Thermodynamic cost of reliability and low temperatures: Tightening Landauer's principle and the second law

Landauer's principle states that the erasure of one bit of information requ ires the free energy kT In 2. We argue that the reliability of the bit eras ure process is bounded by the accuracy inherent in the statistical state of the energy source ("the resources") driving the process. We develop a gene ral framework describing the "thermodynamic worth" of the resources with re spect to reliable bit erasure or good cooling. This worth turns out to be g iven by the distinguishability of the resource's state from its equilibrium state in the sense of a statistical inference problem. Accordingly. Kullba ck-Leibler relative information is a decisive quantity Tor the "worth" of t he resource's state. Due to the asymmetry of relative information. the reli ability of the erasure process is bounded rather by the relative informatio n of the equilibrium state with respect to the actual state than by the rel ative information of the actual state with respect to the equilibrium state (which is the free energy up to constants).