QUANTUM LIMITS TO THE SECOND LAW: First International Conference on Quantum Limits to the Second Law

Quantum Fluctuation Dissipation Relations and the Second Law
View Description Hide DescriptionThe fluctuation‐dissipation relations (FDR) are studied at all levels of the statistical description. The most general FDR are the relations for the fluctuations of many‐body distribution functions. In all cases it is in agreement with the second law of thermodynamics.

Quantum Wave Packet Dynamics: Langevin Equations for Hamiltonian Systems Imbedded into a Heat Bath
View Description Hide DescriptionIn the last decade the relation beween classical and quantum statistics was carefully investigated. Here we study this problem by making use of a wave packet dynamics. We discuss temperature definitions, fluctuation‐dissipation theorems and Langevin equations. The theory is applied to oscillators and atomic electrons embedded into an infinite bath of oscillators.

Dissipative Quantum Dynamics from Wigner Distributions
View Description Hide DescriptionThe short‐memory approximation, a constructive procedure to derive dissipative equations for the macroscopic evolution of micro‐reversible dynamical systems, is applied to the Wigner formulation of quantum mechanics. The dissipative dynamics of a single quantum particle in a confining external potential is shown to take the form of a damped harmonic oscillator whose effective frequency and damping coefficients depend on the shape of the quantum‐mechanical potential.

Heat Flux between Quantum Systems
View Description Hide DescriptionWe consider a composite system consisting of two identical quantum systems. Initially the two subsystems are separated so that the initial state of the system is a product state, and we assume that both factors are canonical equilibrium states, but at different temperatures. Then the two systems are thermally coupled which we describe by a certain class of interactions. We show ‐ at least numerically ‐ the following version of the second law: heat flows always from the hotter to the colder system.

Quantum Brownian motion and its conflict with the second law
View Description Hide DescriptionThe Brownian motion of a harmonically bound quantum particle and coupled to a harmonic quantum bath is exactly solvable. At low enough temperatures the stationary state is non‐Gibbsian due to an entanglement with the bath. This happens when a cloud of bath modes around the particle is formed. Equilibrium thermodynamics for particle plus bath together, does not imply standard thermodynamics for the particle itself at low T. Various formulations of the second law are then invalid. First, the Clausius inequality can be violated. Second, when the width of the confining potential is suddenly changed, there occurs a relaxation to equilibrium during which the rate of entropy production is partly negative. Third, for non‐adiabatic changes of system parameters the rate of energy dissipation can be negative, and, out of equilibrium, cyclic processes are possible which extract work from the bath. Conditions are put forward under which perpetuum mobile of the second kind, having several work extraction cycles, enter the realm of condensed matter physics.

Thomson’s formulation of the second law: an exact theorem and limits of its validity
View Description Hide DescriptionThomson’s formulation of the second law ‐ no work can be extracted from a system coupled to a bath through a cyclic process ‐ is believed to be a fundamental principle of nature. For the equilibrium situation a simple proof is presented, valid for macroscopic sources of work. Thomson’s formulation gets limited when the source of work is mesoscopic, i.e. when its number of degrees of freedom is large but finite. Here work‐extraction from a single equilibrium thermal bath is possible when its temperature is large enough. This result is illustrated by means of exactly solvable models. Finally we consider the Clausius principle: heat goes from high to low temperature. A theorem and some simple consequences for this statement are pointed out.

A Thermodynamical Formulation of Quantum Information
View Description Hide DescriptionWe show that quantum entanglement can be understood and quantified using the same axiomatic approach to thermodynamics pioneered by Caratheodory and later extended by Buchdahl and Giles. This leads to the existence of a unique measure of entanglement for pure states of systems consisting of two subsystems, analogous to the thermodynamical entropy. Thermodynamics and (quantum) information are seen to be just two different manifestations of ordering of (abstract) states connected by (abstract) processes.

