  I argue here that both the first and second laws of thermodynamics, generally
understood to be quintessentially physical in nature, can be equally well
described as being about certain types of information without the need to
invoke physical manifestations for information. In particular, I show that the
statistician's familiar likelihood principle is a general conservation
principle on a par with the first law, and that likelihood itself involves a
form of irrecoverable information loss that can be expressed in the form of
(one version of) the second law. Each of these principles involves a particular
type of information, and requires its own form of bookkeeping to properly
account for information accumulation. I illustrate both sets of books with a
simple coin-tossing (binomial) experiment. In thermodynamics, absolute
temperature T is the link that relates energy-based and entropy-based
bookkeeping systems. I consider the information-based analogue of this link,
denoted here as E, and show that E has a meaningful interpretation in its own
right in connection with statistical inference. These results contribute to a
growing body of theory at the intersection of thermodynamics, information
theory and statistical inference, and suggest a novel framework in which E
itself for the first time plays a starring role.
