The new development pattern has identified two key avenues for the sustained advancement of high-quality agricultural and rural development: digitalisation and low-carbon development. The measurement of the digital economy and the agricultural carbon emission performance, and their spatial and temporal heterogeneity, is a crucial step in promoting the spatial coordination and sustainable development of digitalisation and low-carbon agriculture. This paper employs the entropy value method, SBM model, and coupling coordination degree model to investigate the coupling coordination measurement and spatial-temporal heterogeneity of the performance of the digital economy and agricultural carbon emissions. The data used are provincial panel data from 2013 to 2021. The simulation results demonstrate that, between 2013 and 2021, the digital economy of all provinces exhibited varying degrees of growth, yet the development of the digital economy between provinces exhibited a more pronounced tendency to diverge. Concurrently, the agricultural carbon emission efficiency in China exhibited a fluctuating upward trend. The development of the digital economy and the efficiency of agricultural carbon emission were found to be highly coupled. Their coupling and coordination relationship showed a downward trend followed by an upward trend. In general, it is suggested that we should increase investment in digital economy infrastructure and technology, promote digital agricultural applications, strengthen policy guidance and financial support, establish a coupling coordination mechanism and strengthen farmers’ digital literacy and environmental awareness.

This study constructed a multidimensional indicator system to evaluate spatio-temporal heterogeneity of China’s import and export trade of 31 provinces from 2000 to 2022. This study describes the distribution of China’s import and export trade by using location Gini coefficient and exploratory spatial analysis. Additionally, Multiple linear regression was used to ascertain the extent of contribution by various factors on the spatio-temporal heterogeneity of import and export trade. The simulation results show that inter-provincial import and export trade displayed distinct spatio-temporal differentiation characteristics with a prominent east-to-west disparity from 2000 to 2022. The trade links between various regions of the country have gradually strengthened, with a corresponding high correlation to the level of economic development. GDP, financial expenditure, freight transportation volume, technology market turnover, foreign investment, and disposable income of all residents, significantly influence the per capita export and import volume. In general, it is suggested that China and developing countries should take effective measures to promote balanced trade development, strengthen regional cooperation and coordination, and promote green trade and sustainable development.

The concept and practice of ’livelihood’ has undergone various stages in the development of Western countries. Its core has always focused on eradicating rural poverty and promoting rural development. This study utilizes the entropy value method to measure the comprehensive development level of the livelihood sustainability of farm households. Additionally, the Theil index is used to measure the presentation income gap, and multiple linear regression is utilized to test the impact of the livelihood capital sustainability of farm households on the presentation income gap. Results showed that the the sustainability of farm households’ livelihood capital has a significant negative impact on the urban-rural income gap. In other words, improving the livelihood capital of farm households can significantly reduce the urban-rural income gap. Accordingly, it is proposed that efforts be made to enhance the sustainability of farm households’ livelihoods, and to increase the contribution of the sustainable enhancement of farm households’ livelihood capital to narrowing the rural-urban income gap.