The Gibbs paradox, the Landauer principle and the irreversibility associated with tilted observers

It is well known that, in the context of General Relativity, some spacetimes, when described by a congruence of comoving observers, may consist in a distribution of a perfect (non-dissipative) fluid, whereas the same spacetime as seen by a "tilted"' (Lorentz-boosted) congruence of observers, may exhibit the presence of dissipative processes. As we shall see, the appearence of entropy producing processes are related to the tight dependence of entropy on the specific congruence of observers. This fact is well illustrated by the Gibbs paradox. The appearance of such dissipative processes, as required by the Landauer principle, are necessary, in order to erase the different amount of information stored by comoving observers, with respect to tilted ones.Comment: 10 pages Latex. Invited contribution for the special issue "Advances in Relativistic Statistical Mechanics" published in Entrop

Maxwell's Demon and the Problem of Observers in General Relativity

The fact that real dissipative (entropy producing) processes may be detected by non-comoving observers (tilted), in systems that appear to be isentropic for comoving observers, in general relativity, is explained in terms of the information theory, analogous with the explanation of the Maxwell's demon paradoxComment: 6 pages Latex.1 figure. Published in the special issue of Entropy: Selected Papers from 4th International Electronic Conference on Entropy and Its Application

Landauer Principle and General Relativity

We endeavour to illustrate the physical relevance of the Landauer principle applying it to different important issues concerning the theory of gravitation. We shall first analyze, in the context of general relativity, the consequences derived from the fact, implied by Landauer principle, that information has mass. Next, we shall analyze the role played by the Landauer principle in order to understand why different congruences of observers provide very different physical descriptions of the same space--time. Finally, we shall apply the Landauer principle to the problem of gravitational radiation. We shall see that the fact that gravitational radiation is an irreversible process entailing dissipation, is a straightforward consequence of the Landauer principle and of the fact that gravitational radiation conveys information. An expression measuring the part of radiated energy that corresponds to the radiated information and an expression defining the total number of bits erased in that process, shall be obtained, as well as an explicit expression linking the latter to the Bondi news function.Comment: Published in the special issue of Entropy: The Landauer Principle: Meaning, Physical Roots and Application

What Is the Temperature? Modern Outlook on the Concept of Temperature

The meaning and evolution of the notion of "temperature" (which is a key concept for the condensed and gaseous matter theories) are addressed from the different points of view. The concept of temperature turns out to be much more fundamental than it is conventionally thought. In particular, the temperature may be introduced for the systems built of "small" number of particles and particles in rest. The Kelvin temperature scale may be introduced into the quantum and relativistic physics due to the fact, that the efficiency of the quantum and relativistic Carnot cycles coincides with that of the classical one. The relation of the temperature to the metrics of the configurational space describing the behavior of the system built from non-interacting particles is demonstrated. The Landauer principle asserts that the temperature of the system is the only physical value defining the energy cost of isothermal erasing of the single bit of information. The role of the temperature the cosmic microwave background in modern cosmology is discussed

