Towards quantization Conway Game of Life
Krzysztof Pomorski, Dariusz Kotula

TL;DR
This paper explores a quantum-inspired, dissipative version of Conway's Game of Life using complex non-Hermitian Hamiltonians, revealing thermodynamic behaviors and non-conservation phenomena.
Contribution
It introduces a novel quantum mechanical framework for cellular automata with complex energies and dissipation, linking thermodynamics and quantum concepts.
Findings
System exhibits negative temperatures at equilibrium.
Mass, energy, and temperature diffuse consistent with thermodynamic laws.
Complex-valued mass mimics wave-function behavior.
Abstract
Classical stochastic Conway Game of Life is expressed by the dissipative Schr\"odinger equation and dissipative tight-binding model. This is conducted at the prize of usage of time dependent anomalous non-Hermitian Hamiltonians as with occurrence of complex value potential that do not preserve the normalization of wave-function and thus allows for mimicking creationism or annihilationism of cellular automaton. Simply saying time-dependent complex value eigenenergies are similar to complex values of resonant frequencies in electromagnetic resonant cavities reflecting presence of dissipation that reflects energy leaving the system or being pumped into the system. At the same time various aspects of thermodynamics were observed in cellular automata that can be later reformulated by quantum mechanical pictures. The usage of Shannon entropy and mass equivalence to energy points definition of…
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Taxonomy
TopicsQuantum Mechanics and Applications · Advanced Thermodynamics and Statistical Mechanics · Quantum Computing Algorithms and Architecture
