if the heat capacity of the heat bath is infinite, the canonical distribution is exponential,

Variational and Extremum Principles in Macroscopic Systems

https://books.google.com/books?isbn=0080456146

Stanislaw Sieniutycz, ‎Henrik Farkas - 2010 - ‎Science

More precisely, if the heat capacity of the heat bath is infinite, the canonical distribution is exponential, while if it is constant and finite, the canonical density ...