FUNCTION AND DISSIPATION IN FINITE STATE AUTOMATA - FROM COMPUTING TO INTELLIGENCE AND BACK

Society has benefited from the technological revolution and the tremendous growth in computing powered by Moore\u27s law. However, we are fast approaching the ultimate physical limits in terms of both device sizes and the associated energy dissipation. It is important to characterize these limits in a physically grounded and implementation-agnostic manner, in order to capture the fundamental energy dissipation costs associated with performing computing operations with classical information in nano-scale quantum systems. It is also necessary to identify and understand the effect of quantum in-distinguishability, noise, and device variability on these dissipation limits. Identifying these parameters is crucial to designing more energy efficient computing systems moving forward. In this dissertation, we will provide a physical description of finite state automaton, an abstract tool commonly used to describe computational operations under the Referential Approach to physical information theory. We will derive the fundamental limits of dissipation associated with a state transition in deterministic and probabilistic finite state automaton, and propose efficacy measures to capture how well a particular state transition has been physically realized. We will use these dissipation bounds to understand the limits of dissipation during learning during training and testing phases in feed-forward and recurrent neural networks. This study of dissipation in neural network provides key hints at how dissipation is fundamentally intertwined with learning in physical systems. These ideas connecting energy dissipation, entropy and physical information provide the perfect toolkit to critically analyze the very foundations of computing, and our computational approaches to artificial intelligence. In the second part of this dissertation, we derive the non-equilibrium reliable low dissipation condition for predictive inference in self-organized systems. This brings together the central ideas of homeostasis, prediction and energy efficiency under a single non-equilibrium constraint. The work was further extended to study the relationship between adaptive learning and the reliable high dissipation conditions, and the exploitation-exploration trade-offs in active agents. Using these results, we will discuss the differences between observer dependent and independent computing, and propose an alternative novel descriptive framework of intelligence in physical systems using thermodynamics. This framework is called thermodynamic intelligence and will be used to guide the engineering methodologies (devices and architectures) required to implement these descriptions

Quantum Darwinism and Friends

In honor of Wojciech Zurek’s 70th birthday, this Special Issue is dedicated to recent advances in our understanding the emergence of classical reality, and pays tribute to Zurek’s seminal contributions to our understanding of the Universe. To this end, “Quantum Darwinism and Friends” collects articles that make sense of the apparent chasm between quantum weirdness and classical perception, and provides a snapshot of this fundamental, exciting, and vivid field of theoretical physics

Quantum entanglement

All our former experience with application of quantum theory seems to say: {\it what is predicted by quantum formalism must occur in laboratory}. But the essence of quantum formalism - entanglement, recognized by Einstein, Podolsky, Rosen and Schr\"odinger - waited over 70 years to enter to laboratories as a new resource as real as energy. This holistic property of compound quantum systems, which involves nonclassical correlations between subsystems, is a potential for many quantum processes, including ``canonical'' ones: quantum cryptography, quantum teleportation and dense coding. However, it appeared that this new resource is very complex and difficult to detect. Being usually fragile to environment, it is robust against conceptual and mathematical tools, the task of which is to decipher its rich structure. This article reviews basic aspects of entanglement including its characterization, detection, distillation and quantifying. In particular, the authors discuss various manifestations of entanglement via Bell inequalities, entropic inequalities, entanglement witnesses, quantum cryptography and point out some interrelations. They also discuss a basic role of entanglement in quantum communication within distant labs paradigm and stress some peculiarities such as irreversibility of entanglement manipulations including its extremal form - bound entanglement phenomenon. A basic role of entanglement witnesses in detection of entanglement is emphasized.Comment: 110 pages, 3 figures, ReVTex4, Improved (slightly extended) presentation, updated references, minor changes, submitted to Rev. Mod. Phys

