We revisit here the effect of quantum dissipation on the much - studied problem of Landau diamagnetism, and analyze the results in the light of the third law of thermodynamics. The case of an additional parabolic potential is separately assessed. We find that dissipation arising from strong coupling of the system to its environment qualitatively alters the low-temperature thermodynamic attributes such as the entropy and the specific heat.
Using the path integral approach to equilibrium statistical physics the effect of dissipation on Landau diamagnetism is calculated. The calculation clarifies the essential role of the boundary of the container in which the electrons move. Further, the derived result for diamagnetization also matches with the expression obtained from a time-dependent quantum Langevin equation in the asymptotic limit, provided a certain order is maintained in taking limits. This identification then unifies equilibrium and nonequilibrium statistical physics for a phenomenon like diamagnetism, which is inherently …
In this work, low temperature thermodynamic behaviour in the context of dissipative diamagnetism with anomalous coupling is analyzed. We find that finite dissipation substitutes the zero-coupling result of exponential decay of entropy by a power law behaviour at low temperature. For Ohmic bath, entropy vanishes linearly with temperature, $T$, in conformity with Nernst's theorem. It is also shown that entropy decays faster in the presence of anomalous coupling than that of the usual coordinate-coordinate coupling. It is observed that velocity-velocity coupling is the most advantageous coupling …
In this paper, Landau diamagnetism is revisited in the context of nonextensive statistical thermodynamics. Exact as well as approximate expressions for partition function, magnetization and susceptibility are obtained by using Hilhorst integral transformation which provides exact solutions in the framework of Tsallis statistics. The results have been reassessed with the standard results to illustrate the effect of nonextensivity.
Starting from a quantum Langevin equation (QLE) of a charged particle coupled to a heat bath in the presence of an external magnetic field, we present a fully dynamical calculation of the susceptibility tensor. We further evaluate the position autocorrelation function by using the Gibbs ensemble approach. This quantity is shown to be related to the imaginary part of the dynamical susceptibility, thereby validating the fluctuation-dissipation theorem in the context of dissipative diamagnetism. Finally we present an overview of coherence-to-decoherence transition in the realm of dissipative diam…
We consider the behavior of electrons in an external uniform magnetic field B where the space coordinates perpendicular to B are taken as noncommuting. This results in a generalization of standard thermodynamics. Calculating the susceptibility, we find that the usual Landau diamagnetism is modified. We also compute the susceptibility according to the nonextensive statistics of Tsallis for (1-q)<<1, in terms of the factorization approach. Two methods agree under certain conditions.
We consider a gas of quasi-free quantum particles confined to a finite box, subjected to singular magnetic and electric fields. We prove in great generality that the finite volume grand-canonical pressure is jointly analytic in the chemical potential ant the intensity of the external magnetic field. We also discuss the thermodynamic limit.
We address the issue of generalizing the thermodynamic quantities via $q$-deformation, i.e., via the $q$-algebra that describes $q$-bosons and $q$-fermions. In this study with the application of $q$-deformation to the Landau diamagnetism problem in two dimensions, embedded in a $D$-dimensional space, we will attempt to get a better understanding of the $q$-deformation. We obtain new results for q-deformed internal energy, number of particles, magnetization and magnetic susceptibility, which recover the values already known in the literature in the limit $q\to1$.
