Beyond Landauer erasure

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 1 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 1 bit of memory is $\lambda^{-1}\ln(2)$ where $\lambda$ 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.Comment: 7 pages, 3 figure

Three types of Landauer's erasure principle : a microscopic view

Altres ajuts: acords transformatius de la UABAn important step to incorporate information in the second law of thermodynamics was done by Landauer, showing that the erasure of information implies an increase in heat. Most attempts to justify Landauer's erasure principle are based on thermodynamic argumentations. Here, using just the time-reversibility of classical microscopic laws, we identify three types of the Landauer's erasure principle depending on the relation between the two final environments: the one linked to a logical input 1 and the other to logical input 0. The strong type (which is the original Landauer's formulation) requires the final environments to be in thermal equilibrium. The intermediate type giving the entropy change of kln 2 occurs when the two final environments are identical macroscopic states. Finally, the weak Landauer's principle, providing information erasure with no entropy change, when the two final environments are macroscopically different. Even though the above results are formally valid for classical erasure gates, a discussion on their natural extension to quantum scenarios is presented. This paper strongly suggests that the original Landauer's principle (based on the assumption of thermalized environments) is fully reasonable for microelectronics, but it becomes less reasonable for future few-atoms devices working at THz frequencies. Thus, the weak and intermediate Landauer's principles, where the erasure of information is not necessarily linked to heat dissipation, are worth investigating

Revisiting the damped quantum harmonic oscillator

We reanalyse the quantum damped harmonic oscillator, introducing three less than common features. These are (i) the use of a continuum model of the reservoir rather than an ensemble of discrete oscillators, (ii) an exact diagonalisation of the Hamiltonian by adapting a technique pioneered by Fano, and (iii) the use of the thermofield technique for describing a finite temperature reservoir. We recover in this way a number of well-known and some, perhaps, less familiar results. An example of the latter is an ab initio proof that the oscillator relaxes to the mean-force Gibbs state. We find that special care is necessary when comparing the damped oscillator with its undamped counterpart as the former has two distinct natural frequencies, one associated with short time evolution and the other with longer times

Quantum-Dot Heat Engines

This thesis explores the possibilities of using quantum dots (QDs) in nanoscale energy har- vesters converting heat into electrical energy, i.e. heat engines. From a theory perspective, these possibilities have been investigated for almost two decades, and interest in them seem to continuously increase over time. However, a high degree of experimental control over the manufacturing and operation of QD engines have only recently been achieved. This opens up the possibility of verifying the theory predictions and brings new questions to be answered, which is where this thesis aims at making a contribution. The author’s contributions to the work that the thesis builds upon are theoretical, but are often used together with experimental results for synergistic effects.The thesis starts with an introduction to relevant concepts in classical thermodynamics and a quantum mechanical description of electron states in QDs. This is followed by a discus- sion of electron transport in QDs, as well as an introduction to the master equation based approaches used to model the relevant experimental devices.There are three studies included in the thesis, all of which have been peer-reviewed and published in scientific journals. The details of the physics relevant for each one are presen- ted together with a summary of the studies. The first is an investigation of the performance limits of an experimental implementation of a steady-state QD heat engine, in which the Curzon-Ahlborn efficiency is observed at maximum power and the highest efficiency was in excess of 70% of the Carnot efficiency. This is the first verification that QDs can be used in high efficiency heat engines. The second study investigates how to practically optimize the output power of similar devices, and quantifies how high efficiency one can hope to reach in other implementations of QD engines. The third study proposes an experimental quantum engine based on a double QD where entangled singlet spin states are used to drive the engine. This can be viewed as entanglement acting as the engine’s fuel

Fundamental work cost of quantum processes

Information-theoretic approaches provide a promising avenue for extending the laws of thermodynamics to the nanoscale. Here, we provide a general fundamental lower limit, valid for systems with an arbitrary Hamiltonian and in contact with any thermodynamic bath, on the work cost for the implementation of any logical process. This limit is given by a new information measure—the coherent relative entropy—which accounts for the Gibbs weight of each microstate. The coherent relative entropy enjoys a collection of natural properties justifying its interpretation as a measure of information and can be understood as a generalization of a quantum relative entropy difference. As an application, we show that the standard first and second laws of thermodynamics emerge from our microscopic picture in the macroscopic limit. Finally, our results have an impact on understanding the role of the observer in thermodynamics: Our approach may be applied at any level of knowledge—for instance, at the microscopic, mesoscopic, or macroscopic scales—thus providing a formulation of thermodynamics that is inherently relative to the observer. We obtain a precise criterion for when the laws of thermodynamics can be applied, thus making a step forward in determining the exact extent of the universality of thermodynamics and enabling a systematic treatment of Maxwell-demon-like situations

