Nonextensive thermodynamic functions in the Schrödinger-Gibbs ensemble

Alonso, José L.; Castro, Alberto; Clemente-Gallardo, Jesús; Cuchí, J. C.; Echenique, Pablo; Esteve, J. G.; Falceto, Fernando

doi:10.1103/physreve.91.022137

Cited by 3 publications

(3 citation statements)

References 38 publications

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“…In particular, this was the case when the Schrödinger-Gibbs ensemble was analyzed in Ref. [41]. Nonetheless, notice that S G is a mathematically consistent entropy function, despite the unphysical properties of the Statistical Mechanics it defines.…”

Section: A a Gibbs-entropy For Hybrid Systems?mentioning

confidence: 94%

Entropy and canonical ensemble of hybrid quantum classical systems

et al. 2020

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In this work we generalize and combine Gibbs and von Neumann approaches to build, for the first time, a rigorous definition of entropy for hybrid quantum-classical systems. The resulting function coincides with the two cases above when the suitable limits are considered. Then, we apply the MaxEnt principle for this hybrid entropy function and obtain the natural candidate for the hybrid canonical ensemble (HCE). We prove that the suitable classical and quantum limits of the HCE coincide with the usual classical and quantum canonical ensembles since the whole scheme admits both limits, thus showing that the MaxEnt principle is applicable and consistent for hybrid systems.

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Section: A a Gibbs-entropy For Hybrid Systems?mentioning

confidence: 94%

Entropy and canonical ensemble of hybrid quantum classical systems

et al. 2020

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“…This does not necessarily imply that the true HCE is not stationary. In fact, for purely quantum system, one can also define a Gibbs ensemble [19], that is obviously not the true quantum canonical: both ensembles, the right and the wrong one, are stationary under von Neumann equation. Might this also be the case for hybrid systems?…”

mentioning

confidence: 99%

“…In the quantum space, only orthogonal states should be considered, and hence the use of the delta functions in Eq. (19). One can therefore "discard" the non-orthongonal states in the averaging, by using: gA (µ, ξ) = λ(β) i δ(ψ − ψ i (ξ))A ii (ξ) , (30)…”

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confidence: 99%

Entropy and canonical ensemble of hybrid quantum classical systems

Alonso,

Bouthelier,

Castro

et al. 2020

Preprint

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We generalize von Neumann entropy function to hybrid quantum-classical systems by considering the principle of exclusivity of hybrid events. For non-interacting quantum and classical subsystems, this entropy function separates into the sum of the usual classical (Gibbs) and quantum (von Neumann) entropies, whereas if the two parts do interact, it can be properly separated into the classical entropy for the marginal classical probability, and the conditional quantum entropy.We also deduce the hybrid canonical ensemble (HCE) as the one that maximizes this entropy function, for a fixed ensemble energy average. We prove that the HCE is additive for non-interacting systems for all thermodynamic magnitudes, and reproduces the appropriate classical-and quantumlimit ensembles. Furthermore, we discuss how and why Ehrenfest dynamics does not preserve the HCE and does not yield the correct ensemble averages when time-averages of simulations are considered -even if it can still be used to obtain correct averages by modifying the averaging procedure.

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About the computation of finite temperature ensemble averages of hybrid quantum-classical systems with molecular dynamics

Alonso¹,

Bouthelier-Madre

Castro³

et al. 2021

New J. Phys.

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Molecular or condensed matter systems are often well approximated by hybrid quantum-classical models: the electrons retain their quantum character, whereas the ions are considered to be classical particles. We discuss various alternative approaches for the computation of equilibrium (canonical) ensemble averages for observables of these hybrid quantum-classical systems through the use of molecular dynamics (MD)-i.e. by performing dynamics in the presence of a thermostat and computing time-averages over the trajectories. Often, in classical or ab initio MD, the temperature of the electrons is ignored and they are assumed to remain at the instantaneous ground state given by each ionic configuration during the evolution. Here, however, we discuss the general case that considers both classical and quantum subsystems at finite temperature canonical equilibrium. Inspired by a recent formal derivation for the canonical ensemble for quantum classical hybrids, we discuss previous approaches found in the literature, and provide some new formulas.

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Nonextensive thermodynamic functions in the Schrödinger-Gibbs ensemble

Cited by 3 publications

References 38 publications

Entropy and canonical ensemble of hybrid quantum classical systems

Entropy and canonical ensemble of hybrid quantum classical systems

Entropy and canonical ensemble of hybrid quantum classical systems

About the computation of finite temperature ensemble averages of hybrid quantum-classical systems with molecular dynamics

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