Aspects of the Second Law of Thermodynamics from Quantum Statistical Mechanics to Quantum Information Theory
View Description Hide DescriptionThe Kullback ‐ Leibler inequality is a way of comparing any two density matrices. A technique to set up the density matrix for a physical system is to use the maximum entropy principle, given the entropy as a functional of the density matrix, subject to known constraints. In conjunction with the master equation for the density matrix, these two ingredients allow us to formulate the second law of thermodynamics in its widest possible setting. Thus problems arising in both quantum statistical mechanics and quantum information can be handled. Aspects of thermodynamic concepts such as the Carnot cycle will be discussed. A model is examined to elucidate the role of entanglement in the Landauer erasure problem.

Hopf algebra, thermodynamics and entanglement in quantum field theory
View Description Hide DescriptionThe quantum deformation of the Hopf algebra describes the skeleton of quantum field theory, namely its characterizing feature consisting in the existence of infinitely many unitarily inequivalent representations of the canonical commutation relations. From this we derive the thermal properties of quantum field theory, with the entropy playing the role of the generator of the non‐unitary time evolution. The entanglement of the quantum vacuum appears to be robust against interaction with the environment: on cannot “unknot the knots” in the infinite volume limit.

Microscopic dynamical entropy and nonlocality
View Description Hide DescriptionRecent developments on the complex spectral representation of the evolution operators have shown that irreversibility is a rigorous dynamical process that takes place outside the Hilbert space for non‐integrable systems, both classical and quantum. Irreversibility is a direct consequence of microscopic dynamical processes associated with resonance singularities, rather than our incomplete knowledge. We discuss the excitation process of a quantum unstable particle by scattering of a wave packet. Using complex eigenstates of the Hamiltonian one may construct a microscopic dynamical entropy (or function) without any approximation. In order to have scattering, one has to target the wave packet to the particle. This introduces a nonlocal pre‐collisional correlation giving a low dynamical entropy. During the moment the excited particle is created, there appears an entropy flow from the field to the particle. This lowers the particle component of the entropy, even though the total entropy production is always positive. This implies that the excitation of the particle may be considered as the construction of a non‐equilibrium structure due to entropy flow.

The Second Law and the Extension of Quantum Mechanics
View Description Hide DescriptionThe compatibility of irreversibility, as expressed by the second law of thermodynamics, with ordinary quantum mechanics is a challenging problem. Our solution requires an extension of the latter. Such an extension of a reversible formalism is made possible by the presence of self‐energy processes (already found in quantum electrodynamics) which enables the widening of the dynamics by the introduction of specific additionnal variables leading to the recognition of such processes. A projection technique modeled on the one introduced long ago by the Brussels group defines a subdynamics which is shown to contain entirely the starting formulation (it corresponds now to a restricted class of initial conditions, namely the reversible one). A new kinetic description is obtained in which e.g. collision processes for privileged components arise from the original interaction. This method is applied successively to various models and we focus in this paper on the possible presence of temporal behaviours excluded in ordinary quantum mechanics. Among those differences, the possibility appears of a purely exponential decay for a particle while ordinary quantum mechanics requires long time tails associated with the finite lower bound in the spectrum of the Hamiltonian.

Decoherence, Wave‐Function Collapses, Non‐Ordinary Statistical Mechanics and the Second Principle
View Description Hide DescriptionWe show that the derivation of Lévy statistics from a Liouville‐like approach is still an unresolved problem, even though a satisfactory derivation resting on the Generalized Central Limit Theorem (GCLT) has been obtained. We discuss a quantum relaxation that according to the supposed equivalence between decoherence theory and wave function collapses is expected to be equivalent to the characteristic function of a Lévy process. We notice that this way of proceeding is equivalent to establishing a finite Kolmogorov‐Sinai (KS) entropy, and consequently, a condition compatible with the Second Principle of Thermodynamics even though the connection between this kind of entropy and the Clausius entropy is not yet known. The quantum treatment, based on density rather than the collapse‐induced symbolic sequences, conflicts with this conclusion.

Dynamically Delocalized State and Classicalization of the Quantum Wavepacket
View Description Hide DescriptionWe consider quantum diffusion of the initially localized wave packet in a kicked one‐dimensional disordered system with classical coherent perturbation. The wave packet is delocalized by coupling with time‐dependent perturbation. We numerically show the delocalization and discuss a relation between the “classicalization” of the quantum wave packet and the time‐dependence of the initial phase sensitivity.

