A general framework for straightforward model construction of multi-component thermodynamic equilibrium systems

Mathematical modelling of molecular systems helps elucidating complex phenomena in (bio)chemistry. However, equilibrium conditions in systems consisting of more than two components can typically not be analytically determined without assumptions and resulting (semi-)numerical models are not trivial to derive by the non-expert. Here we present a framework for equilibrium models that utilizes a general derivation method capable of generating custom models for complex molecular systems, based on the simple, reversible reactions describing these systems. Several molecular systems are revisited via the framework and demonstrate the simplicity, the generality and validity of the approach. The ease of use of the framework and the ability to both analyze systems and gain additional insights in the underlying parameters strongly aids the analysis and understanding of molecular equilibrium systems. This conceptual framework severely reduces the time and expertise requirements which currently impede the broad integration of these highly valuable models into chemical research.

Proof Formalism General Quantum Density Commutator Matrix Physics

Formalism proofing general derivation, applying matrix properties operations, showing fundamental relationships with inner product to outer product has been advanced here. This general proof formalism has direct application with physics to quantify quantum density at micro scale level to time commutator at macro scale level. System of operator algebraic equations have been rigorously derived to obtain analytic solutions which are physically acceptable. Extended physics application will include metricizing towards unitarization to achieve gaging Hamiltonian mechanics to electromagnetic gravitational strong theory, towards grand unifying physics atomistic to astrophysics or vice versa via quantum relativistic general physics thereby patching to classical physics fields energy.

Proof Formalism General Quantum Density Commutator Matrix Physics

Formalism proofing general derivation, applying matrix properties operations, showing fundamental relationships with inner product to outer product has been advanced here. This general proof formalism has direct application with physics to quantify quantum density at micro scale level to time commutator at macro scale level. System of operator algebraic equations has been rigorously derived to obtain analytic solutions which are physically acceptable. Extended physics application will include metricizing towards unitarization to achieve gaging Hamiltonian mechanics to electromagnetic gravitational strong theory, towards grand unifying physics atomistic to astrophysics or vice versa via quantum relativistic general physics thereby patching to classical physics fields energy.

Entangled N-photon states for fair and optimal social decision making

Situations involving competition for resources among entities can be modeled by the competitive multi-armed bandit (CMAB) problem, which relates to social issues such as maximizing the total outcome and achieving the fairest resource repartition among individuals. In these respects, the intrinsic randomness and global properties of quantum states provide ideal tools for obtaining optimal solutions to this problem. Based on the previous study of the CMAB problem in the two-arm, two-player case, this paper presents the theoretical principles necessary to find polarization-entangled N-photon states that can optimize the total resource output while ensuring equality among players. These principles were applied to two-, three-, four-, and five-player cases by using numerical simulations to reproduce realistic configurations and find the best strategies to overcome potential misalignment between the polarization measurement systems of the players. Although a general formula for the N-player case is not presented here, general derivation rules and a verification algorithm are proposed. This report demonstrates the potential usability of quantum states in collective decision making with limited, probabilistic resources, which could serve as a first step toward quantum-based resource allocation systems.

The translation between the required return on unlevered and levered equity for explicit cash flows and fixed debt financing

PurposeThe primary purpose of this paper is to develop the translation formula between the required return on unlevered and levered equity for the specific case where cash flows have a finite lifetime and the flow to debt is prespecified. The secondary purpose of this paper is to underpin the importance of the type of stochasticity of cash flows for translation formulas. A general derivation of such formulas and the discount rate in the free cash flow approach is shown.Design/methodology/approachThe paper starts with the same assumptions that have been applied by Modigliani and Miller (1963), Miles and Ezzell (1980) and other researchers. Then the paper develops the mathematical foundations to apply a deterministic backward-iterative scheme for valuing cash flows. After stating the valuation formulas for levered and unlevered equity, debt and tax shields, the authors mathematically derive the relationship between the unlevered return and levered return on equity.FindingsConventional translation formulas apply to very special cases. They can generally not be used for projects with nonconstant leverage and a finite lifetime. In general, translation formulas depend on continuing values, cash flows, leverage, taxation, risk-free rate, etc. In this paper, the translation depends on the structure of the debt in addition to the well-known parameters in conventional formulas. This paper formula contains the Modigliani-Miller translation formula as a special case.Originality/valueThe authors develop a novel formula for the translation of the required return on unlevered to levered equity. With this formula, the authors offer a solution for the consistent valuation of cash flows with a limited lifetime and given debt financing.

Hawking radiation in optics and beyond

Hawking radiation was originally proposed in astrophysics, but it has been generalized and extended to other physical systems receiving the name of analogue Hawking radiation. In the last two decades, several attempts have been made to measure it in a laboratory, and one of the most successful systems is in optics. Light interacting in a dielectric material causes an analogue Hawking effect, in fact, its stimulated version has already been detected and the search for the spontaneous signal is currently ongoing. We briefly review the general derivation of Hawking radiation, then we focus on the optical analogue and present some novel numerical results. Finally, we call for a generalization of the term Hawking radiation. This article is part of a discussion meeting issue ‘The next generation of analogue gravity experiments’.

Orbital Energies and Nuclear Forces in DFT: Interpretation and Validation

The bonding and antibonding character of individual Molecular Orbitals has been previously shown to be related to their orbital energy derivatives with respect to nuclear coordinates, known as Dynamical Orbital Forces. Albeit usually derived from Koopmans' theorem, in this work we show a more general derivation from conceptual DFT, which justifies application in a broader context. The consistency of the approach is validated numerically for valence orbitals in Kohn-Sham DFT. Then, we illustrate its usefulness by showcasing applications in aromatic and antiaromatic systems and in excited state chemistry. Overall, Dynamical Orbital Forces can be used to interpret the results of routine ab initio calculations, be it wavefunction or density based, in terms of forces and occupations.

Orbital Energies and Nuclear Forces in DFT: Interpretation and Validation

The bonding and antibonding character of individual Molecular Orbitals has been previously shown to be related to their orbital energy derivatives with respect to nuclear coordinates, known as Dynamical Orbital Forces. Albeit usually derived from Koopmans' theorem, in this work we show a more general derivation from conceptual DFT, which justifies application in a broader context. The consistency of the approach is validated numerically for valence orbitals in Kohn-Sham DFT. Then, we illustrate its usefulness by showcasing applications in aromatic and antiaromatic systems and in excited state chemistry. Overall, Dynamical Orbital Forces can be used to interpret the results of routine ab initio calculations, be it wavefunction or density based, in terms of forces and occupations.