It is often claimed, that from a quantum system of d levels, and entropy S and heat bath of temperature T one can draw kT(ln d -S) amount of work. However, the usual arguments based on Szilard engine are not fully rigorous. Here we prove the formula within Hamiltonian description of drawing work from a quantum system and a heat bath, at a cost of entropy of the system. We base on the derivation of thermodynamical laws and quantities in [R. Alicki, J. Phys. A, 12, L103 (1979)] within a weak coupling limit. Our result provides fully physical scenario for extracting thermodynamical work from quantum correlations [J. Oppenheim et al. Phys. Rev. Lett. 89, 180402 (2002)]. We also derive Landauer principle as a consquence of second law within the considered model.
We introduce the informational correlation $E^{AB}$ between two interacting quantum subsystems $A$ and $B$ of a quantum system as the number of arbitrary parameters $φ_i$ of a unitary transformation $U^A$ (locally performed on the subsystem $A$) which may be detected in the subsystem $B$ by the local measurements. This quantity indicates whether the state of the subsystem $B$ may be effected by means of the unitary transformation applied to the subsystem $A$. Emphasize that $E^{AB}\neq E^{BA}$ in general. The informational correlations in systems with tensor product initial states are studied …
We present a critical examination of the difficulties with the quantum versions of a lifted weight that are widely used as work storage systems in quantum thermodynamics. To overcome those difficulties, we turn to the strong connections between information and thermodynamics illuminated by Szilard's engine and Landauer's principle, and consider the concept of informational work storage. This concept is in sharp contrast with the usual one of mechanical work storage underlying the idealization of a quantum weight. An informational work storage system based on maximally mixed qubits that does no…
We review recent work on the foundations of thermodynamics in the light of quantum information theory. We adopt a resource-theoretic perspective, wherein thermodynamics is formulated as a theory of what agents can achieve under a particular restriction, namely, that the only state preparations and transformations that they can implement for free are those that are thermal at some fixed temperature. States that are out of thermal equilibrium are the resources. We consider the special case of this theory wherein all systems have trivial Hamiltonians (that is, all of their energy levels are degen…
Several novel approaches have been proposed to resolve the problem of time by relating it to change. We argue using quantum information theory that the Hamiltonian constraint in quantum gravity cannot probe change, so it cannot be used to obtain a meaningful notion of time. This is due to the absence of quantum Fisher information with respect to the quantum Hamiltonian of a time-reparametization invariant system. We also observe that the inability of this Hamiltonian to probe change can be related to its inability to discriminate between states of such a system. However, if the time-reparameti…
The act of measuring a system has profound consequences of dynamical and thermodynamic nature. In particular, the degree of irreversibility ensuing from a non-equilibrium process is strongly affected by measurements aimed at acquiring information on the state of a system of interest: the conditional and unconditional entropy production, which quantify the degree of irreversibility of the open system's dynamics, are related to each other by clearly interpreted informational quantities. Building on a recently proposed collisional-model framework [G. T. Landi {\it et al.}, arXiv:2103.06247], we i…
In this paper a thermodynamical derivation of the quantum potential is pro- posed. Within the framework of Bohmian mechanics we show how the quantum potential can be derived, by adding an additional informational degree of freedom to the ordinary degrees of freedom of a physical system. Such a derivation uses the First Law of thermodynamics for this additional degree of freedom and basic equilibrium thermodynamics methods. By doing that, one may associate a temper- ature to each wave function. Features and behavior of this temperature in different situations is studied.
