Heat capacity in bits

TL;DR

This paper explores the concept of heat capacity in bits through an information-theoretic lens, linking thermodynamic quantities to measures of information uncertainty and revealing new insights into phase transitions and quadratic modes.

Contribution

It introduces a novel interpretation of heat capacity in bits, connecting thermodynamics with information theory and providing a new framework for understanding phase changes and quadratic modes.

Findings

E/kT as a temperature-averaged heat capacity

C_v/k as bits of uncertainty gained per temperature doubling

Independence of C_v/k from energy zero, aiding phase change detection

Abstract

Information theory this century has clarified the 19th century work of Gibbs, and has shown that natural units for temperature kT, defined via 1/T=dS/dE, are energy per nat of information uncertainty. This means that (for any system) the total thermal energy E over kT is the log-log derivative of multiplicity with respect to energy, and (for all b) the number of base-b units of information lost about the state of the system per b-fold increase in the amount of thermal energy therein. For ``un-inverted'' (T>0) systems, E/kT is also a temperature-averaged heat capacity, equaling ``degrees-freedom over two'' for the quadratic case. In similar units the work-free differential heat capacity C_v/k is a ``local version'' of this log-log derivative, equal to bits of uncertainty gained per 2-fold increase in temperature. This makes C_v/k (unlike E/kT) independent of the energy zero, explaining in statistical terms its usefulness for detecting both phase changes and quadratic modes.