Systems Biology: an information-theoretic-based thermo-statistical approach (original) (raw)
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Aapp Physical Mathematical and Natural Sciences, 2008
What is the physical significance of entropy? What is the physical origin of irreversibility? Do entropy and irreversibility exist only for complex and macroscopic systems? Most physicists still accept and teach that the rationalization of these fundamental questions is given by Statistical Mechanics. Indeed, for everyday laboratory physics, the mathematical formalism of Statistical Mechanics (canonical and grand-canonical, Boltzmann, Bose-Einstein and Fermi-Dirac distributions) allows a successful description of the thermodynamic equilibrium properties of matter, including entropy values. However, as already recognized by Schrödinger in 1936, Statistical Mechanics is impaired by conceptual ambiguities and logical inconsistencies, both in its explanation of the meaning of entropy and in its implications on the concept of state of a system. An alternative theory has been developed by Gyftopoulos, Hatsopoulos and the present author to eliminate these stumbling conceptual blocks while maintaining the mathematical formalism so successful in applications. To resolve both the problem of the meaning of entropy and that of the origin of irreversibility we have built entropy and irreversibility into the laws of microscopic physics. The result is a theory, that we call Quantum Thermodynamics, that has all the necessary features to combine Mechanics and Thermodynamics uniting all the successful results of both theories, eliminating the logical inconsistencies of Statistical Mechanics and the paradoxes on irreversibility, and providing an entirely new perspective on the microscopic origin of irreversibility, nonlinearity (therefore including chaotic behavior) and maximal-entropy-generation nonequilibrium dynamics. In this paper we discuss the background and formalism of Quantum Thermodynamics including its nonlinear equation of motion and the main general results. Our objective is to show in a not-too-technical manner that this theory provides indeed a complete and coherent resolution of the century-old dilemma on the meaning of entropy and the origin of irreversibility, including Onsager reciprocity relations and maximal-entropy-generation nonequilibrium dynamics, which we believe provides the microscopic foundations of heat, mass and momentum transfer theories, including all their implications such as Bejan's Constructal Theory of natural phenomena.
Informational–statistical thermodynamics of a complex system
The Journal of Chemical Physics, 2000
We apply a statistical-thermodynamic approach to the study of a particular physical system ͑two sets of nonlinearly coupled oscillators͒, driven far away from equilibrium. Such a system displays a kind of complex behavior consisting in the so-called Fröhlich effect leading in steady-state conditions to a nonequilibrium phase condensation resembling the Bose-Einstein condensation of systems in equilibrium. A kind of ''two-fluid model'' arises: the ''normal nonequilibrium phase'' and Fröhlich condensate or ''nonequilibrium superphase,'' which is shown to be an attractor of the system. We work out some aspects of the irreversible thermodynamics of this dissipative complex system. Particular nonlinear properties are discussed and Lyapunov exponents determined. This kind of system gives a good modeling of polar vibration modes in polymers and biopolymers.
Dynamics and Thermodynamics of Linear Quantum Open Systems
Physical Review Letters, 2013
We study the behavior of networks of quantum oscillators coupled with arbitrary external environments. We analyze the evolution of the quantum state showing that the reduced density matrix of the network always obeys a local master equation with a simple analytical solution. We use this to study the emergence of thermodynamical laws in the long time regime. We demonstrate two main results on thermodynamics: First, we show that it is impossible to build a quantum absorption refrigerator using linear networks (therefore, such refrigerators require non-linearity as a crucial ingredient, as proposed by Kosloff and others ). Then, we show that the third law imposes constraints on the low frequency behavior of the environmental spectral densities. PACS numbers: 03.65.Yz
Irreversible entropy production: From classical to quantum
Reviews of Modern Physics, 2021
Entropy production is a key quantity in any finite-time thermodynamic process. It is intimately tied with the fundamental laws of thermodynamics, embodying a tool to extend thermodynamic considerations all the way to non-equilibrium processes. It is also often used in attempts to provide the quantitative characterization of logical and thermodynamic irreversibility, stemming from processes in physics, chemistry and biology. Notwithstanding its fundamental character, a unifying theory of entropy production valid for general processes, both classical and quantum, has not yet been formulated. Developments pivoting around the frameworks of stochastic thermodynamics, open quantum systems, and quantum information theory have led to substantial progress in such endeavour. This has culminated in the unlocking of a new generation of experiments able to address stochastic thermodynamic processes and the impact of entropy production on them. This paper aims to provide a compendium on the current framework for the description, assessment and manipulation of entropy production. We present both formal aspects of its formulation and the implications stemming from the potential quantum nature of a given process, including a detailed survey of recent experiments.