We investigate two prototypical dissipative bosonic systems under slow driving and arbitrary system-bath coupling strength, recovering their dynamic evolution as well as the heat and work rates, and we verify that thermodynamic laws are respected. Specifically, we look at the damped harmonic oscillator and the damped two-level system. For the former, we study independently the slow time- dependent perturbation in the oscillator frequency and in the coupling strength. For the latter, we concentrate on the slow modulation of the energy gap between the two levels. Importantly, we are able to find…
The standard {\em system-plus-reservoir} approach used in the study of dissipative systems can be meaningfully generalized to a dissipative coupling involving the momentum, instead of the coordinate: the corresponding equation of motion differs from the Langevin equation, so this is called {\em anomalous} dissipation. It occurs for systems where such coupling can indeed be derived from the physical analysis of the degrees of freedom which can be treated as a dissipation bath. Starting from the influence functional corresponding to anomalous dissipation, it is shown how to derive the effective …
Thermodynamics and transport properties of a dissipative particle in a tight-binding model are studied through specific heat and optical conductivity. A weak coupling theory is constituted to study the crossover behavior between the low-temperature region and the high-temperature region analytically. We found that coherent part around zero frequency in the optical conductivity disappears for 0<s<2, where s is an exponent of a spectral function of the environment. Detailed calculation is performed for ohmic damping (s=1). In this case, the specific heat shows an unusual $T$-linear behavior at l…
Dissipative effects in electromagnetism on macroscopic scales are examined by coarse graining the microscopic Maxwell equations with respect to time. We illustrate a procedure to derive the dissipative effects on the macroscopic scale by using a Green-Kubo type expression in terms of the microscopic fluctuations and the correlations between them. The resulting macroscopic Maxwell equations are formulated within the General Equation for the Non-Equilibrium Reversible-Irreversible Coupling (GENERIC) framework, accounting also for inhomogeneous temperature.
In this work we explore the use of thermodynamic length to improve the performance of experimental protocols. In particular, we implement Landauer erasure on a driven electron level in a semiconductor quantum dot, and compare the standard protocol in which the energy is increased linearly in time with the one coming from geometric optimisation. The latter is obtained by choosing a suitable metric structure, whose geodesics correspond to optimal finite-time thermodynamic protocols in the slow driving regime. We show experimentally that geodesic drivings minimise dissipation for slow protocols, …
On the one hand, the dissipated heat of a thermodynamic work extraction process upper bounds the non-predictive information, which the associated system encodes about its environment. Thus, emergent information processing capabilities can be understood from the perspective of a pressure towards high thermodynamic efficiency. On the other hand, the second law of thermodynamics plays a crucial role in the emergence of complex, self-organising dissipative structures. Such structures are thermodynamically favoured, because they can dissipate free energy reservoirs, which would not be accessible ot…
Variational principles play a fundamental role in deriving evolution equations of physics. They are working well in case of nondissipative evolution but for dissipative systems they are not unique, not predictive and not constructive. With methods of modern nonequilibrium thermodynamics, one can derive evolution equations for dissipative phenomena and, surprisingly, can also reproduce the Euler-Lagrange form of the evolution equations for ideal processes. In this work, we examine some demonstrative examples and compare thermodynamic and variational techniques. Then, we argue that instead of se…
Chemical processes in closed systems are poorly controllable since they always relax to equilibrium. Living systems avoid this fate and give rise to a much richer diversity of phenomena by operating under nonequilibrium conditions. Recent experiments in dissipative self-assembly also demonstrated that by opening reaction vessels and steering certain concentrations, an ocean of opportunities for artificial synthesis and energy storage emerges. To navigate it, thermodynamic notions of energy, work and dissipation must be established for these open chemical systems. Here, we do so by building upo…
We consider quantum nonlinear many-body systems with dissipation described within the Caldeira-Leggett model, i.e., by a nonlocal action in the path integral for the density matrix. Approximate classical-like formulas for thermodynamic quantities are derived for the case of many degrees of freedom, with general kinetic and dissipative quadratic forms. The underlying scheme is the pure-quantum self-consistent harmonic approximation (PQSCHA), equivalent to the variational approach by the Feynman-Jensen inequality with a suitable quadratic nonlocal trial action. A low-coupling approximation permi…
Classical-like formulas are given in order to evaluate thermal averages of observables belonging to a quantum nonlinear system with dissipation described by the Caldeira-Leggett model [Phys. Rev. Lett. 46, 211 (1981); Ann. Phys. (N.Y.) 149, 374 (1983)]. The underlying scheme is the pure-quantum self-consistent harmonic approximation, which leads to expressions with a Boltzmann factor involving an effective potential and with a Gaussian average. The latter describes the effect of the fluctuations of purely quantum origin. As an illustration we calculate the coordinate probability distribution f…
The state function entropy and its quantum thermodynamical implication for two typical dissipative systems with anomalous spectral densities are studied by investigating on their low-temperature quantum behavior. In all cases it is found that the entropy decays quickly and vanishes as the temperature approaches zero. This reveals a good conformity with the third law of thermodynamics and provides another evidence for the validity of fundamental thermodynamical laws in the quantum dissipative region.
