Physical Constraints on Global Social-Ecological Energy System

Energy is the main driver of human Social-Ecological System (SES) dynamics. Collective energy properties of human SES can be described applying the principles of statistical mechanics: (i) energy consumption repartition; (ii) efficiency; (iii) performance, as efficient power, in relation to the least-action principle. International Energy Agency data are analyzed through the lens of such principles. Declining physical efficiency and growth of power losses emerge from our analysis. Losses mainly depend on intermediate system outputs and non-energy final output. Energy performance at Country level also depends on efficient power consumption. Better and worse performing Countries are identified accordingly. Five policy-relevant areas are identified in relation to the physical principles introduced in this paper: Improve efficiency; Decouple economic growth from environmental degradation; Focus on high value added and labor-intensive sectors; Rationalize inefficient fossil fuel subsidies that encourage wasteful consumption; Upgrade the technological capabilities. Coherently with our findings, policies should support the following actions: (1) redefine sectoral energy distribution shares; (2) Improve Country-level performance, if needed; (3) Reduce intermediate outputs and non-energy final output; (4) Reduce resources supply to improve eco-efficiency together with system performance.

Effective action of string theory at order $$\alpha '$$ in the presence of boundary

Recently, using the assumption that the string theory effective action at the critical dimension is background independent, the classical on-shell effective action of the bosonic string theory at order $$\alpha '$$ α ′ in a spacetime manifold without boundary has been reproduced, up to an overall parameter, by imposing the O(1, 1) symmetry when the background has a circle. In the presence of the boundary, we consider a background which has boundary and a circle such that the unit normal vector of the boundary is independent of the circle. Then the O(1, 1) symmetry can fix the bulk action without using the lowest order equation of motion. Moreover, the above constraints and the constraint from the principle of the least action in the presence of boundary can fix the boundary action, up to five boundary parameters. In the least action principle, we assume that not only the values of the massless fields but also the values of their first derivatives are arbitrary on the boundary. We have also observed that the cosmological reduction of the leading order action in the presence of the Hawking–Gibbons boundary term, produces zero cosmological boundary action. Imposing this as another constraint on the boundary couplings at order $$\alpha '$$ α ′ , we find the boundary action up to two parameters. For a specific value for these two parameters, the gravity couplings in the boundary become the Chern–Simons gravity plus another term which has the Laplacian of the extrinsic curvature.

An Action Principle for Biological Systems

In the analysis of physical systems, the forces and mechanics of all system changes as codified in the Newtonian laws can be redefined by the methods of Lagrange and Hamilton through an identification of the governing action principle as a more general framework for dynamics. For the living system, it is the dimensional and relational structure of its biologic continuum (both internal and external to the organism) that creates the signature informational metrics and course configurations for the action dynamics associated with any natural systems phenomena. From this dynamic information theoretic framework, an action functional can be also derived in accordance with the methods of Lagrange. The experiential process of acquiring information and translating it into actionable meaning for adaptive responses is the driving force for changes in the living system. The core axiomatic procedure of this adaptive process should include an innate action principle that can determine the system’s directional changes. This procedure for adaptive system reconciliation of divergences from steady state within the biocontinuum can be described by an information metric formulation of the process for actionable knowledge acquisition that incorporates the axiomatic inference of the Kullback’s Principle of Minimum Discrimination Information powered by the mechanics of survival replicator dynamics. This entropic driven trajectory naturally minimizes the biocontinuum information gradient differences like a least action principle and is an inference procedure for directional change. If the mathematical expression of this process is the Lagrangian integrand for adaptive changes within the biocontinuum, then it is also considered as an action functional for the living system.

Null shells and double layers in quadratic gravity

For a singular hypersurface of arbitrary type in quadratic gravity motion equations were obtained using only the least action principle. It turned out that the coefficients in the motion equations are zeroed with a combination corresponding to the Gauss-Bonnet term. Therefore it does not create neither double layers nor thin shells. It has been demonstrated that there is no “external pressure” for any type of null singular hypersurface. It turned out that null spherically symmetric singular hupersurfaces in quadratic gravity cannot be a double layer, and only thin shells are possible. The system of motion equations in this case is reduced to one which is expressed through the invariants of spherical geometry along with the Lichnerowicz conditions. Spherically symmetric null thin shells were investigated for spherically symmetric solutions of conformal gravity as applications, in particular, for various vacua and Vaidya-type solutions.