Extracting Work from a Single Heat Bath via Vanishing Quantum Coherence II: Microscopic Model
View Description Hide DescriptionIn a recent paper a quantum heat engine operating on radiation pressure from a single mode radiation field which drives a piston engine was presented. A thermally excited atomic beam serves as the high temperature energy source and a lower temperature heat bath acts as the entropy sink. We here extend the previous macroscopic (quantum thermodynamical) analysis by developing a microscopic (quantum statistical) analysis. This provides insight into engine operation and questions related to the second law. The same quantum phase effects that yield lasing without inversion and ultraslow light, also make possible extensions of Carnot cycle operation; e.g., extraction of energy from a single heat bath, and efficiency beyond the Carnot limit.

The Photo‐Carnot Cycle: The Preparation Energy for Atomic Coherence
View Description Hide DescriptionWe consider a Carnot cycle engine in which the working medium is a photon gas inside a cavity with perfectly reflecting walls. The thermal baths responsible for supplying heat to the radiation field is a stream of three‐level atoms. The phase of the atomic coherence provides a new and interesting control parameter. Here we discuss the questions pertaining to the preparation energy of atomic coherence with an explicit calculation of the associated entropy change.

Dimer as a Challenge to the Second law
View Description Hide DescriptionEven such a simple system as an asymmetric dimer cooperating with two baths can be used to challenge the Second law of thermodynamics. Only a specific coupling to the baths and a specific regime is needed.

An exactly solvable model of quantum relaxation: Check of the modified Davies weak coupling theory
View Description Hide DescriptionA model for stationary electronic transport through a one‐dimensional chain of two leads attached to a perturbed central region (quantum dot) is presented. In the investigated regime a theory for a similar model of phonon transport recently proposed by Čápek predicts a striking phenomenon of permanent current between the leads. This result, based on a rigorous but asymptotic Davies theory, is in contradiction to the zero current yielded by direct transport calculations which can be carried out in the presented model. The permanent current is found to be within the error of the asymptotic expansion for finite couplings, and cancelling terms of the same order are identified.

Role of electronic‐vibrational interaction in the short‐time coherent and long‐time dissipative dynamics of energy relaxation
View Description Hide DescriptionTime dynamics of two electronic states (e.g. ground and excited states) coupled to a harmonic vibrational mode is investigated. The relaxation of vibrational energy is of the zeroth‐order in a vibration‐induced coupling of electronic states. Depending on model parameters of the electronic‐vibrational interaction various curves of occupation probability of the excited electronic state were found, but in general, three time intervals were observed: a) For short times, coherent oscillations strongly corelated with vibrational dynamics are observed. b) For longer times, the occupation probability decays almost exponentially with a rate constant increasing with the rate of vibrational relaxation and electronic‐vibrational interaction. c) For asymptotically long times, a non‐zero excited state occupation probability is found even for low temperature, which is in a contradiction with the canonical Boltzmann distribution. The role of parameters and type of the electronic‐vibrational interaction is discussed. When the radiative transition from the excited to the ground state is taken into account the excited state population decreases. Intensity of this process is discussed.

Integrable Quantum Mechanics, the Permutation Group and the Second Law
View Description Hide DescriptionGiven an integrable (solvable) quantum system with many equivalent degrees of freedom it is inevitable that consideration of the permutation group will arise. For example the least degenerate stationary states of the system must fall into irreducible representations of the permutation group. The ground state, as well as a class of low‐lying excited states, must fall into a particular irreducible representation. It will be demonstrated that a superposition of states within this representation leads to marginal probability distributions (partial traces), which are time‐independent. These marginal probability distributions are constant in time, but not in space. They provide a resource that can be exploited in reversible quasi‐static (equilibrium) changes of state, i.e. they are a quantum contribution to the entropy. They are necessarily an essential part of any quantum statement of the second law.

Thermal Equilibrium as a Local Phenomenon
View Description Hide DescriptionIt is possible for a pseudo‐equilibrium to be achieved locally even if conservation laws or dissipative processes prevent the establishment of thermal equilibrium globally. Thus, in general, there is no compelling reason to expect the Second Law to apply globally ‐ although it generally does. We illustrate using some toy‐model examples that are simple to work out.