Beyond Landauer Erasure

Abstract

In thermodynamics, one considers thermal systems and the maximization of entropy subject to the conservation of energy. A consequence is Landauer's erasure principle, which states that the erasure of one bit of information requires a minimum energy cost equal to kT ln(2), where T is the temperature of a thermal reservoir used in the process and k is Boltzmann's constant. Jaynes, however, argued that the maximum entropy principle could be applied to any number of conserved quantities, which would suggest that information erasure may have alternative costs. Indeed, we showed recently that by using a reservoir comprising energy degenerate spins and subject to conservation of angular momentum, the cost of information erasure is in terms of angular momentum rather than energy. Here, we extend this analysis and derive the minimum cost of information erasure for systems where different conservation laws operate. We find that, for each conserved quantity, the minimum resource needed to erase one bit of memory is λ −1 ln(2), where λ is related to the average value of the conserved quantity. The costs of erasure depend, fundamentally, on both the nature of the physical memory element and the reservoir with which it is coupled.

Beyond heat baths II: framework for generalized thermodynamic resource theories

“…This opening is hoped to facilitate experimental tests of one-shot statistical mechanics. 4 Interconversions amongst information, energy, and angular momentum were analyzed outside of resource theories in [36,37]. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 The generalization opens questions to investigation.…”

“…Resourcefulness can be stored in particle number, electric polarization, gravitational mass, etc. Angular momentum is treated as a resource in [36,37]. Suppose that W denotes a positive number.…”

“…III D. Additionally, I introduce batteries whose resourcefulness manifests in degrees of freedom other than energy (e.g., in a high particle concentration). (Angular momentum was identified as such a degree of freedom independently in [36,37].) Also the open questions are original.…”

Thermodynamic resource theories, non-commutativity and maximum entropy principles

“…This shows how simple trade-offs exist for erasure in the presence of multiple conserved charges. One could also compare with [9], where the authors show that if erasure is performed with respect to angular momentum degrees of freedom that are not degenerate in energy, equation (9) cannot be achieved.…”

Implications of non-Markovian quantum dynamics for the Landauer bound

“…In particular, the role of memory effects (which are believed to be a key cause of the emergence of non-Markovian effects) in logically irreversible processes has recently attracted some attention [26,27] in light of the relevance that Landauer principle has for information processing at both the classical and quantum level [28,29,34]. The relevance of the principle at the quantum scale has been largely debated, with contributions both at the theoretical [24,26,27,30,59,[32][33][34][35] and the experimental level [36][37][38].…”