Landauer's principle states that the erasure of information must be a dissipative process. In this paper, we carefully analyze the recording and erasure of information on a physical memory. On the one hand, we show that in order to record some information, the memory has to be driven out of equilibrium. On the other hand, we derive a differential version of Landauer's principle: We link the rate at which entropy is produced at every time of the erasure process to the rate at which information is erased.
We study the problem of the energetic cost of information erasure by looking at it through the lens of the Jarzynski equality. We observe that the Landauer bound, $\langle W \rangle \geq kT \ln 2$, on average dissipated work $\langle W \rangle$ associated to an erasure process, literally emerges from the underlying second law bound as formulated by Kelvin, $\langle W \rangle \geq 0$, as consequence of a spontaneous breaking of the Crooks-Tasaki fluctuation-symmetry, that accompanies logical irreversibility. We illustrate and corroborate this insight with numerical simulations of the process of…
The second law of thermodynamics is probabilistic in nature. Its formulation requires that the state of a system be described by a probability distribution. A natural question, thereby, arises as to whether a prior knowledge about the state of the system affects the second law. This question has now been nurtured over a century and its inception was done by C. Maxwell through his famous thought experiment wherein comes the idea of Maxwell's demon. The next important step in this direction was provided by L. Szilard who demonstrated a theoretical model for an information engine incorporating Ma…
It is demonstrated how to construct a Galois connection between two related systems with entropy. The construction, called the Landauer's connection, describes coupling between two systems with entropy. It is straightforward and transfers changes in one system to the other one preserving ordering structure induced by entropy. The Landauer's connection simplifies the description of the classical Landauer's principle for computational systems. Categorification and generalization of the Landauer's principle opens area of modelling of various systems in presence of entropy in abstract terms.
We study the thermodynamic cost associated with the erasure of one bit of information over a finite amount of time. We present a general framework for minimizing the average work required when full control of a system's microstates is possible. In addition to exact numerical results, we find simple bounds proportional to the variance of the microscopic distribution associated with the state of the bit. In the short-time limit, we get a closed expression for the minimum average amount of work needed to erase a bit. The average work associated with the optimal protocol can be up to a factor of f…
Landauer's erasure principle states that the irreversible erasure of a one-bit memory, embedded in a thermal environment, is accompanied with a work input of at least $k_{\text{B}}T\ln2$. Fundamental to that principle is the assumption that the physical states representing the two possible logical states are close to thermal equilibrium. Here, we propose and theoretically analyze a minimalist mechanical model of a one-bit memory operating with squeezed thermal states. It is shown that the Landauer energy bound is exponentially lowered with increasing squeezing factor. Squeezed thermal states, …
Landauer's principle is, roughly, the principle that there is an entropic cost associated with implementation of logically irreversible operations. Though widely accepted in the literature on the thermodynamics of computation, it has been the subject of considerable dispute in the philosophical literature. Both the cogency of proofs of the principle and its relevance, should it be true, have been questioned. In particular, it has been argued that microscale fluctuations entail dissipation that always greatly exceeds the Landauer bound. In this article Landauer's principle is treated within sta…
We show that any external intervention (insertion or removal of a partition) that destroys the equilibrium or brings it in a system always requires work and heat to ensure that the first law is obeyed, a fact that has been completely overlooked in the literature. As a consequence, there is no second law violation. We discuss the ramifications of our finding for information principles of Szilard and Landauer and show that no information entropy is needed. The relevance of this result for Maxwell's demon is also considered.