Thermodynamics and synchronization in open quantum systems

Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Físicas, Departamento de Física Atómica Molecular y Nuclear, leída el 11-07-2017Los efectos disipativos tienen profundas consecuencias en el comportamiento y las propiedades de los sistemas cuánticos [72]. La inevitable interacción con el entorno circundante, con el cual los sistemas intercambian continuamente información, energía, momento angular o materia, es la última responsable de los fenómenos de decoherencia y de la emergencia del comportamiento clásico [490, 614]. Sin embargo, existe un amplio régimen intermedio en el cual efectos disipativos y cuánticos coexisten, dando lugar a una amplia gama de ricos y sorprendentes fenómenos que apenas están empezando a ser comprendidos. Además, las innovadoras técnicas desarrolladas recientemente para controlar y manipular sistemas cuánticos en el laboratorio han hecho esta fenomenología accesible experimentalmente y potencialmente aplicable [244, 586]. En esta tesis exploraremos desde un punto de vista teórico algunas de las conexiones entre efectos disipativos y cuánticos en lo concerniente a dos principales aspectos: el comportamiento termodinámico de los sistemas cuánticos y la relación entre las correlaciones dinámicas y cuánticas compartidas por éstos. Las correlaciones cuánticas son una de las características más sorprendentes de la naturaleza y han atraído un notable interés desde la misma formulación de la teoría cuántica. La comprensión de los mecanismos subyacentes que generan, preservan, o destruyen estas correlaciones resulta de gran importancia a la hora de explorar la frontera cuántico-clásica [597], mientras que es esencial en el diseño de esquemas en los que la decoherencia pueda ser evitada en aplicaciones prácticas [35, 143, 562]. Por otra parte, otro tipo importante de correlaciones dinámicas de caracter más tradicionalmente clásico son los fenómenos de sincronización, que han sido estudiados en un amplio rango de sistemas físicos, químicos y biológicos [433]. La sincronización puede aparecer como un comportamiento espontáneo y cooperativo de diferentes unidades que oscilan y que, cuando se acoplan, adaptan sus ritmos a una frecuencia común. Este fenómeno de sincronización mutua ha sido considerado con profusión desde un punto de vista clásico [249, 263, 606], mientras que los rasgos genuinamente cuánticos de la sincronización estan empezando ahora a ser investigados...Dissipation effects have profound consequences in the behavior and properties of quantum systems. The unavoidable interaction with the surrounding environment, with whom systems continuously exchange information, energy, angular momentum or matter, is ultimately responsible of decoherence phenomena and the emergence of classical behavior. However, there exist a wide intermediate regime in which the interplay between dissipative and quantum effects gives rise to a plethora of rich and striking phenomena that has only started to be understood. In addition, the recent breakthrough techniques in controlling and manipulating quantum systems in the laboratory has made this phenomenology accessible in experiments and potentially applicable. In this thesis we aim to explore from a theoretical point of view some of the connections between dissipative and quantum effects. We focus on three main topics: the relation between dynamical and quantum correlations, the thermodynamical properties of fluctuations, and the performance of quantum thermal machines. First, we study the emergence of transient and asymptotic spontaneous synchronization induced by dissipation in harmonic quantum systems and its connections with quantum correlations. Our results show that synchronization may be used a witnesses for the slow decay or even the preservation of quantum discord in many situations of interest. Furthermore, we develop methods for engineering it in complex harmonic networks or selected clusters, where noiseless subsystems can be obtained by tuning one or few system parameters. Second, we explore the quantum versions of work and entropy production fluctuation relations. We derive a general fluctuation theorem valid for a broad class of open systems dynamics and discuss the meaning of the quantity fulfilling it. Importantly, our theorem overcomes the prototypical assumption of ideal thermal reservoirs. We also study the possibility of split entropy production in arbitrary quantum processes into adiabatic and non-adiabatic contributions, each of them fulfilling an independent fluctuation theorem. Contrary to the classical case, quantum effects may break the split, and we discuss the necessary conditions to enforce it. Our findings are illustrated in three relevant examples for quantum thermodynamics. Finally, we focus on the role quantum effects in the performance of quantum thermal machines. We analyze the case of an optimized quantum Otto cycle powered by a squeezed thermal reservoir. Our previous results allow us to characterize the many striking nonequilibrium features that arise, including work extraction from a single reservoir or multi-task regimes combining both refrigeration of a cold reservoir and work extraction at the same time. On the other hand, we also explore the role of the Hilbert space dimension in the performance of autonomous quantum thermal machines. Our results point that adding extra levels constitutes a thermodynamical resource. For the case of autonomous fridges, we further obtain a statement on the third law of thermodynamics in terms of their number of levels: reaching zero temperature requires an infinite Hilbert space dimension. The research results presented in this thesis are complemented with a broad introduction to the field of open quantum systems and quantum thermodynamics. There, we review the state of the art on these topics and the reader will find the main methods and tools used along the thesis.Depto. de Estructura de la Materia, Física Térmica y ElectrónicaFac. de Ciencias FísicasTRUEunpu