Hamilton Equations, Commutator, and Energy Conservation

We show that the classical Hamilton equations of motion can be derived from the energy conservation condition. A similar argument is shown to carry to the quantum formulation of Hamiltonian dynamics. Hence, showing a striking similarity between the quantum formulation and the classical formulation. Furthermore, it is shown that the fundamental commutator can be derived from the Heisenberg equations of motion and the quantum Hamilton equations of motion. Also, that the Heisenberg equations of motion can be derived from the Schrödinger equation for the quantum state, which is the fundamental postulate. These results are shown to have important bearing for deriving the quantum Maxwell’s equations.

Quantum Entropic Gravity with Quantum Field Theory and General Relativity : A First Approach with Bijective Physics

The purpose of this paper is to find a quantum formulation of entropic gravity, incorporating the bijective theory. In a first part, we will describe the basis of the bijective theory. In a second part, we will incorporate the stress energy quantum tensor defined in the linear approximation of the Einstein’s equation in its quantum version to entropy. In the third part, we will integrate the bijective theory with the newly created relativistic quantum entropy. This will lead us four part where we will formalize quantum entropic gravity.

Quantum Entropic Gravity with Quantum Field Theory and General Relativity : A First Approach with Bijective Physics

The purpose of this paper is to find a quantum formulation of entropic gravity, incorporating the bijective theory. In a first part, we will describe the basis of the bijective theory. In a second part, we will incorporate the stress energy quantum tensor defined in the linear approximation of the Einstein’s equation in its quantum version to entropy. In the third part, we will integrate the bijective theory with the newly created relativistic quantum entropy. This will lead us four part where we will formalize quantum entropic gravity.

Magnetic Otto Engine for an Electron in a Quantum Dot: Classical and Quantum Approach

We study the performance of a classical and quantum magnetic Otto cycle with a quantum dot as a working substance using the Fock-Darwin model with the inclusion of the Zeeman interaction. Modulating an external/perpendicular magnetic field, we found in the classical approach an oscillating behavior in the total work that is not perceptible under the quantum formulation. Also, we compare the work and efficiency of this system for different regions of the Entropy, $S(T,B)$, diagram where we found that the quantum version of this engine always shows a reduced performance in comparison to his classical counterpart.

Quantum entropic regularization of matrix-valued optimal transport

This article introduces a new notion of optimal transport (OT) between tensor fields, which are measures whose values are positive semidefinite (PSD) matrices. This “quantum” formulation of optimal transport (Q-OT) corresponds to a relaxed version of the classical Kantorovich transport problem, where the fidelity between the input PSD-valued measures is captured using the geometry of the Von-Neumann quantum entropy. We propose a quantum-entropic regularization of the resulting convex optimization problem, which can be solved efficiently using an iterative scaling algorithm. This method is a generalization of the celebrated Sinkhorn algorithm to the quantum setting of PSD matrices. We extend this formulation and the quantum Sinkhorn algorithm to compute barycentres within a collection of input tensor fields. We illustrate the usefulness of the proposed approach on applications to procedural noise generation, anisotropic meshing, diffusion tensor imaging and spectral texture synthesis.

A quantum Samaritan’s dilemma cellular automaton

The dynamics of a spatial quantum formulation of the iterated Samaritan’s dilemma game with variable entangling is studied in this work. The game is played in the cellular automata manner, i.e. with local and synchronous interaction. The game is assessed in fair and unfair contests, in noiseless scenarios and with disrupting quantum noise.