Nonequilibrium phenomena are ubiquitous in nature and in a wide range of systems, including cold atomic gases and solid-state materials. While these phenomena are challenging to describe both theoretically and experimentally, they are essential for the fundamental understanding of many-body systems and practical devices. In the context of spintronics, when a magnetic insulator (MI) is subjected to a thermal gradient, a pure spin current is generated in the form of magnons without the presence and dissipation of a charge current-attractive for reducing energy consumption and central to the emerging field of spin caloritronics. However, the experimental methods for directly quantifying a spin current in insulators and for probing local phonon-magnon nonequilibrium and the associated magnon chemical potential are largely missing. Here, we apply a heating laser to generate a thermal gradient in the MI yttrium iron garnet (YIG), Y3Fe5O12, and evaluate two components of the spin current, driven by temperature and chemical potential gradients, respectively. The experimental method and theory approach for evaluating quasiparticle chemical potential can be applied for analogous phenomena in other many-body systems.