Landauer's bound relates changes in the entropy of a system with the inevitable dissipation of heat to the environment. The bound, however, becomes trivial in the limit of zero temperature. Here we show that it is possible to derive a tighter bound which remains non-trivial even as $T\to 0$. As in the original case, the only assumption we make is that the environment is in a thermal state. Nothing is said about the state of the system or the kind of system-environment interaction. Our bound is valid for all temperatures and is always tighter than the original one, tending to it in the limit of…
A major role of robots is to assist in assembly by moving building blocks and by exerting forces, e.g. to snap parts together. At the molecular scale, diffusive transport and thermal forces permit self-assembly, and molecular robots can only accelerate the process by performing work. This raises the question if - similar to Landauer's principle in computing - there is a lower limit to the work done by a robot for a given acceleration of an assembly process. Here, a brief analysis suggests that a doubling of a reaction rate by robotic manipulation requires at least kBTln2 in energy expenditure,…
Quantum Szilard engine constitutes an adequate interplay of thermodynamics, information theory and quantum mechanics. Szilard engines are in general operated by a Maxwell's Demon where Landauer's principle resolves the apparent paradoxes. Here we propose a Szilard engine setup without featuring an explicit Maxwell's demon. In a demonless Szilard engine, the acquisition of which-side information is not required, but erasure and the related heat dissipation still take place implicitly by the very nature of the work extraction process. We see that the insertion of the partition in a quantum Szila…
The Landauer principle states that at least $k_B T \ln 2$ of energy is required to erase a 1-bit memory, with $k_B T$ the thermal energy of the system. We study the effects of inertia on this bound using as one-bit memory an underdamped micro-mechanical oscillator confined in a double-well potential created by a feedback loop. The potential barrier is precisely tunable in the few $k_B T$ range. We measure, within the stochastic thermodynamic framework, the work and the heat of the erasure protocol. We demonstrate experimentally and theoretically that, in this underdamped system, the Landauer b…
Fooling the Landauer bound with a demon biased thermal bath
Institut de science et d’ingénierie supramoléculaires (ISIS) - UMR 7006, université de Strasbourg et CNRS（斯特拉斯堡大学与法国国家科学研究中心超分子科学与工程研究所）；CNRS, ENS de Lyon, Laboratoire de Physique（法国国家科学研究中心里昂高等师范学校物理实验室）
The Landauer principle states that any logically irreversible information processing must be accompanied by dissipation into the environment. In this study, we investigate the heat dissipation associated with finite-time information erasure and the effect of quantum coherence in such processes. By considering a scenario wherein information is encoded in an open quantum system whose dynamics are described by the Markovian Lindblad equation, we show that the dissipated heat is lower-bounded by the conventional Landauer cost, as well as a correction term inversely proportional to the operational …
We discuss, using recent results on the Landauer's bound in multivalued logic, the difficulties and pitfalls of how to apply this principle. The presentation is based on Szilard's version of Maxwell's demon experiment and use of equilibrium Thermodynamics. Different versions of thermodynamical/mechanical memory are presented - one-hot encoding version and the implementation based on reversed Szilard's experiment. Relation of the Landauer's principle to Galois connection is explained in detail.
Quantum Landauer's principle provides a fundamental lower bound for energy dissipation occurred with information erasure in the quantum regime. While most studies have related the entropy reduction incorporated with the erasure to the lower bound~(entropic bound), recent efforts have also provided another lower bound associated with the thermal fluctuation of the dissipated energy~(thermodynamic bound). The coexistence of the two bounds has stimulated comparative studies of their properties; however, these studies were performed for systems where the time-evolution of diagonal (population) and…
Landauer's principle states that information erasure requires heat dissipation. Landauer's original result focused on equilibrium memories. We here investigate the reset of information stored in a nonequilibrium state of a symmetric two-state memory. We derive a nonequilibrium generalization of the erasure principle and demonstrate that the corresponding bounds on work and heat may be reduced to zero. We further introduce reset protocols that harness the initial preparation energy and entropy and so allow to reach these nonequilibrium bounds. We finally provide numerical simulations with reali…
Landauer's principle laid the main foundation for the development of modern thermodynamics of information. However, in its original inception the principle relies on semiformal arguments and dissipative dynamics. Hence, if and how Landauer's principle applies to unitary quantum computing is less than obvious. Here, we prove an inequality bounding the change of Shannon information encoded in the logical quantum states by quantifying the energetic cost of Hamiltonian gate operations. The utility of this bound is demonstrated by outlining how it can be applied to identify energetically optimal qu…
Computations implemented on a physical system are fundamentally limited by the laws of physics. A prominent example for a physical law that bounds computations is the Landauer principle. According to this principle, erasing a bit of information requires a concentration of probability in phase space, which by Liouville's theorem is impossible in pure Hamiltonian dynamics. It therefore requires dissipative dynamics with heat dissipation of at least $k_BT\log 2$ per erasure of one bit. Using a concrete example, we show that when the dynamic is confined to a single energy shell it is possible to c…
Thermodynamics and information have intricate inter-relations. The justification of the fact that information is physical, is done by inter-linking information and thermodynamics - through Landauer's principle. This modern approach towards information recently has improved our understanding of thermodynamics, both in classical and quantum domains. Here we show thermodynamics as a consequence of information conservation. Our approach can be applied to most general situations, where systems and thermal-baths could be quantum, of arbitrary sizes and even could posses inter-system correlations. Th…
