Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Revising and Extending the Linear Response Theory for Statistical
  Mechanical Systems: Evaluating Observables as Predictors and Predictands   Linear response theory has developed into a formidable set of tools for
studying the forced behaviour of a large variety of systems - including out of
equilibrium ones. In this paper we provide a new angle on the problem, by
studying under which conditions it is possible to perform predictions on the
response of a given observable of a system to perturbations, using one or more
other observables of the same system as predictors, and thus bypassing the need
to know all the details of the acting forcing. Thus, we break the rigid
separation between forcing and response, which is key in linear response
theory, and revisit the concept of causality. As a result, the surrogate Green
functions one constructs for predicting the response of the observable of
interest may have support that is not necessarily limited to the nonnegative
time axis. This implies that not all observables are equally good as
predictands when a given forcing is applied, as result of the properties of
their corresponding susceptibility. In particular, problems emerge from the
presence of complex zeros. We derive general explicit formulas that, in absence
of such pathologies, allow one to reconstruct the response of an observable of
interest to N independent forcings by using as predictors N other observables.
We provide a thorough test of the theory and of the possible pathologies by
using numerical simulations of the paradigmatic Lorenz '96 model. Our results
are potentially relevant for problems like the reconstruction of data from
proxy signals, like in the case of paleoclimate, and, in general, the analysis
of signals and feedbacks in complex systems where our knowledge on the system
is limited, as in neurosciences. Our technique might also be useful for
reconstructing the response to forcings of a spatially extended system in a
given location by looking at the response in a separate location.

6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph