4,290 research outputs found
A Pedagogical Intrinsic Approach to Relative Entropies as Potential Functions of Quantum Metrics: the - Family
The so-called -z-\textit{R\'enyi Relative Entropies} provide a huge
two-parameter family of relative entropies which includes almost all well-known
examples of quantum relative entropies for suitable values of the parameters.
In this paper we consider a log-regularized version of this family and use it
as a family of potential functions to generate covariant symmetric
tensors on the space of invertible quantum states in finite dimensions. The
geometric formalism developed here allows us to obtain the explicit expressions
of such tensor fields in terms of a basis of globally defined differential
forms on a suitable unfolding space without the need to introduce a specific
set of coordinates. To make the reader acquainted with the intrinsic formalism
introduced, we first perform the computation for the qubit case, and then, we
extend the computation of the metric-like tensors to a generic -level
system. By suitably varying the parameters and , we are able to recover
well-known examples of quantum metric tensors that, in our treatment, appear
written in terms of globally defined geometrical objects that do not depend on
the coordinates system used. In particular, we obtain a coordinate-free
expression for the von Neumann-Umegaki metric, for the Bures metric and for the
Wigner-Yanase metric in the arbitrary -level case.Comment: 50 pages, 1 figur
Bayesian estimates of free energies from nonequilibrium work data in the presence of instrument noise
The Jarzynski equality and the fluctuation theorem relate equilibrium free
energy differences to non-equilibrium measurements of the work. These relations
extend to single-molecule experiments that have probed the finite-time
thermodynamics of proteins and nucleic acids. The effects of experimental error
and instrument noise have not previously been considered. Here, we present a
Bayesian formalism for estimating free-energy changes from non-equilibrium work
measurements that compensates for instrument noise and combines data from
multiple driving protocols. We reanalyze a recent set of experiments in which a
single RNA hairpin is unfolded and refolded using optical tweezers at three
different rates. Interestingly, the fastest and farthest-from-equilibrium
measurements contain the least instrumental noise, and therefore provide a more
accurate estimate of the free energies than a few slow, more noisy,
near-equilibrium measurements. The methods we propose here will extend the
scope of single-molecule experiments; they can be used in the analysis of data
from measurements with AFM, optical, and magnetic tweezers.Comment: 8 page
Homogenization of degenerate cross-diffusion systems
Two-scale homogenization limits of parabolic cross-diffusion systems in a
heterogeneous medium with no-flux boundary conditions are proved. The
heterogeneity of the medium is reflected in the diffusion coefficients or by
the perforated domain. The diffusion matrix is of degenerate type and may be
neither symmetric nor positive semi-definite, but the diffusion system is
assumed to satisfy an entropy structure. Uniform estimates are derived from the
entropy production inequality. New estimates on the equicontinuity with respect
to the time variable ensure the strong convergence of a sequence of solutions
to the microscopic problems defined in perforated domains
Self-attracting self-avoiding walk
This article is concerned with self-avoiding walks (SAW) on
that are subject to a self-attraction. The attraction, which rewards instances
of adjacent parallel edges, introduces difficulties that are not present in
ordinary SAW. Ueltschi has shown how to overcome these difficulties for
sufficiently regular infinite-range step distributions and weak
self-attractions. This article considers the case of bounded step
distributions. For weak self-attractions we show that the connective constant
exists, and, in , carry out a lace expansion analysis to prove the
mean-field behaviour of the critical two-point function, hereby addressing a
problem posed by den Hollander
The Nonequilibrium Thermodynamics of Small Systems
The interactions of tiny objects with their environment are dominated by
thermal fluctuations. Guided by theory and assisted by micromanipulation tools,
scientists have begun to study such interactions in detail.Comment: PDF file, 13 pages. Long version of the paper published in Physics
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