%

Ergodicity of One-dimensional Systems Coupled to the Logistic Thermostat

Tapias¹,

Bravetti²,

Sanders³

2017

CMST

Self Cite

View full text Add to dashboard Cite

Abstract:We analyze the ergodicity of three one-dimensional Hamiltonian systems, with harmonic, quartic and Mexican-hat potentials, coupled to the logistic thermostat. As criteria for ergodicity we employ: the independence of the Lyapunov spectrum with respect to initial conditions; the absence of visual "holes" in two-dimensional Poincaré sections; the agreement between the histograms in each variable and the theoretical marginal distributions; and the convergence of the global joint distribution to the theoretical one, as measured by the Hellinger distance. Taking a large number of random initial conditions, for certain parameter values of the thermostat we find no indication of regular trajectories and show that the time distribution converges to the ensemble one for an arbitrarily long trajectory for all the systems considered. Our results thus provide a robust numerical indication that the logistic thermostat can serve as a single one-parameter thermostat for stiff one-dimensional systems.

show abstract

“…Contact geometry [58,59] hasn't received much attention in physics literature until the recent years. This geometric setting is widely used to study thermodynamics [38,40,41], mechanical systems with Rayleigh dissipation [60,61] as well as statistical mechanics [62]. Contact geometry is the odd dimensional counterpart of the more familiar symplectic geometry [63].…”

Section: Introductionmentioning

confidence: 99%

Contact geometry and thermodynamics of black holes in AdS spacetimes

Ghosh

Bhamidipati

2019

Phys. Rev. D

View full text Add to dashboard Cite

In this paper we discuss a formulation of extended phase space thermodynamics of black holes in Anti de Sitter (AdS) space-time, from the contact geometry point of view. Thermodynamics of black holes can be understood within the framework of contact geometry as flows of vector fields generated by Hamiltonian functions on equilibrium submanifolds in the extended phase space, that naturally incorporates the structure of a contact manifold. Deformations induced by the contact vector fields are used to construct various maps among thermodynamic quantities. Thermodynamic variables and equations of state of Schwarzschild black holes are mapped to that of Reissner-Nordstrom black holes in AdS, with charge as the deformation parameter. In addition, the equations of state of general black holes in AdS are shown to emerge from the high temperature ideal gas limit equations, via suitable deformations induced by contact vector fields. The Hamilton-Jacobi formalism analogous to mechanics is set up and the corresponding characteristic curves of contact vector fields are explicitly obtained, to model thermodynamic processes of black holes. Extension to thermodynamic cycles in this framework is also discussed.

show abstract

Thermostat algorithm for generating target ensembles

Cited by 39 publications

References 27 publications

Contact Hamiltonian Dynamics: The Concept and Its Use

Contact Hamiltonian Dynamics: The Concept and Its Use

Ergodicity of One-dimensional Systems Coupled to the Logistic Thermostat

Contact geometry and thermodynamics of black holes in AdS spacetimes

Contact Info

Product

Resources

About