5,657 research outputs found
Entropy? Honest!
Here we deconstruct, and then in a reasoned way reconstruct, the concept of
"entropy of a system," paying particular attention to where the randomness may
be coming from. We start with the core concept of entropy as a COUNT associated
with a DESCRIPTION; this count (traditionally expressed in logarithmic form for
a number of good reasons) is in essence the number of possibilities---specific
instances or "scenarios," that MATCH that description. Very natural (and
virtually inescapable) generalizations of the idea of description are the
probability distribution and of its quantum mechanical counterpart, the density
operator.
We track the process of dynamically updating entropy as a system evolves.
Three factors may cause entropy to change: (1) the system's INTERNAL DYNAMICS;
(2) unsolicited EXTERNAL INFLUENCES on it; and (3) the approximations one has
to make when one tries to predict the system's future state. The latter task is
usually hampered by hard-to-quantify aspects of the original description,
limited data storage and processing resource, and possibly algorithmic
inadequacy. Factors 2 and 3 introduce randomness into one's predictions and
accordingly degrade them. When forecasting, as long as the entropy bookkeping
is conducted in an HONEST fashion, this degradation will ALWAYS lead to an
entropy increase.
To clarify the above point we introduce the notion of HONEST ENTROPY, which
coalesces much of what is of course already done, often tacitly, in responsible
entropy-bookkeping practice. This notion, we believe, will help to fill an
expressivity gap in scientific discourse. With its help we shall prove that ANY
dynamical system---not just our physical universe---strictly obeys Clausius's
original formulation of the second law of thermodynamics IF AND ONLY IF it is
invertible. Thus this law is a TAUTOLOGICAL PROPERTY of invertible systems!Comment: 27 pages, 11 figures. Published in the journal "Entropy" in June
2016. Abstracts from referee's reports quoted right after the abstrac
Statistical Physics of the Glass Phase
This paper gives an introduction to some of the statistical physics problems
which appear in the study of structural glasses. It is a shortened and updated
version of a more detailed review paper which has appeared in cond-mat/0005173.Comment: 10 pages, 4 figures, Proceedings of Statphys 2
The Dynamic Phase Transition for Decoding Algorithms
The state-of-the-art error correcting codes are based on large random
constructions (random graphs, random permutations, ...) and are decoded by
linear-time iterative algorithms. Because of these features, they are
remarkable examples of diluted mean-field spin glasses, both from the static
and from the dynamic points of view. We analyze the behavior of decoding
algorithms using the mapping onto statistical-physics models. This allows to
understand the intrinsic (i.e. algorithm independent) features of this
behavior.Comment: 40 pages, 29 eps figure
Tight bounds for LDPC and LDGM codes under MAP decoding
A new method for analyzing low density parity check (LDPC) codes and low
density generator matrix (LDGM) codes under bit maximum a posteriori
probability (MAP) decoding is introduced. The method is based on a rigorous
approach to spin glasses developed by Francesco Guerra. It allows to construct
lower bounds on the entropy of the transmitted message conditional to the
received one. Based on heuristic statistical mechanics calculations, we
conjecture such bounds to be tight. The result holds for standard irregular
ensembles when used over binary input output symmetric channels. The method is
first developed for Tanner graph ensembles with Poisson left degree
distribution. It is then generalized to `multi-Poisson' graphs, and, by a
completion procedure, to arbitrary degree distribution.Comment: 28 pages, 9 eps figures; Second version contains a generalization of
the previous resul
SciTech News Volume 71, No. 3 (2017)
Columns and Reports
From the Editor.........................3
Division News
Science-Technology Division....5
Chemistry Division....................8
Conference Report, Marion E, Sparks Professional Development Award Recipient..9
Engineering Division................10
Engineering Division Award, Winners Reflect on their Conference Experience..15
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of the Engineering Division .....18
Architecture, Building Engineering, Construction, and Design Section of the Engineering Division................20
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