Landauer’s Principle of Minimum Energy Might Place Limits on the Detectability of Gravitons of Certain Mass

According to Landauer’s principle, the energy of a particle may be used to record or erase N number of information bits within the thermal bath. The maximum number of information N recorded by the particle in the heat bath is found to be inversely proportional to its temperature T. If at least one bit of information is transferred from the particle to the medium, then the particle might exchange information with the medium. Therefore for at least one bit of information, the limiting mass that can carry or transform information assuming a temperature T= 2.73 K is equal to m = 4.718´10-40 kg which is many orders of magnitude smaller that the masse of most of today’s elementary particles. Next, using the corresponding temperature of a graviton relic and assuming at least one bit of information the corresponding graviton mass is calculated and from that, a relation for the number of information N carried by a graviton as a function of the graviton mass mgr is derived. Furthermore, the range of information number contained in a graviton is also calculated for the given range of graviton mass as given by Nieto and Goldhaber, from which we find that the range of the graviton is inversely proportional to the information number N. Finally, treating the gravitons as harmonic oscillators in an enclosure of size R we derive the range of a graviton as a function of the cosmological parameters in the present era.

On the derivation of a nonlinear generalized Langevin equation

We recast the Zwanzig's derivation of a non linear generalized Langevin equation (GLE) for a heavy particle interacting with a heat bath in a more general framework showing that it is necessary to readjust the Zwanzig's definitions of the kernel matrix and noise vector in the GLE in order to be able performing consistently the continuum limit. As shown by Zwanzig, the non linear feature of the resulting GLE is due to the non linear dependence of the equilibrium map by the heavy particle variables. Such an equilibrium map represents the global equilibrium configuration of the heat bath particles for a fixed (instantaneous) configuration of the system. Following the same derivation of the GLE, we show that a deeper investigation of the equilibrium map, considered in the Zwanzig's Hamiltonian, is necessary. Moreover, we discuss how to get an equilibrium map given a general interaction potential. Finally, we provide a renormalization procedure which allows to divide the dependence of the equilibrium map by coupling coefficient from the dependence by the system variables yielding a more rigorous mathematical structure of the non linear GLE.

Battery Charging in Collision Models with Bayesian Risk Strategies

We constructed a collision model where measurements in the system, together with a Bayesian decision rule, are used to classify the incoming ancillas as having either high or low ergotropy (maximum extractable work). The former are allowed to leave, while the latter are redirected for further processing, aimed at increasing their ergotropy further. The ancillas play the role of a quantum battery, and the collision model, therefore, implements a Maxwell demon. To make the process autonomous and with a well-defined limit cycle, the information collected by the demon is reset after each collision by means of a cold heat bath.

Block Factorization of the Relative Entropy via Spatial Mixing

We consider spin systems in the d-dimensional lattice $${\mathbb Z} ^d$$ Z d satisfying the so-called strong spatial mixing condition. We show that the relative entropy functional of the corresponding Gibbs measure satisfies a family of inequalities which control the entropy on a given region $$V\subset {\mathbb Z} ^d$$ V ⊂ Z d in terms of a weighted sum of the entropies on blocks $$A\subset V$$ A ⊂ V when each A is given an arbitrary nonnegative weight $$\alpha _A$$ α A . These inequalities generalize the well known logarithmic Sobolev inequality for the Glauber dynamics. Moreover, they provide a natural extension of the classical Shearer inequality satisfied by the Shannon entropy. Finally, they imply a family of modified logarithmic Sobolev inequalities which give quantitative control on the convergence to equilibrium of arbitrary weighted block dynamics of heat bath type.

Entanglement entropy of asymptotically flat non-extremal and extremal black holes with an island

The island rule for the entanglement entropy is applied to an eternal Reissner–Nordström black hole. The key ingredient is that the black hole is assumed to be in thermal equilibrium with a heat bath of an arbitrary temperature and so the generalized entropy is treated as being off-shell. Taking the on-shell condition to the off-shell generalized entropy, we find the generalized entropy and then obtain the entanglement entropy following the island rule. For the non-extremal black hole, the entanglement entropy grows linearly in time and can be saturated after the Page time as expected. The entanglement entropy also has a well-defined Schwarzschild limit. In the extremal black hole, the island prescription provides a logarithmically growing entanglement entropy in time and a constant entanglement entropy after the Page time. In the extremal black hole, the boundary of the island hits the curvature singularity where the semi-classical approximations appear invalid. To avoid encountering the curvature singularity, we apply this procedure to the Hayward black hole regular at the origin. Consequently, the presence of the island in extremal black holes can provide a finite entanglement entropy, which might imply non-trivial vacuum configurations of extremal black holes.

Stochastic Generalized Active Space Self-Consistent Field: Theory and Application

An algorithm to perform stochastic generalized active space calculations, Stochastic-GAS, is presented, that uses the Slater determinant based FCIQMC algorithm as configuration interaction eigensolver. Stochastic-GAS allows the construction and stochastic optimization of preselected truncated configuration interaction wave functions, either to reduce the computational costs of large active space wave function optimizations, or to probe the role of specific electron correlation pathways. As for the conventional GAS procedure, the preselection of the truncated wave function is based on the selection of multiple active subspaces while imposing restrictions on the interspace excitations. Both local and cumulative minimum and maximum occupation number constraints are supported by Stochastic-GAS. The occupation number constraints are efficiently encoded in precomputed probability distributions, using the precomputed heat bath algorithm, which removes nearly all runtime overheads of GAS. This strategy effectively allows the FCIQMC dynamics to a priori exclude electronic configurations that are not allowed by GAS restrictions. Stochastic-GAS reduced density matrices are stochastically sampled, allowing orbital relaxations via Stochastic-GASSCF, and direct evaluation of properties that can be extracted from density matrices, such as the spin expectation value. Three test case applications have been chosen to demonstrate the flexibility of Stochastic-GAS: (a) the Stochastic-GASSCF optimization of a stack of five benzene molecules, that shows the applicability of Stochastic-GAS towards fragment-based chemical systems; (b) an uncontracted stochastic MRCISD calculation that correlates 96 electrons and 159 molecular orbitals, and uses a large (32, 34) active space reference wave function for an Fe(II)-porphyrin model system, showing how GAS can be applied to systematically recover dynamic electron correlation, and how in the specific case of the Fe(II)-porphyrin dynamic correlation further differentially stabilizes the triplet over the quintet spin state; (c) the study of an Fe4S4 cluster's spin-ladder energetics via highly truncated stochastic-GAS wave functions, where we show how GAS can be applied to understand the competing spin-exchange and charge-transfer correlating mechanisms in stabilizing different spin-states.