On the Separability of Physical Systems

Anton S. Arkhipov

A hypothesis is presented that non-separability of degrees of freedom is the fundamental property underlying consciousness in physical systems. The amount of consciousness in a system is determined by the extent of non-separability and the number of degrees of freedom involved. Non-interacting and feedforward systems have zero consciousness, whereas most systems of interacting particles appear to have low non-separability and consciousness. By contrast, brain circuits exhibit high complexity and weak but tightly coordinated interactions, which appear to support high non-separability and therefore high amount of consciousness. The hypothesis applies to both classical and quantum cases, and we highlight the formalism employing the Wigner function (which in the classical limit becomes the Liouville density function) as a potentially fruitful framework for characterizing non-separability and, thus, the amount of consciousness in a system. The hypothesis appears to be consistent with both the Integrated Information Theory and the Orchestrated Objective Reduction Theory and may help reconcile the two. It offers a natural explanation for the physical properties underlying the amount of consciousness and points to methods of estimating the amount of non-separability as promising ways of characterizing the amount of consciousness.

Thomas M. Corwin

Lazar Mayants

Elisa Rebolini, Julien Toulouse, Andrew M. Teale +2 more

In this paper, an alternative method to range-separated linear-response time-dependent density-functional theory and perturbation theory is proposed to improve the estimation of the energies of a physical system from the energies of a partially interacting system. Starting from the analysis of the Taylor expansion of the energies of the partially interacting system around the physical system, we use an extrapolation scheme to improve the estimation of the energies of the physical system at an intermediate point of the range-separated or linear adiabatic connection where either the electron--electron interaction is scaled or only the long-range part of the Coulomb interaction is included. The extrapolation scheme is first applied to the range-separated energies of the helium and beryllium atoms and of the hydrogen molecule at its equilibrium and stretched geometries. It improves significantly the convergence rate of the energies toward their exact limit with respect to the range-separation parameter. The range-separated extrapolation scheme is compared with a similar approach for the linear adiabatic connection, highlighting the relative strengths and weaknesses of each approach.

D J Newman

Ivana Ilić, Jelena M. Višnjić, Vojislav V. Mitić +2 more

In this paper, the new mathematical correlation of two quantum systems that were initially allowed to interact and then separated is being formulated and analyzed. These correlations are illustrated by many examples and are also connected with fractals at a certain level. The main idea of the paper arises from the EPR paradox, the paradox of Einstein, Podolsky, and Rosen that occurs when the measurement of a physical observable performed on one system has an immediate effect on the other separate system being entangled with it. That is a physical phenomenon, especially when the particles are separated by a large distance. In this paper, we define distant correlations as the advanced method for the exact interpretation of strong connection and influence among those particles even when they are widely separated. On the given topological space (X,τ), we define a notion of τ-metric such that the set X is a τ-metric space and we prove some properties of these spaces. By using this new proposed model, we nullify the contradiction that appears in the EPR paradox. An illustrative example involving fractals is given. This innovative mathematical approach to this physical phenomenon may be attractive for future research in the field of quantum physics.