Nonextensive thermodynamic functions in the Schrödinger-Gibbs ensemble.

Schrödinger suggested that thermodynamical functions cannot be based on the gratuitous allegation that quantum-mechanical levels (typically the orthogonal eigenstates of the Hamiltonian operator) are the only allowed states for a quantum system [E. Schrödinger, Statistical Thermodynamics (Courier Dover, Mineola, 1967)]. Different authors have interpreted this statement by introducing density distributions on the space of quantum pure states with weights obtained as functions of the expectation value of the Hamiltonian of the system. In this work we focus on one of the best known of these distributions and prove that, when considered in composite quantum systems, it defines partition functions that do not factorize as products of partition functions of the noninteracting subsystems, even in the thermodynamical regime. This implies that it is not possible to define extensive thermodynamical magnitudes such as the free energy, the internal energy, or the thermodynamic entropy by using these models. Therefore, we conclude that this distribution inspired by Schrödinger's idea cannot be used to construct an appropriate quantum equilibrium thermodynamics.

Ehrenfest dynamics is purity non-preserving: a necessary ingredient for decoherence.

We discuss the evolution of purity in mixed quantum/classical approaches to electronic nonadiabatic dynamics in the context of the Ehrenfest model. As it is impossible to exactly determine initial conditions for a realistic system, we choose to work in the statistical Ehrenfest formalism that we introduced in Alonso et al. [J. Phys. A: Math. Theor. 44, 396004 (2011)]. From it, we develop a new framework to determine exactly the change in the purity of the quantum subsystem along with the evolution of a statistical Ehrenfest system. In a simple case, we verify how and to which extent Ehrenfest statistical dynamics makes a system with more than one classical trajectory, and an initial quantum pure state become a quantum mixed one. We prove this numerically showing how the evolution of purity depends on time, on the dimension of the quantum state space D, and on the number of classical trajectories N of the initial distribution. The results in this work open new perspectives for studying decoherence with Ehrenfest dynamics.

Efficient formalism for large-scale ab initio molecular dynamics based on time-dependent density functional theory.

A new "on the fly" method to perform Born-Oppenheimer ab initio molecular dynamics (AIMD) simulations is presented. Inspired by Ehrenfest dynamics in time-dependent density functional theory, the electronic orbitals are evolved by a Schrödinger-like equation, where the orbital time derivative is multiplied by a parameter. This parameter controls the time scale of the fictitious electronic motion and speeds up the calculations with respect to standard Ehrenfest dynamics. In contrast with other methods, wave function orthogonality needs not be imposed as it is automatically preserved, which is of paramount relevance for large-scale AIMD simulations.

Classification of amino acids induced by their associated matrices.

In this paper we carry out an analysis of different types of potential and substitution matrices for amino acids, oriented to give a classification of the latter. The cluster decomposition is obtained, in a fully unsupervised way, from the subdominant ultrametric associated to the distance between amino acids induced by the corresponding matrix. In the comparative study, by looking at the classifications obtained from diverse matrices, we can get information on how they account for the different chemical-physical properties of the amino acids.

A general clustering approach with application to the Miyazawa-Jernigan potentials for amino acids.

In this article, we address the problem of classification of amino acids. Starting from the Miyazawa-Jernigan matrix obtained from the relative positions of amino acids in the crystal structure of globular proteins, we develop a fully unsupervised method of classification for the amino acids. The method is based in the subdominant ultrametric associated to the distance induced by the Miyazawa-Jernigan matrix and the maximum likelihood principle to determine the cluster structure. We obtain a classification consistent with the five groups used in the literature, although with some peculiarities. We also show the stability of our results against changes of the method used to classify the amino acids. Proteins 2004.