How can we derive the evolution equations of dissipative systems? What is the relation between the different approaches? How much do we understand the fundamental aspects of a second law based framework? Is there a hierarchy of dissipative and ideal theories at all? How far can we reach with the new methods of nonequilibrium thermodynamics?
A novel experimental paradigm and a novel modelling approach are presented to investigate oscillatory human motor performance by means of a key concept from condensed matter physics, namely, thermodynamic state variables. To this end, in the novel experimental paradigm participants performed pendulum swinging movements at self-selected oscillation frequencies in contrast to earlier studies in which pacing signals were used. Moreover, in the novel modelling approach, a canonical-dissipative limit cycle oscillator model was used with a conservative part that accounts for nonharmonic oscillator c…
New exact results about the nonequilibrium thermodynamics of open quantum systems at arbitrary timescales are obtained by considering all possible variations of initial conditions of a system, its environment, and correlations between them. First we obtain a new quantum-information theoretic equality for entropy production, valid for an arbitrary initial joint state of system and environment. For any finite-time process with a fixed initial environment, we then show that the contraction of the system's distinction -- relative to the minimally dissipative state -- exactly quantifies its thermod…
The thermodynamic uncertainty relations (TURs), originally discovered for classical systems, dictate the trade-off between dissipation and fluctuations of irreversible current, specifying a minimal bound that constrains the two quantities. In a series of effort to extend the relation to the one under more generalized conditions, it has been noticed that the bound is less tight in open quantum processes. To study the origin of the loose bounds, we consider an external field-driven transition dynamics of two-level quantum system weakly coupled to the bosonic bath as a model of open quantum syste…
Chern-Simons gauge field theory has provided a natural framework to gain deep insight about many novel phenomena in two-dimensional condensed matter. We investigate the nonequilibrium thermodynamics properties of a (two-dimensional) dissipative harmonic particle when the Abelian topological gauge action and the (linear) Brownian motion dynamics are treated on an equal footing. We find out that the particle exhibits remarkable magneticlike features in the quantum domain that are beyond the celebrated Landau diamagnetism: this could be viewed as the non-relativistic Brownian counterpart of the c…
Wasserstein-2 gradient flows and the geometry of entropy production in classical and quantum stochastic thermodynamics
Universidad de La Laguna（拉古纳大学）；Instituto Universitario de Estudios Avanzados (IUdEA), Universidad de La Laguna（拉古纳大学高级研究研究所）；University of California, Irvine（加州大学尔湾分校）；ICREA-Complex Systems Lab, Pompeu Fabra University（庞培法布拉大学）；The University of Tokyo（东京大学）
We apply the large-deviation method to study trajectories in dissipative quantum systems. We show that in the long time limit the statistics of quantum jumps can be understood from thermodynamic arguments by exploiting the analogy between large-deviation and free-energy functions. This approach is particularly useful for uncovering properties of rare dissipative trajectories. We also prove, via an explicit quantum mapping, that rare trajectories of one system can be realized as typical trajectories of an alternative system.
