Equivalence between finite state stochastic machine, non-dissipative and dissipative tight-binding and Schroedinger model

TL;DR

This paper demonstrates the mathematical equivalence between finite state stochastic machines and quantum models like tight-binding and Schrödinger systems, showing classical systems can simulate quantum phenomena such as entanglement and superposition.

Contribution

It establishes a formal link allowing classical stochastic models to replicate quantum effects, including entanglement, superposition, and dissipation, with potential applications in quantum-like computation and communication.

Findings

Classical epidemic models can reproduce quantum entanglement.

Finite state stochastic machines can simulate Rabi oscillations.

Classical models can mimic Aharonov-Bohm effects in quantum systems.

Abstract

The mathematical equivalence between finite state stochastic machine and non-dissipative and dissipative quantum tight-binding and Schroedinger model is derived. Stochastic Finite state machine is also expressed by classical epidemic model and can reproduce the quantum entanglement emerging in the case of electrostatically coupled qubits described by von-Neumann entropy both in non-dissipative and dissipative case. The obtained results shows that quantum mechanical phenomena might be simulated by classical statistical model as represented by finite state stochastic machine. It includes the quantum like entanglement and superposition of states. Therefore coupled epidemic models expressed by classical systems in terms of classical physics can be the base for possible incorporation of quantum technologies and in particular for quantum like computation and quantum like communication. The classical density matrix is derived and described by the equation of motion in terms of anticommutator. Existence of Rabi like oscillations is pointed in classical epidemic model. Furthermore the existence of Aharonov-Bohm effect in quantum systems can also be reproduced by the classical epidemic model or in broader sense by finite state stochastic machine. Every quantum system made from quantum dots and described by simplistic tight-binding model by use of position-based qubits can be effectively described by classical statistical model encoded in finite stochastic state machine with very specific structure of S matrix that has twice bigger size as it is the case of quantum matrix Hamiltonian. Furthermore the description of linear and non-linear stochastic finite state machine is mapped to tight-binding and Schroedinger model. The concept of N dimensional complex time is incorporated into tight-binding model, so the description of dissipation in most general case is possible.