A hot spring is a spring that is produced by the emergence of geothermally heated groundwater from the Earth's crust. There are geothermal hot springs in many locations all over the crust of the earth.

There is no universally accepted definition of a hot spring. For example, one can find the phrase hot spring defined as

The related term "warm spring" is defined as a spring with water temperature less than a hot spring by many sources, although Pentecost et al. (2003) suggest that the phrase "warm spring" is not useful and should be avoided. The US NOAA Geophysical Data Center defines a "warm spring" as a spring with water between 20 and 50 °C (68 and 122 °F).

The water issuing from a hot spring is heated by geothermal heat, i.e., heat from the Earth's mantle. In general, the temperature of rocks within the earth increases with depth. The rate of temperature increase with depth is known as the geothermal gradient. If water percolates deeply enough into the crust, it will be heated as it comes into contact with hot rocks. The water from hot springs in non-volcanic areas is heated in this manner.

Xiao Yu (蕭瑀) (574–647), courtesy name Shiwen (時文), formally Duke Zhenbian of Song (宋貞褊公), was an imperial prince of the Chinese dynasty Liang Dynasty who later became an official for Sui Dynasty and Tang Dynasty, serving as a chancellor at times during the reigns of Emperor Gaozu of Tang and Emperor Taizong of Tang.

Xiao Yu was born in 574, during the reign of his father Emperor Ming of Western Liang, who claimed the throne of Liang Dynasty but whose territory was limited to a small amount of territory around his capital Jiangling. Emperor Ming was at that time also a vassal of the much larger Northern Zhou, and received protection from Northern Zhou forces against rival Chen Dynasty. (As Emperor Ming and his father Emperor Xuan had little territory and relied on protection by Northern Zhou and its predecessor state Western Wei and successor state Sui Dynasty (which took over Northern Zhou in 581), traditional historians often did not consider them true emperors of Liang Dynasty.) In 582, Xiao Yu was created the Prince of Xin'an. He was known for his filial piety.