In the paper, "Time & clocks: A thermodynamic approach" Lucia and Grisolia describe the connections between the physical nature of time and macroscopic irreversibility in thermodynamics. They also discuss the possibility of constructing a thermodynamic clock that links the two, through an approach based on the behaviour of a black body. Their work primarily focuses on the macroscopic irreversibilty, and their attempt to define 'thermodynamic time' is grounded on the concepts from non-equilibrium thermodynamics such as, entropy generation and time-dependent thermodynamic fluxes - in and out of the system. In this letter, we present a first principles approach based on the Maupertuis principle to describe the connection between time and thermodynamics for equilibrium phenomena. Our novel interpretation of the temperature as a functional allows us to extend our formalism to irreversible processes when the local equilibrium hypothesis is satisfied. Through our framework we also establish a functional relationship between equilibrium and non-equilibrium time-scales while distinguishing between the two.
According to thermodynamics, the inevitable increase of entropy allows the past to be distinguished from the future. From this perspective, any clock must incorporate an irreversible process that allows this flow of entropy to be tracked. In addition, an integral part of a clock is a clockwork, that is, a system whose purpose is to temporally concentrate the irreversible events that drive this entropic flow, thereby increasing the accuracy of the resulting clock ticks compared to counting purely random equilibration events. In this article, we formalise the task of autonomous temporal probabil…
The thermodynamic uncertainty relation expresses a seemingly universal trade-off between the cost for driving an autonomous system and precision in any output observable. It has so far been proven for discrete systems and for overdamped Brownian motion. Its validity for the more general class of underdamped Brownian motion, where inertia is relevant, was conjectured based on numerical evidence. We now disprove this conjecture by constructing a counterexample. Its design is inspired by a classical pendulum clock, which uses an escapement to couple the motion of an oscillator to another degree o…
Feedback-Enhanced Quantum Metrology and Clock Precision under Thermodynamic Uncertainty
Key Laboratory of Intelligent Optoelectronic Devices and Chips of Jiangsu Higher Education Institutions, School of Physical Science and Technology, Suzhou University of Science and Technology（江苏高校智能光电器件与芯片重点实验室，苏州科技大学物理科学与技术学院）；Advanced Technology Research Institute of Taihu Photon Center, School of Physical Science and Technology, Suzhou University of Science and Technology（太湖光子中心先进技术研究院，苏州科技大学物理科学与技术学院）；Department of Physics, Zhejiang Normal University（浙江师范大学物理系）
Brownian clocks are biomolecular networks that can count time. A paradigmatic example are proteins that go through a cycle thus regulating some oscillatory behaviour in a living system. Typically, such a cycle requires free energy often provided by ATP hydrolysis. We investigate the relation between the precision of such a clock and its thermodynamic costs. For clocks driven by a constant thermodynamic force, a given precision requires a minimal cost that diverges as the uncertainty of the clock vanishes. In marked contrast, we show that a clock driven by a periodic variation of an external pr…
We consider an isolated autonomous quantum machine, where an explicit quantum clock is responsible for performing all transformations on an arbitrary quantum system (the engine), via a time-independent Hamiltonian. In a general context, we show that this model can exactly implement any energy-conserving unitary on the engine, without degrading the clock. Furthermore, we show that when the engine includes a quantum work storage device we can approximately perform completely general unitaries on the remainder of the engine. This framework can be used in quantum thermodynamics to carry out arbitr…
The role of coherence in quantum thermodynamics has been extensively studied in the recent years and it is now well-understood that coherence between different energy eigenstates is a resource independent of other thermodynamics resources, such as work. A fundamental remaining open question is whether the laws of quantum mechanics and thermodynamics allow the existence of a coherence distillation machine, i.e., a machine that, by possibly consuming work, obtains pure coherent states from mixed states, at a nonzero rate. This is related to another fundamental question: Starting from many copies…
Living systems regulate many aspects of their behavior through periodic oscillations of molecular concentrations, which function as `biochemical clocks.' These clocks are intrinsically subject to thermal fluctuations, so that the duration of a full oscillation cycle is random. Their success in carrying out their biological function is thought to depend on the degree to which these fluctuations in the cycle period can be suppressed. Biochemical oscillators also require a constant supply of free energy in order to break detailed balance and maintain their cyclic dynamics. For a given free energy…
We consider an out-of-equilibrium lattice model consisting of 2D discrete rotators, in contact with heat reservoirs at different temperatures. The equilibrium counterpart of such model, the clock-model, exhibits three phases; a low-temperature ordered phase, a quasi-liquid phase, and a high-temperature disordered phase, with two corresponding phase transitions. In the out-of-equilibrium model the simultaneous breaking of spatial symmetry and thermal equilibrium give rise to directed rotation of the spin variables. In this regime the system behaves as a thermal machine converting heat currents …
The Abdus Salam International Center for Theoretical Physics（阿卜杜斯·萨拉姆国际理论物理中心）；Atominstitut, Technische Universität Wien（维也纳工业大学原子研究所）；Institute for Quantum Optics and Quantum Information - IQOQI Vienna, Austrian Academy of Sciences（奥地利科学院维也纳量子光学与量子信息研究所）；Dipartimento di Fisica, Università di Napoli Federico II（那不勒斯费德里科二世大学物理系）；Institute for Cross-Disciplinary Physics and Complex Systems (IFISC), UIB-CSIC（巴利阿里群岛-西班牙国家科研委员会跨学科物理与复杂系统研究所）