Information-theoretic equilibrium and observable thermalization
A crucial point in statistical mechanics is the definition of the notion of thermal equilibrium, which can be given as the state that maximises the von Neumann entropy, under the validity of some constraints. Arguing that such a notion can never be experimentally probed, in this paper we propose a new notion of thermal equilibrium, focused on observables rather than on the full state of the quantum system. We characterise such notion of thermal equilibrium for an arbitrary observable via the maximisation of its Shannon entropy and we bring to light the thermal properties that it heralds. The relation with Gibbs ensembles is studied and understood. We apply such a notion of equilibrium to a closed quantum system and show that there is always a class of observables which exhibits thermal equilibrium properties and we give a recipe to explicitly construct them. Eventually, an intimate connection with the Eigenstate Thermalisation Hypothesis is brought to light. To understand under which conditions thermodynamics emerges from the microscopic dynamics is the ultimate goal of statistical mechanics. However, despite the fact that the theory is more than 100 years old, we are still discussing its foundations and its regime of applicability. The ordinary way in which thermal equilibrium properties are obtained, in statistical mechanics, is through a complete characterisation of the thermal form of the state of the system. One way of deriving such form is by using Jaynes principle 1-4 , which is the constrained maximisation of von Neumann entropy S vN = − Trρ logρ. Jaynes showed that the unique state that maximises S vN (compatibly with the prior information that we have on the system) is our best guess about the state of the system at the equilibrium. The outcomes of such procedure are the so-called Gibbs ensembles. In the following we argue that such a notion of thermal equilibrium, de facto is not experimentally testable because it gives predictions about all possible observables of the system, even the ones which we are not able to measure. To overcome this issue, we propose a weaker notion of thermal equilibrium, specific for a given observable. The issue is particularly relevant for the so-called "Pure states statistical mechanics" 5-19 , which aims to understand how and in which sense thermal equilibrium properties emerge in a closed quantum system, under the assumption that the dynamic is unitary. In the last fifteen years we witnessed a revival of interest in these questions , mainly due to remarkable progresses in the experimental investigation of isolated quantum systems 20-25. The high degree of manipulability and isolation from the environment that we are able to reach nowadays makes possible to experimentally investigate such questions and to probe the theoretical predictions. The starting point of Jaynes' derivation of statistical mechanics is that S vN is a way of estimating the uncertainty that we have about which pure state the system inhabits. Unfortunately we know from quantum information theory that it does not address all kind of ignorance we have about the system. Indeed, it is not the entropy of an observable (though the state is observable); its conceptual meaning is not tied to something that we can measure. This issue is intimately related with the way we acquire information about a system, i.e. via measurements. The process of measuring an observable on a quantum system allows to probe only the diagonal part of the density matrix λ ρ λ i i , when this is written in the observable eigenbasis λ { } i. For such a reason, from the experimental point of view, it is not possible to assess whether a many-body quantum system is at thermal equilibrium (e.g. Gibbs state ρ G): the number of observables needed to probe all the density matrix elements is too big. In any experimentally reasonable situation we have access only to a few (sometimes just one or two) observables. It is 1 tomic ann aser sicss arennon aaoratorr niiersitt of OOforr arrs oaa OOforr O1 333. Centre for uantum eccnooooiess ationaa niiersitt of innaporee 1177433 innapore. 3 Department of Physics, National niiersitt of innapore cience Driie 3 1171 innapore. 4 Center for Quantum Information, Institute for Interiscippinar Information ciences sinua niiersit 1000844 eiiin ina. * These authors contributed eeua to tis wor. orresponence an reeuests for materias souu e aressee to .. emai: faio.ana pppsics.oo.ac.uuu receiiee: 13 Octooer 016 acceptee: 31 anuarr 017 Puuuissee: 07 arcc 017 OPEN
The role of quantum information in thermodynamics—a topical review
Journal of Physics A: Mathematical and Theoretical, 2016
This topical review article gives an overview of the interplay between quantum information theory and thermodynamics of quantum systems. We focus on several trending topics including the foundations of statistical mechanics, resource theories, entanglement in thermodynamic settings, fluctuation theorems and thermal machines. This is not a comprehensive review of the diverse field of quantum thermodynamics; rather, it is a convenient entry point for the thermo-curious information theorist. Furthermore this review should facilitate the unification and understanding of different interdisciplinary approaches emerging in research groups around the world.