Open quantum systems are studied from the thermodynamical point of view unifying the principle of maximum informational entropy and the hypothesis of relaxation times hierarchy. The result of the unification is a non-Markovian and local in time master equation that provides a direct connection of dynamical and thermodynamical properties of open quantum systems. The power of the approach is illustrated with the application to the damped harmonic oscillator and the damped driven two-level system resulting in analytical expressions for the non-Markovian and non-equilibrium entropy and inverse tem…
We put forth a unifying formalism for the description of the thermodynamics of continuously monitored systems, where measurements are only performed on the environment connected to a system. We show, in particular, that the conditional and unconditional entropy production, which quantify the degree of irreversibility of the open system's dynamics, are related to each other by the Holevo quantity. This, in turn, can be further split into an information gain rate and loss rate, which provide conditions for the existence of informational steady-states (ISSs), i.e. stationary states of a condition…
Ulsan National Institute of Science and Technology (UNIST)（蔚山科学技术院）；Nanyang Technological University（南洋理工大学）；National University of Singapore（新加坡国立大学）；Leibniz Universität Hannover（汉诺威莱布尼茨大学）
There are many ways to decompose the Hilbert space H of a composite quantum system into tensor product subspaces. Different subsystem decompositions generally imply different interaction Hamiltonians V, and therefore different expectation values for subsystem observables. This means that thE uniqueness of physical predictions is not guaranteed, despite the uniqueness of the total Hamiltonian H and the total Hilbert space. Here we use Clausius' version of the second law of thermodynamics (CSL) and standard identifications of thermodynamic quantities to identify possible subsystem decompositions…
We present results concerning aspects of quantum thermodynamics under the background of non-Hermitian quantum mechanics for the dynamics of a quantum harmonic oscillator. Since a better control over the parameters in quantum thermodynamics processes is desired, we use concepts from collisional model to introduce a simple prototype of thermal reservoir based on $\mathcal{PT}$-symmetric Hamiltonians and study its effects under the thermalization process of a single harmonic oscillator prepared in a displaced thermal state. We verify that controlling the $\mathcal{PT}$-symmetric features of the r…
Quantum thermodynamics seeks to extend non-equilibrium stochastic thermodynamics to small quantum systems where non-classical features are essential to its description. Such a research area has recently provided meaningful theoretical and experimental advances by exploring the wealth and the power of quantum features along with informational aspects of a system's thermodynamics. The relevance of such investigations is related to the fact that quantum technological devices are currently at the forefront of science and engineering applications. This short review article provides an overview of s…
Based on recently introduced efficient quantum state tomography schemes, we propose a scalable method for the tomography of unitary processes and the reconstruction of one-dimensional local Hamiltonians. As opposed to the exponential scaling with the number of subsystems of standard quantum process tomography, the method relies only on measurements of linearly many local observables and either (a) the ability to prepare eigenstates of locally informationally complete operators or (b) access to an ancilla of the same size as the to-be-characterized system and the ability to prepare a maximally …
Quantum work is usually determined from two projective measurements of the energy at the beginning and at the end of a thermodynamic process. However, this paradigm cannot be considered thermodynamically consistent as it does not account for the thermodynamic cost of these measurements. To remedy this conceptual inconsistency we introduce a novel paradigm that relies only on the expected change of the average energy given the initial energy eigenbasis. In particular, we completely omit quantum measurements in the definition of quantum work, and hence quantum work is identified as a thermodynam…
Despite progress in quantum Hamiltonian complexity, little is known about the computational complexity of quantum physics at the thermodynamic limit. Even defining the problem is not straight forward. We study the complexity of estimating the ground energy of a fixed, translationally invariant Hamiltonian in the thermodynamic limit, to within a given precision; the number of bits $n$ for the precision is the sole input to the problem. The complexity of this problem captures how difficult it is for the physicist to measure or compute another digit in the approximation of a physical quantity in …
Dissipative adaptation is a general thermodynamic mechanism that explains self-organization in a broad class of driven classical many-body systems. It establishes how the most likely (adapted) states of a system subjected to a given drive tend to be those following trajectories of highest work absorption, followed by dissipated heat to the reservoir. Here, we extend the dissipative adaptation phenomenon to the quantum realm. We employ a fully-quantized exactly solvable model, where the source of work on a three-level system is a single-photon pulse added to a zero-temperature infinite environm…
Mechanics can be founded on a principle relating the uncertainty delta-q in the trajectory of an observable particle to its motion relative to the observer. From this principle, p.delta-q=const., p being the q-conjugated momentum, mechanical laws are derived and the meaning of the Lagrangian and Hamiltonian functions are discussed. The connection between the presented principle and Hamilton's Least Action Principle is examined. Wave mechanics and Schrodinger equation appear without additional assumptions by choosing the representation for delta-q in the case the motion is not trajectory descri…
The nonequilibrium thermodynamics of an open (classical or quantum) system in strong contact with a single heat bath can be conveniently described in terms of the Hamiltonian of mean force. However, the conventional formulation is limited by the necessity to measure differences in equilibrium properties of the system-bath composite. We make use of the freedom involved in defining thermodynamic quantities, which leaves the thermodynamics unchanged, to show that the Hamiltonian of mean force can be inferred from measurements on the system alone, up to that irrelevant freedom. In doing so, we ref…
We develop the strong coupling quantum thermodynamics based on the solution of the exact master equation. We find that both the Hamiltonian and the temperature must be renormalized due to the system-reservoir couplings. With the renormalized Hamiltonian and temperature, the exact steady state of open quantum systems can be expressed as a standard Gibbs state. The exact steady-state particle distributions obey the Bose-Einstein distribution or the Fermi-Dirac distribution only for the renormalized energy and temperature. In this formulation, heat and work are quantum mechanically defined, from …
We study the quantum entropy of systems that are described by general non-Hermitian Hamiltonians, including those which can model the effects of sinks or sources. We generalize the von Neumann entropy to the non- Hermitian case and find that one needs both the normalized and non-normalized density operators in order to properly describe irreversible processes. It turns out that such a generalization monitors the onset of disorder in quantum dissipative systems. We give arguments for why one can consider the generalized entropy as the informational entropy describing the flow of information bet…
Quantum systems driven by time-dependent Hamiltonians are considered here within the framework of steepest-entropy-ascent quantum thermodynamics (SEAQT) and used to study the thermodynamic characteristics of such systems. In doing so, a generalization of the SEAQT framework valid for all such systems is provided, leading to the development of an ab initio physically relevant expression for the intra-relaxation time, an important element of this framework and one that had as of yet not been uniquely determined as an integral part of the theory. The resulting expression for the relaxation time i…
Thermodynamic entropy is not an entirely satisfactory measure of information of a quantum state. This entropy for an unknown pure state is zero, although repeated measurements on copies of such a pure state do communicate information. In view of this, we propose a new measure for the informational entropy of a quantum state that includes information in the pure states and the thermodynamic entropy. The origin of information is explained in terms of an interplay between unitary and non-unitary evolution. Such complementarity is also at the basis of the so-called interaction-free measurement.
