  The dynamics of wealth distribution plays a critical role in the economic
market, hence an understanding of its nonequilibrium statistical mechanics is
of great importance to human society. For this aim, a simple and efficient
one-dimensional (1D) lattice gas automaton (LGA) is presented for wealth
distribution of agents with or without saving propensity. The LGA comprises two
stages, i.e., random propagation and economic transaction. During the former
phase, an agent either remains motionless or travels to one of its neighboring
empty sites with a certain probability. In the subsequent procedure, an
economic transaction takes place between a pair of neighboring agents randomly.
It requires at least 4 neighbors to present correct simulation results. The LGA
reduces to the simplest model with only random economic transaction if all
agents are neighbors and no empty sites exist. The 1D-LGA has a higher
computational efficiency than the 2D-LGA and the famous Chakraborti-Chakrabarti
economic model. Finally, the LGA is validated with two benchmarks, i.e., the
wealth distributions of individual agents and dual-earner families. With the
increasing saving fraction, both the Gini coefficient and Kolkata index (for
individual agents or two-earner families) reduce, while the deviation degree
(defined to measure the difference between the probability distributions with
and without saving propensities) increases. It is demonstrated that the wealth
distribution is changed significantly by the saving propensity which alleviates
wealth inequality.
