Entanglement entropy between real and virtual particles in ϕ4\phi ^{4} quantum field theory

The aim of this work is to compute the entanglement entropy of real and virtual particles by rewriting the generating functional of $\phi ^{4}$ theory as a mean value between states and observables defined through the correlation functions. Then the von Neumann definition of entropy can be applied to these quantum states and in particular, for the partial traces taken over the internal or external degrees of freedom. This procedure can be done for each order in the perturbation expansion showing that the entanglement entropy for real and virtual particles behaves as $\ln (m_{0})$. In particular, entanglement entropy is computed at first order for the correlation function of two external points showing that mutual information is identical to the external entropy and that conditional entropies are negative for all the domain of $m_{0}$. In turn, from the definition of the quantum states, it is possible to obtain general relations between total traces between different quantum states of a r theory. Finally, discussion about the possibility of taking partial traces over external degrees of freedom is considered, which implies the introduction of some observables that measure space-time points where interaction occurs.Comment: 4 figure

Five approaches to exact open-system dynamics: Complete positivity, divisibility and time-dependent observables

To extend the classical concept of Markovianity to an open quantum system, different notions of the divisibility of its dynamics have been introduced. Here we analyze this issue by five complementary approaches: equations of motion, real-time diagrammatics, Kraus-operator sums, as well as time-local (TCL) and nonlocal (Nakajima-Zwanzig) quantum master equations. As a case study featuring several types of divisible dynamics, we examine in detail an exactly solvable noninteracting fermionic resonant level coupled arbitrarily strongly to a fermionic bath at arbitrary temperature in the wideband limit. In particular, the impact of divisibility on the time-dependence of the observable level occupation is investigated and compared with typical Markovian approximations. We find that the loss of semigroup-divisibility is accompanied by a prominent reentrant behavior: Counter to intuition, the level occupation may temporarily \emph{increase} significantly in order to reach a stationary state with \emph{smaller} occupation, implying a reversal of the measurable transport current. In contrast, the loss of the so-called completely-positive divisibility is more subtly signaled by the \emph{prohibition} of such current reversals in specific time-intervals. Experimentally, it can be detected in the family of transient currents obtained by varying the initial occupation. To quantify the nonzero footprint left by the system in its effective environment, we determine the exact time-dependent state of the latter as well as related information measures such as entropy, exchange entropy and coherent information.Comment: Submitted to The Journal of Chemical Physics, 19 pages + 14 pages of appendices with 13 figures. Significantly extended introduction and discussion, no results change

Statistical and entanglement entropy for black holes in quantum geometry

We analyze the relationship between entanglement (or geometric) entropy with statistical mechanical entropy of horizon degrees of freedom when described in the framework of isolated horizons in loop quantum gravity. We show that, once the relevant degrees of freedom are identified, the two notions coincide. The key ingredient linking the two notions is the structure of quantum geometry at Planck scale implied by loop quantum gravity, where correlations between the inside and outside of the black hole are mediated by eigenstates of the horizon area operator.Comment: References adde

Why Do We Believe in the Second Law?

Claims of exceptions to the second law of thermodynamics are generally met with extreme skepticism that is quite reasonable given the great confidence placed in the second law. But what specifically is the basis for that confidence? The perspective from which we approach experimental or theoretical results that call into question the absolute status of the second law depends greatly on our understanding of why it must be true. For example, a belief that there are solid theoretical arguments demonstrating that the second law must be true leads to a very different perspective than a belief that the law is simply a generalization of empirical observations. This paper will briefly survey and examine some of the basic arguments on which our confidence in the second law might be based, to help provide a well-informed perspective for evaluating the various claims presented at this conference.Comment: 6 pages, to appear in Proc. of "First International Conference on Quantum Limits to the Second Law," July 2002, editor D.P. Sheeha

Information measures and classicality in quantum mechanics

We study information measures in quantu mechanics, with particular emphasis on providing a quantification of the notions of classicality and predictability. Our primary tool is the Shannon - Wehrl entropy I. We give a precise criterion for phase space classicality and argue that in view of this a) I provides a measure of the degree of deviation from classicality for closed system b) I - S (S the von Neumann entropy) plays the same role in open systems We examine particular examples in non-relativistic quantum mechanics. Finally, (this being one of our main motivations) we comment on field classicalisation on early universe cosmology.Comment: 35 pages, LATE