We consider several low--dimensional chaotic maps started in far-from-equilibrium initial conditions and we study the process of relaxation to equilibrium. In the case of conservative maps the Boltzmann-Gibbs entropy S(t) increases linearly in time with a slope equal to the Kolmogorov-Sinai entropy rate. The same result is obtained also for a simple case of dissipative system, the logistic map, when considered in the chaotic regime. A very interesting results is found at the chaos threshold. In this case, the usual Boltzmann-Gibbs is not appropriate and in order to have a linear increase, as f…
Controlling thermodynamic cycles to minimize the dissipated heat is a longstanding goal in thermodynamics, and more recently, a central challenge in stochastic thermodynamics for nanoscale systems. Here, we introduce a theoretical and computational framework for optimizing nonequilibrium control protocols that can transform a system between two distributions in a minimally dissipative fashion. These protocols optimally transport a system along paths through the space of probability distributions that minimize the dissipative cost of a transformation. Furthermore, we show that the thermodynamic…
Thermodynamics of dissipative quantum systems with double-well potentials is studied by the path-integral Monte Carlo (PIMC) method without truncation to the two-state model. For efficient simulation at low temperatures, we develop a new scheme of local update based on approximate decomposition of the Boltzmann weight to the Gaussian distributions. Localization transition induced by ohmic dissipation is clarified numerically for arbitrary potential barriers.
Zhejiang Key Laboratory of Quantum State Control and Optical Field Manipulation, Department of Physics, Zhejiang Sci-Tech University（浙江理工大学物理系量子态控制与光场调控浙江省重点实验室）；School of Physics and Astronomy, Beijing Normal University（北京师范大学物理与天文学院）；Key Laboratory of Multiscale Spin Physics (Ministry of Education), Beijing Normal University（北京师范大学多尺度自旋物理教育部重点实验室）
The probability operator for a generic non-equilibrium quantum system is derived. The corresponding stochastic, dissipative Schrödinger equation is also given. The dissipative and stochastic propagators are linked by the fluctuation-dissipation theorem that is derived from the unitary condition on the time propagator. The dissipative propagator is derived from thermodynamic force and entropy fluctuation operators that are in general non-linear.
Using the quasi-equilibrium Helmholtz energy (qHE), defined as the thermodynamic work in a quasi-static process, we investigate the thermal properties of both an isothermal process and a transition process between the adiabatic and isothermal states (adiabatic transition). Here, the work is defined by the change in energy from a steady-state to another state under a time-dependent perturbation. In particular, the work for a quasi-static change is regarded as thermodynamic work. We employ a system--bath model that involves time-dependent perturbations in both the system and the system--bath int…
In macroscopic systems behavior is usually reproducible and fluctuations, which are deviations from the typically observed mean values, are small. But almost all inverse problems in the physical and biological sciences are ill-posed and these fluctuations are highly 'amplified'. Using stochastic thermodynamics we describe a system in equilibrium kicked to a state far from equilibrium and the following dissipative process back to equilibrium. From the observed value at a certain time after the kick the magnitude of the kick should be estimated, which is such an ill-posed inverse problem and flu…
Engineered dynamical maps combining coherent and dissipative transformations of quantum states with quantum measurements, have demonstrated a number of technological applications, and promise to be a crucial tool in quantum thermodynamic processes. Here, we exploit the control on the effective open spin qutrit dynamics of an NV center, to experimentally realize an autonomous feedback process (Maxwell demon) with tunable dissipative strength. The feedback is enabled by random measurement events that condition the subsequent dissipative evolution of the qutrit. The efficacy of the autonomous Max…
In this work, we expose the role of environment, confinement and external magnetic field ($B$) in determining the low temperature thermodynamic behaviour in the context of cyclotron motion of a charged oscillator with anomalous dissipative coupling involving the momentum instead of the much studied coordinate coupling. Explicit expressions for different quantum thermodynamic functions (QTF) are obtained at low temperatures for different quantum heat bath characterized by spectral density function, $μ(ω)$. The power law fall of different QTF are in conformity with third law of thermodynamics. B…
The quantum thermodynamic property of the fractional damping system is investigated extensively. A fractional power-law decaying entropy function is revealed which presents another evidence for the validity of the third law of thermodynamics in the quantum dissipative region. Several non-trivial characters are excavated such as that the entropy varies from a non-linear diverging function to a semi-linear decaying function of the fractional exponent as the temperature tends to absolute zero.
