Applications of the divergence theorem in Bayesian inference and MaxEnt

Davis, Sergio; Gutiérrez, Gonzalo

doi:10.1063/1.4959043

Cited by 12 publications

(5 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…which is a result already obtained by Rickayzen [8] for the microcanonical ensemble by a different method. Note that this identity, as written above, is not only valid for P( x) corresponding to the canonical ensemble, but for an arbitrary distribution [13,16].…”

Section: Estimators For Temperature In Constrained Systemsmentioning

confidence: 99%

“…. , S N )) [13,16]. In this way, equation ( 20) is an important, new result, that thanks to the freedom to choose the vector field ω , allows one to obtain different temperature estimators for spin systems.…”

Section: Temperature For the Magnetic Systemmentioning

confidence: 99%

“…Applications and testing in molecular dynamics simulations can be found in [9][10][11][12]. A proof on the existence of such estimators in any ensemble is given in [13].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Configurational temperature in constrained systems: the case of spin dynamics

Gutiérrez

Davis

Palma

2018

J. Phys. A: Math. Theor.

Self Cite

View full text Add to dashboard Cite

A general mathematical expression to estimate the temperature in computer simulations of constrained systems is obtained. Using a recently derived theorem which relates the ensemble average of thermodynamics conjugate variables we obtain a family of temperature estimators for constrained systems based solely on the configurational state. We present explicit formulas for the case of a classical spin system governed by Heisenberg type Hamiltonians. The expressions can be considered an extension of the equipartition theorem for spin variables, and are useful in practical situations to monitor the temperature in spin dynamics simulation, as well as to gain a deeper understanding of the meaning of temperature.

show abstract

Section: Estimators For Temperature In Constrained Systemsmentioning

confidence: 99%

Section: Temperature For the Magnetic Systemmentioning

confidence: 99%

See 1 more Smart Citation

Configurational temperature in constrained systems: the case of spin dynamics

Gutiérrez

Davis

Palma

2018

J. Phys. A: Math. Theor.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Note that this identity, as written above, is not only valid for P ( x) given by Eq. 1 but for an arbitrary distribution [12]. Now we consider the particular case in which P depends on the configurations x through the Hamiltonian of the system H: P ( x) = ρ(H( x)), which leads to the identity:…”

Section: Temperature Estimator Independent Of the Statistical Ensmentioning

confidence: 99%

Ensemble-free configurational temperature for spin systems

Palma¹,

Gutiérrez²,

Davis³

2016

Phys. Rev. E

View full text Add to dashboard Cite

An estimator for the dynamical temperature in an arbitrary ensemble is derived in the framework of Bayesian statistical mechanics and the maximum entropy principle. We test this estimator numerically by a simulation of the two-dimensional XY-model in the canonical ensemble. As this model is critical in the whole region of temperatures below the Berezinski-Kosterlitz-Thouless critical temperature TBKT , we use a generalization of Wolff's uni-cluster algorithm. The numerical results allow us to confirm the robustness of the analytical expression for the microscopic estimator of the temperature. This microscopic estimator has also the advantage that it gives a direct measure of the thermalization process and can be used to compute absolute errors associated to statistical fluctuations. In consequence, this estimator allows for a direct, absolute and astringent test of the ergodicity of the underlying Markov process, which encodes the algorithm used in a numerical simulation.

show abstract

“…In this work we want to introduce some recent fluctuation identities in statistical mechanics, namely the conjugate variables theorem (CVT) [15,16] into this problem. Fluctuation identities can be applied to the standard statistical mechanics successfully, recovering a large number of properties related to the expectation values and the fluctuations of the Hamiltonian and other observables.…”

Section: Introductionmentioning

confidence: 99%

Fluctuation theorems in nonextensive statistics

Umpierrez¹,

Davis²

2019

Preprint

Self Cite

View full text Add to dashboard Cite

Nonextensive statistics is a formalism of statistical mechanics that describes the ocurrence of power-law distributions in complex systems, particularly the so-called q-exponential family of distributions. In this work we present the use of fluctuation theorems for q-canonical ensembles as a powerful tool to readily obtain statistical properties. In particular, we have obtained strong conditions for the possible values of q depending on the density of states of the system.

show abstract

Applications of the divergence theorem in Bayesian inference and MaxEnt

Cited by 12 publications

References 14 publications

Configurational temperature in constrained systems: the case of spin dynamics

Configurational temperature in constrained systems: the case of spin dynamics

Ensemble-free configurational temperature for spin systems

Fluctuation theorems in nonextensive statistics

Contact Info

Product

Resources

About