Abstract: We investigated the relaxation behavior of lipid membranes close to the chain melting transition using pressure jump calorimetry with a temperature accuracy of about $10^{-3}$K. We found relaxation times in the range from seconds up to about a minute, depending on vesicular state. The relaxation times are within error proportional to the heat capacity. We provide a statistical thermodynamics theory that rationalizes the close relation between heat capacity and relaxation times. It is based on our recent finding that enthalpy and volume changes close to the melting transition are proportional functions.