Minimal energy cost to initialize a bit with tolerable error

Landauer Bound in the Context of Minimal Physical Principles: Meaning, Experimental Verification, Controversies and Perspectives

The physical roots, interpretation, controversies, and precise meaning of the Landauer principle are surveyed. The Landauer principle is a physical principle defining the lower theoretical limit of energy consumption necessary for computation. It states that an irreversible change in information stored in a computer, such as merging two computational paths, dissipates a minimum amount of heat kBTln2 per a bit of information to its surroundings. The Landauer principle is discussed in the context of fundamental physical limiting principles, such as the Abbe diffraction limit, the Margolus-Levitin limit, and the Bekenstein limit. Synthesis of the Landauer bound with the Abbe, Margolus-Levitin, and Bekenstein limits yields the minimal time of computation, which scales as τmin~hkBT. Decreasing the temperature of a thermal bath will decrease the energy consumption of a single computation, but in parallel, it will slow the computation. The Landauer principle bridges John Archibald Wheeler's "it from bit" paradigm and thermodynamics. Experimental verifications of the Landauer principle are surveyed. The interrelation between thermodynamic and logical irreversibility is addressed. Generalization of the Landauer principle to quantum and non-equilibrium systems is addressed. The Landauer principle represents the powerful heuristic principle bridging physics, information theory, and computer engineering.

Generalized Landauer bound from absolute irreversibility

In this work, we introduce a generalization of the Landauer bound for erasure processes that stems from absolutely irreversible dynamics. Assuming that the erasure process is carried out in an absolutely irreversible way so that the probability of observing some trajectories is zero in the forward process but finite in the reverse process, we derive a generalized form of the bound for the average erasure work, which is valid also for imperfect erasure and asymmetric bits. The generalized bound obtained is tighter than or, at worst, as tight as existing ones. Our theoretical predictions are supported by numerical experiments and the comparison with data from previous works.

Work statistics in slow thermodynamic processes

We apply the adiabatic approximation to slow but finite-time thermodynamic processes and obtain the full counting statistics of work. The average work consists of change in free energy and the dissipated work, and we identify each term as a dynamical- and geometric-phase-like quantity. An expression for the friction tensor, the key quantity in thermodynamic geometry, is explicitly given. The dynamical and geometric phases are proved to be related to each other via the fluctuation-dissipation relation.

Minimally Dissipative Information Erasure in a Quantum Dot via Thermodynamic Length

In this Letter, we explore the use of thermodynamic length to improve the performance of experimental protocols. In particular, we implement Landauer erasure on a driven electron level in a semiconductor quantum dot, and compare the standard protocol in which the energy is increased linearly in time with the one coming from geometric optimization. The latter is obtained by choosing a suitable metric structure, whose geodesics correspond to optimal finite-time thermodynamic protocols in the slow driving regime. We show experimentally that geodesic drivings minimize dissipation for slow protocols, with a bigger improvement as one approaches perfect erasure. Moreover, the geometric approach also leads to smaller dissipation even when the time of the protocol becomes comparable with the equilibration timescale of the system, i.e., away from the slow driving regime. Our results also illustrate, in a single-electron device, a fundamental principle of thermodynamic geometry: optimal finite-time thermodynamic protocols are those with constant dissipation rate along the process.