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Entropy Bounds and Dark Energy
, 2008
"... Entropy bounds render quantum corrections to the cosmological constant Λ finite. Under certain assumptions, the natural value of Λ is of order the observed dark energy density ∼ 10 −10 eV 4, thereby resolving the cosmological constant problem. We note that the dark energy equation of state in these ..."
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Entropy bounds render quantum corrections to the cosmological constant Λ finite. Under certain assumptions, the natural value of Λ is of order the observed dark energy density ∼ 10 −10 eV 4, thereby resolving the cosmological constant problem. We note that the dark energy equation of state
Entropy Bounds and String Cosmology
, 1999
"... After discussing some old (and notsoold) entropy bounds both for isolated systems and in cosmology, I will argue in favour of a “Hubble entropy bound ” holding in the latter context. I will then apply this bound to recent developments in string cosmology, show that it is naturally saturated throug ..."
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After discussing some old (and notsoold) entropy bounds both for isolated systems and in cosmology, I will argue in favour of a “Hubble entropy bound ” holding in the latter context. I will then apply this bound to recent developments in string cosmology, show that it is naturally saturated
DEFINING ENTROPY BOUNDS ∗
, 2008
"... Bekenstein’s conjectured entropy bound for a system of linear size R and energy E, S ≤ 2πER, has counterexamples for many of the ways in which the “system, ” R, E, and S may be defined. Here new ways are proposed to define these quantities for arbitrary nongravitational quantum field theories in fla ..."
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Bekenstein’s conjectured entropy bound for a system of linear size R and energy E, S ≤ 2πER, has counterexamples for many of the ways in which the “system, ” R, E, and S may be defined. Here new ways are proposed to define these quantities for arbitrary nongravitational quantum field theories
DEFINING ENTROPY BOUNDS ∗
, 2000
"... Bekenstein’s conjectured entropy bound for a system of linear size R and energy E, S ≤ 2πER, has counterexamples for many of the ways in which the “system, ” R, E, and S may be defined. Here new ways are proposed to define these quantities for arbitrary nongravitational quantum field theories in fla ..."
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Bekenstein’s conjectured entropy bound for a system of linear size R and energy E, S ≤ 2πER, has counterexamples for many of the ways in which the “system, ” R, E, and S may be defined. Here new ways are proposed to define these quantities for arbitrary nongravitational quantum field theories
Entropy bounds on Bayesian learning
, 2006
"... An observer of a process (xt) believes the process is governed by Q whereas the true law is P. We bound the expected average distance between P(xt x1,..., xt−1) and Q(xt x1,..., xt−1) for t = 1,..., n by a function of the relative entropy between the marginals of P and Q on the n first realization ..."
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An observer of a process (xt) believes the process is governed by Q whereas the true law is P. We bound the expected average distance between P(xt x1,..., xt−1) and Q(xt x1,..., xt−1) for t = 1,..., n by a function of the relative entropy between the marginals of P and Q on the n first
Abbreviated title: Entropy bounds
"... For a graph G = (V, E) and x: E → ℜ + satisfying � e∋v xe = 1 for each v ∈ V, set h(x) = � e xe log(1/xe) (with log = log 2). We show that for any nvertex G, random (not necessarily uniform) perfect matching f satisfying a mild technical condition, and xe = Pr(e ∈ f), H(f) < h(x) − n log e + o ..."
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+ o(n) 2 (where H is binary entropy). This implies a similar bound for random Hamiltonian cycles. Specializing these bounds completes a proof, begun in [5], of a quite precise determination of the numbers of perfect matchings and Hamiltonian cycles in Dirac graphs (graphs with minimum degree at least
Results 1  10
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2,660