Fundamental work cost of quantum processes

Information-theoretic approaches provide a promising avenue for extending the laws of thermodynamics to the nanoscale. Here, we provide a general fundamental lower limit, valid for systems with an arbitrary Hamiltonian and in contact with any thermodynamic bath, on the work cost for the implementation of any logical process. This limit is given by a new information measure—the coherent relative entropy—which accounts for the Gibbs weight of each microstate. The coherent relative entropy enjoys a collection of natural properties justifying its interpretation as a measure of information and can be understood as a generalization of a quantum relative entropy difference. As an application, we show that the standard first and second laws of thermodynamics emerge from our microscopic picture in the macroscopic limit. Finally, our results have an impact on understanding the role of the observer in thermodynamics: Our approach may be applied at any level of knowledge—for instance, at the microscopic, mesoscopic, or macroscopic scales—thus providing a formulation of thermodynamics that is inherently relative to the observer. We obtain a precise criterion for when the laws of thermodynamics can be applied, thus making a step forward in determining the exact extent of the universality of thermodynamics and enabling a systematic treatment of Maxwell-demon-like situations

The Resource Theoretic Paradigm of Quantum Thermodynamics with Control

The resource theory of quantum thermodynamics has been a very successful theory and has generated much follow up work in the community. It requires energy preserving unitary operations to be implemented over a system, bath, and catalyst as part of its paradigm. So far, such unitary operations have been considered a "free" resource of the theory. However, this is only an idealisation of a necessarily inexact process. Here, we include an additional auxiliary control system which can autonomously implement the unitary by turning "on/off " an interaction. However, the control system will inevitable be degraded by the back-action caused by the implementation of the unitary. We derive conditions on the quality of the control device so that the laws of thermodynamics do not change; and prove --- by utilising a good quantum clock --- that the laws of quantum mechanics allow the back-reaction to be small enough so that these conditions are satisfiable. Our inclusion of non-idealised control into the resource framework also rises interesting prospects, which were absent when considering idealised control. Namely: 1) the emergence of a 3rd law --- without the need for the assumption of a light-cone. 2) the inability to apply the 2nd laws out of equilibrium. Our results and framework unify the field of autonomous thermal machines with the thermodynamic quantum resource theoretic one, and lay the groundwork for all quantum processing devices to be unified with fully autonomous machines.Comment: 10+52 page

Quantum Coarse-Graining: An Information-Theoretic Approach to Thermodynamics

We investigate fundamental connections between thermodynamics and quantum information theory. First, we show that the operational framework of thermal operations is nonequivalent to the framework of Gibbs-preserving maps, and we comment on this gap. We then introduce a fully information-theoretic framework generalizing the above by making further abstraction of physical quantities such as energy. It is technically convenient to work with and reproduces known results for finite-size quantum thermodynamics. With our framework we may determine the minimal work cost of implementing any logical process. In the case of information processing on memory registers with a degenerate Hamiltonian, the answer is given by the max-entropy, a measure of information known from quantum information theory. In the general case, we obtain a new information measure, the "coherent relative entropy", which generalizes both the conditional entropy and the relative entropy. It satisfies a collection of properties which justifies its interpretation as an entropy measure and which connects it to known quantities. We then present how, from our framework, macroscopic thermodynamics emerges by typicality, after singling out an appropriate class of thermodynamic states possessing some suitable reversibility property. A natural thermodynamic potential emerges, dictating possible state transformations, and whose differential describes the physics of the system. The textbook thermodynamics of a gas is recovered as well as the form of the second law relating thermodynamic entropy and heat exchange. Finally, noting that quantum states are relative to the observer, we see that the procedure above gives rise to a natural form of coarse-graining in quantum mechanics: Each observer can consistently apply the formalism of quantum information according to their own fundamental unit of information.Comment: Ph. D. thesis, ETH Zurich (301 pages). Chaps. 1-3,9 are introductory and/or reviews; Chaps. 4,6 discuss previously published results (reproduces content from arXiv:1406.3618, New J. Phys. 2015 and from arXiv:1211.1037, Nat. Comm. 2015); Chaps. 5,7,8,10 are as of yet unpublished (introducing our information-theoretic framework, the coherent relative entropy, and quantum coarse-graining

Quantum Causal Structure and Quantum Thermodynamics

This thesis reports progress in two domains, namely causal structures and microscopic thermodynamics, both of which are highly pertinent in the development of quantum technologies. Causal structures fundamentally influence the development of protocols for quantum cryptography and microscopic thermodynamics is crucial for the design of quantum computers. The first part is dedicated to the analysis of causal structure, which encodes the relationship between observed variables, in general restricting the set of possible correlations between them. Our considerations rely on a recent entropy vector method, which we first review. We then develop new techniques for deriving entropic constraints to differentiate between causal structures. We provide sufficient conditions for entropy vectors to be realisable within a causal structure and derive new, improved necessary conditions in terms of so-called non-Shannon inequalities. We also report that for a family of causal structures, including the bipartite Bell scenario and the bilocal causal structure, entropy vectors are unable to distinguish between classical and quantum causes, in spite of the existence of quantum correlations that are not classically reproducible. Hence, further development is needed in order to understand cause from a quantum perspective. In the second part we explore an axiomatic framework for modelling error-tolerant processes in microscopic thermodynamics. Our axiomatisation allows for the accommodation of finite precision levels, which is crucial for describing experiments in the microscopic regime. Moreover, it is general enough to permit the consideration of different error types. The framework leads to the emergence of manageable quantities that give insights into the feasibility and expenditure of processes, which for adiabatic processes are shown to be smooth entropy measures. Our framework also leads to thermodynamic behaviour at the macroscopic scale, meaning that for thermodynamic equilibrium states a unique function provides necessary and sufficient conditions for state transformations, like in the traditional second law