An Evidential Interpretation of the 1st and 2nd Laws of Thermodynamics

TL;DR

This paper reinterprets the first and second laws of thermodynamics as principles about information conservation and loss, linking thermodynamics with information theory and statistical inference through a novel framework involving an information measure E.

Contribution

It introduces an information-based analogue of thermodynamic laws, providing a new perspective that unifies thermodynamics and information theory with a novel interpretative framework.

Findings

Likelihood principle as a conservation law similar to the first law

Likelihood involves irrecoverable information loss akin to the second law

E serves as an information-theoretic analogue of temperature T

Abstract

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.