Causality in Discrete Time Physics Derived from Maupertuis Reduced Action Principle

Causality describes the process and consequences from an action: a cause has an effect. Causality is preserved in classical physics as well as in special and general theories of relativity. Surprisingly, causality as a relationship between the cause and its effect is in neither of these theories considered a law or a principle. Its existence in physics has even been challenged by prominent opponents in part due to the time symmetric nature of the physical laws. With the use of the reduced action and the least action principle of Maupertuis along with a discrete dynamical time physics yielding an arrow of time, causality is defined as the partial spatial derivative of the reduced action and as such is position- and momentum-dependent and requests the presence of space. With this definition the system evolves from one step to the next without the need of time, while (discrete) time can be reconstructed.

Time-dependent variational dynamics for nonadiabatically coupled nuclear and electronic quantum wavepackets in molecules

We propose a methodology to unify electronic and nuclear quantum wavepacket dynamics in molecular processes including nonadiabatic chemical reactions. The canonical and traditional approach in the full quantum treatment both for electrons and nuclei rests on the Born–Oppenheimer fixed nuclei strategy, the total wavefunction of which is described in terms of the Born–Huang expansion. This approach is already realized numerically but only for small molecules with several number of coupled electronic states for extremely hard technical reasons. Besides, the stationary-state view of the relevant electronic states based on the Born–Oppenheimer approximation is not always realistic in tracking real-time electron dynamics in attosecond scale. We therefore incorporate nuclear wavepacket dynamics into the scheme of nonadiabatic electron wavepacket theory, which we have been studying for a long time. In this scheme thus far, electron wavepackets are quantum mechanically propagated in time along nuclear paths that can naturally bifurcate due to nonadiabatic interactions. The nuclear paths are in turn generated simultaneously by the so-called matrix force given by the electronic states involved, the off-diagonal elements of which represent the force arising from nonadiabatic interactions. Here we advance so that the nuclear wavepackets are directly taken into account in place of path (trajectory) approximation. The nuclear wavefunctions are represented in terms of the Cartesian Gaussians multiplied by plane waves, which allows for feasible calculations of atomic and molecular integrals together with the electronic counterparts in a unified manner. The Schrödinger dynamics of the simultaneous electronic and nuclear wavepackets are to be integrated by means of the dual least action principle of quantum mechanics [K. Takatsuka, J. Phys. Commun. 4, 035007 (2020)], which is a time-dependent variational principle. Great contributions of Vincent McKoy in the electron dynamics in the fixed nuclei approximation and development in time-resolved photoelectron spectroscopy are briefly outlined as a guide to the present work.

The Concept of Symmetry and the Theory of Perception

Perceptual constancy refers to the fact that the perceived geometrical and physical characteristics of objects remain constant despite transformations of the objects such as rigid motion. Perceptual constancy is essential in everything we do, like recognition of familiar objects and scenes, planning and executing visual navigation, visuomotor coordination, and many more. Perceptual constancy would not exist without the geometrical and physical permanence of objects: their shape, size, and weight. Formally, perceptual constancy and permanence of objects are invariants, also known in mathematics and physics as symmetries. Symmetries of the Laws of Physics received a central status due to mathematical theorems of Emmy Noether formulated and proved over 100 years ago. These theorems connected symmetries of the physical laws to conservation laws through the least-action principle. We show how Noether's theorem is applied to mirror-symmetrical objects and establishes mental shape representation (perceptual conservation) through the application of a simplicity (least-action) principle. This way, the formalism of Noether's theorem provides a computational explanation of the relation between the physical world and its mental representation.

Lagrange formalism in field theory

This chapter is devoted to a general discussion of classical field theory. It presents the minimum information required about classical fields for the subsequent treatment of quantum theory in the rest of the book. The Lagrange formalism for the fields is introduced, based on the least action principle. Global symmetries are described, and the proof of Noether's theorem given. In addition, the energy-momentum tensor for a field system is constructed as an example.