Non-equilibrium dynamics: quantum systems and foundations of quantum mechanics
The European Physical Journal Special Topics
This text presents a brief overview of the recent development of topics addressed by the original papers of this volume related to nonequilibrium phenomena in various (especially mesoscopic) systems and the foundations of quantum physics. A selection of relevant literature is included. 2 The European Physical Journal Special Topics time evolution of systems; quantum to classical transitions; dynamics of quantum phase transitions; and topological states of systems. The above mentioned phenomena, related problems and challenges occur in many fields of physics, astrophysics, chemistry, and biology. As for systems, which enable study of various related questions, mesoscopic systems are especially suitable for this purpose due to their vast variety of structures and parameters. Various systems, of natural and artificial origin, can exhibit mesoscopic features depending on inner parameters of those systems and interactions with their environment. Typical mesoscopic systems can be of nanoscale size, composed from atoms (molecules). Nanoscale structures include not only very small physical structures, but also structures occurring in living cells, as for example complex molecules, proteins and molecular motors. At the same time, nanoscale technologies enable the preparation of well-defined artificial structures composed of between a few to hundreds of atoms (molecules) to create an enormous diversity of systems with well-defined inner parameters which can be influenced by external fields. These structures can be studied by methods of condensed matter physics and quantum optics in such detail that affords a deeper understanding of quantum physics, as represented by quantum interference, entanglement, the uncertainty principle, quantum measurement and what is often termed "non-locality". Of particular interest are carbon allotropes, quantum wires and dots, microcavities, single molecule nanomagnets, molecular motors and active gels, various structures in living cells, as well as specific arrangements featuring cold atoms and molecules which can exhibit macroscopic quantum effects and which can be used for testing methods of quantum many-body theory. Recent advances in technologies have led to enormous improvements of measurement, imaging and observation techniques at microscopic, mesoscopic and macroscopic scales. At the same time, various methods allow investigation into not only equilibrium features, but also time evolution of classical and quantum systems (which are in general far from equilibrium) at different time scales. This increasing ability to study subtle details of the dynamics of systems yields new versions of old questions and creates new challenges in many fields of physics. A good understanding of the time evolution of both classical and quantum systems is essential for an explanation of many observations and experiments of contemporary physics. Observed systems must often be treated as non-equilibrium, open systems in which their behavior is influenced not only by their inner parameters, but also by properties of their environment and time dependent external fields. The theory of non-equilibrium behavior of quantum many-body systems is, however, far from complete. There are lasting and extremely important problems related to modern technologies, including questions of irreversible behavior of real systems in comparison with reversible microscopic laws, emergence of classical macroscopic behavior from microscopic quantum behavior, charge (electron), spin and heat transport, limits to "phenomenological" thermodynamic descriptions, and the problem of how to describe properly open quantum systems far from equilibrium, especially in the case of strong interaction between a small system and reservoirs. Another challenging problem is stochastic behavior of systems caused either by innate features of the systems or by noise related to the fact that the studied systems are open. Studies of quantum and temperature fluctuations, as well as quantum noise, dephasing and dissipation create an essential part of the research in this direction. Recently, various versions of non-equilibrium fluctuation and fluctuationdissipation theorems for quantum systems have been discussed. These studies are of key importance since the fluctuations, dissipation and noise are closely related to the performance and the reliability of both artificially created nano-devices as well as natural "engines", as are for example molecular motors in cells.
The role of interactions in open quantum systems and the second law of thermodynamics
Journal- Korean Physical Society
In open quantum systems, it is difficult to know whether the system is in equilibrium or nonequilibrium. In order to investigate the role of interactions between the system and its environment in open quantum systems, we derive a formula which relates the Hamiltonian of the system to entropy. In this formula, these interactions inside the system and the entropy of the system are not connected to each other; only these interactions between the system and its environment are related to the entropy. Thus, this formula enables us to discriminate the types of interactions between the system and its environment; one type of interaction increases the entropy of the system, and the other type of interaction does not change the entropy of the system. We find that a certain type of interaction between the system and its environment causes a nonequilibrium state of the system. The criteria for the types of interactions between the system and its environment are specifically given by studying the entropy.
Statistical entropy of open quantum systems
Physical Review E, 2016
Dissipative quantum systems are frequently described within the framework of the so-called "system-plus-reservoir" approach. In this work we assign their description to the Maximum Entropy Formalism and compare the resulting thermodynamic properties with those of the wellestablished approaches. Due to the non-negligible coupling to the heat reservoir, these systems are non-extensive by nature, and the former task may require the use of non-extensive parameter dependent informational entropies. In doing so, we address the problem of choosing appropriate forms of those entropies in order to describe a consistent thermodynamics for dissipative quantum systems. Nevertheless, even having chosen the most successful and popular forms of those entropies, we have proven our model to be a counterexample where this sort of approach leads us to wrong results. I.