How is mammalian life span related to resting metabolic rate?

In mammalian biology, the relationship between life span and resting metabolic rate is generally inverse: as the rate of living increases, life span tends to decrease, provided that brain and body weight are held constant.1

This relationship is mathematically expressed in the equation $L=5.5E^{0.54}{S}^{-0.34}{M}^{-0.42}$, where $L$ is life span, $E$ is brain weight, $S$ is body weight, and $M$ is metabolic rate. The negative coefficient for metabolic rate ($M^{-0.42}$) indicates that higher energy expenditure per gram of tissue is associated with shorter longevity.1

While larger animals often live longer, this is frequently due to their high positive correlation with brain weight and their negative correlation with metabolic rate, rather than body size alone. Some mammals, such as bats, can circumvent this trend by entering torpor or hibernation, which significantly reduces their metabolic rate and extends their life span despite their small size.12