Our previous works have shown the statistical mechanics of self-gravitating system. In this paper, we will show its thermodynamics and compare our results with observations and simulations. We propose that our statistical mechanics can be based on ergodicity breaking and Boltzmann entropy, and its assumptions do not contradict with the reality. With the principle of statistical mechanics, we will show our definition of temperature and then the capacity of self-gravitating systems. We find that the gravothermal catastrophe may be a special case of our theory. Our results also provide new explan…
The formalism of state estimation and hidden Markov models (HMMs) can simplify and clarify the discussion of stochastic thermodynamics in the presence of feedback and measurement errors. After reviewing the basic formalism, we use it to shed light on a recent discussion of phase transitions in the optimized response of an information engine, for which measurement noise serves as a control parameter. The HMM formalism also shows that the value of additional information shows a maximum at intermediate signal-to-noise ratios. Finally, we discuss how systems open to information flow can apparently…
The problem of time is a notable obstacle towards the recognition of quantum theory as the ultimate fundamental description of nature. Quantum theory may not be complete if founded upon classical notions. Louis de Broglie, seeming to be more or less convinced about the ontology of his proposed matter waves, tried to develop a theory of sub-quantum degrees of freedom relying on statistical thermodynamics. He realized a quantum particle as a fluctuating dense corpuscle formed via non-linear effects from a sub-quantum medium. A wave on the medium guides the vibrating corpuscle. He argued that an …
This paper gives a concise, mathematically rigorous description of phenomenological equilibrium thermodynamics for single-phase systems in the absence of chemical reactions and external forces. The present approach is similar to that of Callen, who introduces in his well-known thermodynamics book the basic concepts by means of a few postulates from which everything else follows. His setting is modified to match the more fundamental approach based on statistical mechanics. Thermodynamic stability is derived from kinematical properties of states outside equilibrium by rigorous mathematical argum…
A variant of continuous nonequilibrium thermodynamic theory based on the postulate of the scale invariance of the local relation between generalized fluxes and forces has been proposed. This single postulate replaces the assumptions on local equilibrium and on the known relation between thermodynamic fluxes and forces, which are widely used in classical nonequilibrium thermodynamics. It has been shown that such a modification not only makes it possible to deductively obtain the main results of classical linear nonequilibrium thermodynamics, but also provides a number of statements for a nonlin…
Non-equilibrium symmetry of cyclic first-passage times
University of Padova（帕多瓦大学）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Okinawa Institute of Science and Technology Graduate University（冲绳科学技术大学院大学）；Center for Systems Biology Dresden（德累斯顿系统生物学中心）；Max Planck Institute of Molecular Cell Biology and Genetics（马克斯·普朗克分子细胞生物学与遗传学研究所）
We discuss the relevance of geometric concepts in the theory of stochastic differential equations for applications to the theory of non-equilibrium thermodynamics of small systems. In particular, we show how the Eells-Elworthy-Malliavin covariant construction of the Wiener process on a Riemann manifold provides a physically transparent formulation of optimal control problems of finite-time thermodynamic transitions. Based on this formulation, we turn to an evaluative discussion of recent results on optimal thermodynamic control and their interpretation.
A model of coupled molecular oscillators is proposed to study nonequilibrium thermodynamics of synchronization. We find that synchronization of nonequilibrium oscillators costs energy even when the oscillator-oscillator coupling is conservative. By solving the steady state of the many-body system analytically, we show that the system goes through a nonequilibrium phase transition driven by energy dissipation, and the critical energy dissipation depends on both the frequency and strength of the exchange reactions. Moreover, our study reveals the optimal design for achieving maximum synchronizat…
The ongoing discussion whether thermodynamic properties can be extracted from a (possibly approximate) quantum mechanical time evolution using time averages is fed with an instructive example. It is shown for the harmonic oscillator how the Hilbert space or an appropriately defined phase space must be populated in terms of coherent states in order to obtain the quantum result respectively the classical one.
Local Shannon entropy lies at the heart of modern thermodynamics, with much discussion of trajectory-dependent entropy production. When taken at both boundaries of a process in phase space, it reproduces the second law of thermodynamics over a finite time interval for small scale systems. However, given that entropy is an ensemble property, it has never been clear how one can assign such a quantity locally. Given such a fundamental omission in our knowledge, we construct a new ensemble composed of trajectories reaching an individual microstate, and show that locally defined entropy, informatio…
In these lecture notes, the basic principles of stochastic thermodynamics are developed starting with a closed system in contact with a heat bath. A trajectory undergoes Markovian transitions between observable meso-states that correspond to a coarse-grained description of, e.g., a biomolecule or a biochemical network. By separating the closed system into a core system and into reservoirs for ligands and reactants that bind to, and react with the core system, a description as an open system controlled by chemical potentials and possibly an external force is achieved. Entropy production and fur…
From the Horowitz-Esposito stochastic thermodynamical description of information flows in dynamical systems [J. M. Horowitz and M. Esposito, Phys. Rev. X4, 031015 (2014)], it is known that while the second law of thermodynamics is satisfied by a joint system, the entropic balance for the subsystems is adjusted by a term related to the mutual information exchange rate between the two subsystems. In this article, we present a quantitative discussion of the conceptual link between the Horowitz-Esposito analysis and the Liang-Kleeman work on information transfer between dynamical system components…
