82 research outputs found
Resource theories of knowledge
How far can we take the resource theoretic approach to explore physics?
Resource theories like LOCC, reference frames and quantum thermodynamics have
proven a powerful tool to study how agents who are subject to certain
constraints can act on physical systems. This approach has advanced our
understanding of fundamental physical principles, such as the second law of
thermodynamics, and provided operational measures to quantify resources such as
entanglement or information content. In this work, we significantly extend the
approach and range of applicability of resource theories. Firstly we generalize
the notion of resource theories to include any description or knowledge that
agents may have of a physical state, beyond the density operator formalism. We
show how to relate theories that differ in the language used to describe
resources, like micro and macroscopic thermodynamics. Finally, we take a
top-down approach to locality, in which a subsystem structure is derived from a
global theory rather than assumed. The extended framework introduced here
enables us to formalize new tasks in the language of resource theories, ranging
from tomography, cryptography, thermodynamics and foundational questions, both
within and beyond quantum theory.Comment: 28 pages featuring figures, examples, map and neatly boxed theorems,
plus appendi
Smarandache Near-rings
Generally, in any human field, a Smarandache Structure on a set A means a
weak structure W on A such that there exists a proper subset B contained in A
which is embedded with a stronger structure S.
These types of structures occur in our everyday's life, that's why we study
them in this book.
Thus, as a particular case:
A Near-ring is a non-empty set N together with two binary operations '+' and
'.' such that (N, +) is a group (not necessarily abelian), (N, .) is a
semigroup. For all a, b, c belonging to N we have (a + b) . c = a . c + b . c
A Near-field is a non-empty set P together with two binary operations '+' and
'.' such that (P, +) is a group (not-necessarily abelian), {P\{0}, .) is a
group. For all a, b, c belonging to P we have (a + b) . c = a . c + b . c
A Smarandache Near-ring is a near-ring N which has a proper subset P
contained in N, where P is a near-field (with respect to the same binary
operations on N).Comment: 200 pages, 50 tables, 20 figure
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