## 1 Introduction  
Coal is a significant energy source worldwide, but coal mining presents considerable safety and environmental hazards, including coal and gas outbursts that pose a significant risk of fatality and property damage [1, 2]. An instantaneous coal outburst is an abrupt and violent ejection of coal and gas during underground mining [3, 4], characterized by the sudden emission of a large quantity of gas accompanying pulverized coal into the underground roadways in a short period of time [1, 2]. Despite the recognized correlation between coal gas outbursts and factors such as gas contents in coal, geological conditions, and ground stress, the underlying mechanisms responsible for outbursts are not yet fully comprehended [5, 6, 7]. With the increase in burial depth, the outburst intensity increases remarkably. This is mainly due to changes in geological structure and coal seam thickness, which affect gas pressure and ground stress. As a result, the failure mode changes from tensile to shear failure, with higher unloading rates making tensile failure more likely. Additionally, under a higher gas desorption rate, the scope of the non-failure zone becomes smaller [8]. Coal is an adsorbent material with complex structures. More than 90% of methane gas is absorbed into the coal matrix; the rest is free gas existing in the pores of the coal. The impact of volatiles on the porous structure of coal samples and the resulting changes in methane adsorption capacity [9]. Volatile-related deformations in the coal's porous structure influenced methane adsorption behavior. Microstructural characterizations revealed that volatiles could be found trapped in the pores or cross-linked in the network, with each state affecting different aspects of coal-coal interactions and the overall structure of coal. Coal consists of fracture networks and coal matrix blocks that are interlocked and distributed without overlapping relationships [10; 11]. Matrix blocks in coal contain numerous pores that serve as storage sites for gas and facilitate its flow. Gas is primarily extracted through fractures and pore channels within the coal [12]. The emission of gas from coal is often associated with three phenomena: specific **desorption** from the coal surface, **gas diffusion** within the grains, and gas filtration through a system of fractures in the coal bed [13; 14]. Outburst-prone coal is characterized by low mechanical strength and easily crumbles into tiny particles, typically below 1 mm in size. Coal breakage will not only result in changes in particle size distribution but also accelerate gas desorption from coal to release a huge amount of gas, which may participate directly or indirectly in the outburst process [15; 16]. The effect of coal size needs to be considered in the outburst process [17]. Therefore, deep insights into coal and gas outbursts require analyzing gas desorption rate variations in gas-containing coal pre- and post-crushing. It has already been recognized in addressing the outburst issue that the desorption rate of gas from coal is closely associated with the tendency of coal outbursts [18; 19]. The rapid gas desorption from powdered coal plays a decisive role in gas outbursts [20; 21]. Furthermore, the gas release during the initial stage is closely linked to the level of outburst risk [22]. As a result, certain coal-producing countries developed a standard procedure for an index known as the initial gas emission velocity, which involves measuring the amount of gas released over time from coal cuttings collected from soft coal layers within coalbeds [23]. Therefore, analyzing the relationship between coal breakage and gas desorption rate can aid in understanding the significant gas release that occurs during the outburst process. The main factors affecting gas desorption rate involve gas adsorption equilibrium pressure and coal particle size. The desorption amount increases with higher equilibrium pressure and smaller coal particles [24]. [PERSON] and [PERSON] et al.