Information Processing in Quantum Thermodynamic Systems: an Autonomous Hamiltonian Approach
University of Massachusetts, Boston（马萨诸塞大学波士顿分校）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；University of Maryland, Baltimore County（马里兰大学巴尔的摩分校）；Quantum Science Institute, University of Maryland, Baltimore County（马里兰大学巴尔的摩分校量子科学研究所）
Operational quantum stochastic thermodynamics is a recently proposed theory to study the thermodynamics of open systems based on the rigorous notion of a quantum stochastic process or quantum causal model. In there, a stochastic trajectory is defined solely in terms of experimentally accessible measurement results, which serve as the basis to define the corresponding thermodynamic quantities. In contrast to this observer-dependent point of view, a `black box', which evolves unitarily and can simulate a quantum causal model, is constructed here. The quantum thermodynamics of this big isolated s…
We investigate further the relationship between the entanglement spectrum of a composite many-body system and the energy spectrum of a subsystem making use of concepts of canonical thermodynamics. In many important cases the entanglement Hamiltonian is, in the limit of strong coupling between subsystems, proportional to the energy Hamiltonian of the subsystem. The proportionality factor is an appropriately defined coupling parameter, suggesting to interpret the latter as a inverse temperature. We identify a condition on the entanglement Hamiltonian which rigorously guarantees this interpretati…
Noncommuting conserved quantities have recently launched a subfield of quantum thermodynamics. In conventional thermodynamics, a system of interest and an environment exchange quantities -- energy, particles, electric charge, etc. -- that are globally conserved and are represented by Hermitian operators. These operators were implicitly assumed to commute with each other, until a few years ago. Freeing the operators to fail to commute has enabled many theoretical discoveries -- about reference frames, entropy production, resource-theory models, etc. Little work has bridged these results from ab…
Non-Hermitian Hamiltonians possessing a discrete real spectrum motivated a remarkable research activity in quantum physics and new insights have emerged. In this paper we formulate concepts of statistical thermodynamics for systems described by non-Hermitian Hamiltonians with real eigenvalues. We mainly focus on the case where the energy and another observable are the conserved quantities. The notion of entropy and entropy inequalities are central in our approach, which treats equilibrium thermodynamics.
The fabrication, utilisation, and efficiency of quantum technologies rely on a good understanding of quantum thermodynamic properties. Many-body systems are often used as hardware for these quantum devices, but interactions between particles make the complexity of related calculations grow exponentially with the system size. Here we explore and systematically compare `simple' and `hybrid' approximations to the average work and entropy variation built on static density functional theory concepts. These approximations are computationally cheap and could be applied to large systems. We exemplify …
By solving the exact master equation of open quantum systems, we formulate the quantum thermodynamics from weak to strong couplings. The open quantum systems exchange matters, energies and information with their reservoirs through quantum particles tunnelings that are described by the generalized Fano-Anderson Hamiltonians. We find that the exact solution of the reduced density matrix of these systems approaches a Gibbs-type state in the steady-state limit for both the weak and strong system-reservoir coupling strengths. When the couplings become strong, thermodynamic quantities of the system …
We define a diagonal entropy (d-entropy) for an arbitrary Hamiltonian system as $S_d=-\sum_n ρ_{nn}\ln ρ_{nn}$ with the sum taken over the basis of instantaneous energy states. In equilibrium this entropy coincides with the conventional von Neumann entropy $S_n=-{\rm Tr}\, ρ\lnρ$. However, in contrast to $S_n$, the d-entropy is not conserved in time in closed Hamiltonian systems. If the system is initially in stationary state then in accord with the second law of thermodynamics the d-entropy can only increase or stay the same. We also show that the d-entropy can be expressed through the energy…
The information on a quantum process acquired through measurements plays a crucial role in the determination of its non-equilibrium thermodynamic properties. We report on the experimental inference of the stochastic entropy production rate for a continuously monitored mesoscopic quantum system. We consider an optomechanical system subjected to continuous displacement Gaussian measurements and characterise the entropy production rate of the individual trajectories followed by the system in its stochastic dynamics, employing a phase-space description in terms of the Wigner entropy. Owing to the …
