Linear Quantum Entropy and Non-Hermitian Hamiltonians

We consider the description of open quantum systems with probability sinks (or sources) in terms of general non-Hermitian Hamiltonians.~Within such a framework, we study novel possible definitions of the quantum linear entropy as an indicator of the flow of information during the dynamics. Such linear entropy functionals are necessary in the case of a partially Wigner-transformed non-Hermitian Hamiltonian (which is typically useful within a mixed quantum-classical representation). Both the case of a system represented by a pure non-Hermitian Hamiltonian as well as that of the case of non-Hermitian dynamics in a classical bath are explicitly considered.Comment: Entropy, Special Issue "Entropy in Quantum Systems and Quantum Field Theory (QFT)

Hexatic phase and water-like anomalies in a two-dimensional fluid of particles with a weakly softened core

We study a two-dimensional fluid of particles interacting through a spherically-symmetric and marginally soft two-body repulsion. This model can exist in three different crystal phases, one of them with square symmetry and the other two triangular. We show that, while the triangular solids first melt into a hexatic fluid, the square solid is directly transformed on heating into an isotropic fluid through a first-order transition, with no intermediate tetratic phase. In the low-pressure triangular and square crystals melting is reentrant provided the temperature is not too low, but without the necessity of two competing nearest-neighbor distances over a range of pressures. A whole spectrum of water-like fluid anomalies completes the picture for this model potential.Comment: 26 pages, 14 figures; printed article available at http://link.aip.org/link/?jcp/137/10450

Phase diagram of softly repulsive systems: The Gaussian and inverse-power-law potentials

We redraw, using state-of-the-art methods for free-energy calculations, the phase diagrams of two reference models for the liquid state: the Gaussian and inverse-power-law repulsive potentials. Notwithstanding the different behavior of the two potentials for vanishing interparticle distances, their thermodynamic properties are similar in a range of densities and temperatures, being ruled by the competition between the body-centered-cubic (BCC) and face-centered-cubic (FCC) crystalline structures and the fluid phase. We confirm the existence of a reentrant BCC phase in the phase diagram of the Gaussian-core model, just above the triple point. We also trace the BCC-FCC coexistence line of the inverse-power-law model as a function of the power exponent $n$ and relate the common features in the phase diagrams of such systems to the softness degree of the interaction.Comment: 22 pages, 8 figure

Residual multiparticle entropy for a fractal fluid of hard spheres

La entropía multipartícula residual (EMPR) de un fluido se define como la diferencia, Δs, entre el exceso de entropía por partícula (en relación con un gas ideal con la misma temperatura y densidad), el sex y la contribución de la correlación de pares, s2. Así, la RMPE representa la contribución neta al sex debido a las correlaciones espaciales que implican tres, cuatro o más partículas. Un criterio heurístico de "ordenamiento" identifica la desaparición de la RMPE como una firma subyacente de una inminente transición estructural o termodinámica del sistema de una condición menos ordenada a otra más organizada espacialmente (la congelación es un ejemplo típico). Independientemente de ello, el conocimiento de la RMPE es importante para evaluar el impacto de las correlaciones multipartículas no pares en la entropía del fluido. Recientemente, una se ha propuesto una simple propuesta para las propiedades termodinámicas y estructurales de un fluido de la esfera dura en la dimensión fraccionaria 1 < d < 3 (Santos, A.; López de Haro, M. Phys. Rev. E 2016, 93, 062126). El objetivo de este trabajo es utilizar este enfoque para evaluar la EMPRESA en función tanto de d como de la fracción de empaquetamiento φ. Se observa que, para cualquier dimensionalidad d, la EMPRESA toma valores negativos para pequeñas densidades, alcanza un mínimo negativo de Δsmin en una fracción de empaquetamiento φmin, y luego aumenta rápidamente, volviéndose positiva más allá de una cierta fracción de empaquetamiento φ0. Curiosamente, mientras que tanto φmin y φ0 disminuyen monótonamente a medida que la dimensionalidad aumenta, el valor de Δs min exhibe un comportamiento no monótono, alcanzando un mínimo absoluto en una dimensionalidad fraccional d ≈ 2,38. Un gráfico de la escala RMPE Δs / │ Δs min │ muestra un comportamiento cuasi universal en la región --0,14 ≤ φ -- φ0 ≤ 0.02.The residual multiparticle entropy (RMPE) of a fluid is defined as the difference, Δs, between the excess entropy per particle (relative to an ideal gas with the same temperature and density), sex, and the pair-correlation contribution, s2. Thus, the RMPE represents the net contribution to sex due to spatial correlations involving three, four, or more particles. A heuristic “ordering” criterion identifies the vanishing of the RMPE as an underlying signature of an impending structural or thermodynamic transition of the system from a less ordered to a more spatially organized condition (freezing is a typical example). Regardless of this, the knowledge of the RMPE is important to assess the impact of non-pair multiparticle correlations on the entropy of the fluid. Recently, an accurate and simple proposal for the thermodynamic and structural properties of a hard-sphere fluid in fractional dimension 1 < d < 3 has been proposed (Santos, A.; López de Haro, M. Phys. Rev. E 2016, 93, 062126). The aim of this work is to use this approach to evaluate the RMPE as a function of both d and the packing fraction φ. It is observed that, for any given dimensionality d, the RMPE takes negative values for small densities, reaches a negative minimum Δsmin at a packing fraction φmin, and then rapidly increases, becoming positive beyond a certain packing fraction φ0. Interestingly, while both φ min and φ0 monotonically decrease as dimensionality increases, the value of Δsmin exhibits a nonmonotonic behavior, reaching an absolute minimum at a fractional dimensionality d ≈ 2.38. A plot of the scaled RMPE Δs / │ Δsmin │shows a quasiuniversal behavior in the region --0,14 ≤ φ -- φ0 ≤ 0.02.• Agencia Estatal de Investigación de España. Beca FIS2016-76359-P (I+D+i) • Junta de Extremadura. Beca GR18079 • Parcialmente financiadas por el Fondo Europeo de Desarrollo Fondos RegionalespeerReviewe

Entropy-based measure of structural order in water

We analyze the nature of the structural order established in liquid TIP4P water in the framework provided by the multi-particle correlation expansion of the statistical entropy. Different regimes are mapped onto the phase diagram of the model upon resolving the pair entropy into its translational and orientational components. These parameters are used to quantify the relative amounts of positional and angular order in a given thermodynamic state, thus allowing a structurally unbiased definition of low-density and high-density water. As a result, the structurally anomalous region within which both types of order are simultaneously disrupted by an increase of pressure at constant temperature is clearly identified through extensive molecular-dynamics simulations.Comment: 5 pages, 2 figures, to appear in Phys. Rev. E (Rapid Communication

New editorial accomplishments

We report on the awarding of the "SPARC Europe Seal for Open Access Journals" and on a licensing agreement recently entered with EBSCO Publishing