The information-carrying capacity of a memory is known to be a thermodynamic
resource facilitating the conversion of heat to work. Szilard's engine
explicates this connection through a toy example involving an energy-degenerate
two-state memory. We devise a formalism to quantify the thermodynamic value of
memory in general quantum systems with nontrivial energy landscapes. Calling
this the thermal information capacity, we show that it converges to the
non-equilibrium Helmholtz free energy in the thermodynamic limit. We compute
the capacity exactly for a general two-state (qubit) memory away from the
thermodynamic limit, and find it to be distinct from known free energies. We
outline an explicit memory--bath coupling that can approximate the optimal
qubit thermal information capacity arbitrarily well.Comment: 6 main + 7 appendix pages; 5 main + 2 appendix figure
