Stochastic cellular automaton

Quantum mechanics

Theoretical physics

Algorithm

Extension (predicate logic)

Conserved quantity

Mathematical physics

Boundary (topology)

Boundary value problem

Steady state (chemistry)

Computer science

Reversible cellular automaton

Classical mechanics

Statistical physics

Physical chemistry

Thermodynamics

Automaton

Physics

Integrable system

Mathematics

Cellular automaton

Astronomy

Nondeterministic finite automaton

Mobile automaton

Mathematical analysis

Automata theory

Chemistry

Programming language

Block cellular automaton

Non-equilibrium thermodynamics

Journal of Physics A Mathematical and Theoretical

Recently Prosen and Mej\'ia-Monasterio (J. Phys. A: Math. Theor. 49 (2016) 185003) obtained exact nonequilibrium steady states of an integrable and reversible cellular automaton driven by some stochastic boundary conditions. In this paper, we explore the possible extensions of their method by generalizing the boundary conditions. As the result, we find two cases where such an extension is possible. One is the case where a special condition is satisfied in a generalized boundary condition. The other is obtained by considering a conserved quantity as energy and boundaries as heat reservoirs. The latter includes the original solution as the special case. Properties of the both solutions are discussed.

Two extensions of exact nonequilibrium steady states of a boundary-driven cellular automaton