Towards quantization Conway Game of LifeKrzysztof Pomorski^1,³, Dariusz Kotula^2,3 1: Institute of PhysicsLodz University of Technology, Lodz, Poland2: Faculty of Computer Science and TelecommunicationCracow University of Technology, Cracow, Poland3: Quantum Hardware Systems, Lodz, Poland

Classical stochastic Conway Game of Life is expressed by the dissipative Schrodinger equation and dissipative tight-binding model. This is conducted at the prize of usage of time dependent anomalous non-Hermitian Schroedinger 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. At the same time various aspects of thermodynamics were observed in cellular automata system that can be later reformulated by quantum mechanical pictures. The usage of Shannon entropy and mass equivalence to energy points definition of cellular automata temperature. Contrary to intuitive statement the system dynamical equilibrium is always reflected by negative Conway temperatures. Conway-Schrrodinger equation is formulated.