Maxwell's Demon Research Articles

Maxwell's Demon in Quantum Mechanics.

Maxwell’s Demon is a thought experiment devised by J. C. Maxwell in 1867 in order to show that the Second Law of thermodynamics is not universal, since it has a counter-example. Since the Second Law is taken by many to provide an arrow of time, the threat to its universality threatens the account of temporal directionality as well. Various attempts to “exorcise” the Demon, by proving that it is impossible for one reason or another, have been made throughout the years, but none of them were successful. We have shown (in a number of publications) by a general state-space argument that Maxwell’s Demon is compatible with classical mechanics, and that the most recent solutions, based on Landauer’s thesis, are not general. In this paper we demonstrate that Maxwell’s Demon is also compatible with quantum mechanics. We do so by analyzing a particular (but highly idealized) experimental setup and proving that it violates the Second Law. Our discussion is in the framework of standard quantum mechanics; we give two separate arguments in the framework of quantum mechanics with and without the projection postulate. We address in our analysis the connection between measurement and erasure interactions and we show how these notions are applicable in the microscopic quantum mechanical structure. We discuss what might be the quantum mechanical counterpart of the classical notion of “macrostates”, thus explaining why our Quantum Demon setup works not only at the micro level but also at the macro level, properly understood. One implication of our analysis is that the Second Law cannot provide a universal lawlike basis for an account of the arrow of time; this account has to be sought elsewhere.

Soliton Maxwell demons and long-tailed statistics in fluctuating optical fields.

We demonstrate experimentally in biased photorefractive crystals that collisions between random-amplitude optical spatial solitons produce long-tailed statistics from input Gaussian fluctuations. The effect is mediated by Raman nonlocal corrections to Kerr self-focusing that turn soliton-soliton interaction into a Maxwell demon for the output wave amplitude.

Steering Heat Engines: A Truly Quantum Maxwell Demon.

We address the question of verifying the quantumness of thermal machines. A Szilárd engine is truly quantum if its work output cannot be described by a local hidden state model, i.e., an objective local statistical ensemble. Quantumness in this scenario is revealed by a steering-type inequality which bounds the classically extractable work. A quantum Maxwell demon can violate that inequality by exploiting quantum correlations between the work medium and the thermal environment. While for a classical Szilárd engine an objective description of the medium always exists, any such description can be ruled out by a steering task in a truly quantum case.

Measurement Induced Synthesis of Coherent Quantum Batteries

Quantum coherence represented by a superposition of energy eigenstates is, together with energy, an important resource for quantum technology and thermodynamics. Energy and quantum coherence however, can be complementary. The increase of energy can reduce quantum coherence and vice versa. Recently, it was realized that steady-state quantum coherence could be autonomously harnessed from a cold environment. We propose a conditional synthesis of N independent two-level systems (TLS) with partial quantum coherence obtained from an environment to one coherent system using a measurement able to increase both energy and coherence simultaneously. The measurement process acts here as a Maxwell demon synthesizing the coherent energy of individual TLS to one large coherent quantum battery. The measurement process described by POVM elements is diagonal in energy representation and, therefore, it does not project on states with quantum coherence at all. We discuss various strategies and their efficiency to reach large coherent energy of the battery. After numerical optimization and proof-of-principle tests, it opens way to feasible repeat-until-success synthesis of coherent quantum batteries from steady-state autonomous coherence.

Nonequilibrium System as a Demon.

Maxwell demons are creatures that are imagined to be able to reduce the entropy of a system without performing any work on it. Conventionally, such a Maxwell demon's intricate action consists of measuring individual particles and subsequently performing feedback. We show that much simpler setups can still act as demons: we demonstrate that it is sufficient to exploit a nonequilibrium distribution to seemingly break the second law of thermodynamics. We propose both an electronic and an optical implementation of this phenomenon, realizable with current technology.

Autonomous conversion of information to work in quantum dots

We consider an autonomous implementation of Maxwell's demon in a quantum dot architecture. As in the original thought experiment, only the second law of thermodynamics is seemingly violated when disregarding the demon. The autonomous architecture allows us to compare descriptions in terms of information to a more traditional, thermoelectric characterization. Our detailed investigation of information-to-work conversion is based on fluctuation relations and second law like inequalities in addition to the average heat and charge currents. By introducing a time-reversal on the level of individual electrons, we find a novel fluctuation relation that is not connected to any symmetry of the moment generating function of heat and particle flows. Furthermore, we show how an effective Markovian master equation with broken detailed balance for the system alone can emerge from a full description, allowing for an investigation of the entropic cost associated to breaking detailed balance. Interestingly, while the entropic cost of performing a perfect measurement diverges, the entropic cost of breaking detailed balance does not. Our results connect various approaches and idealized scenarios found in the literature and can be tested experimentally with present day technology.

Stochastic thermodynamics with arbitrary interventions.

We extend the theory of stochastic thermodynamics in three directions: (i) instead of a continuously monitored system we consider measurements only at an arbitrary set of discrete times, (ii) we allow for imperfect measurements and incomplete information in the description, and (iii) we treat arbitrary manipulations (e.g., feedback control operations) which are allowed to depend on the entire measurement record. For this purpose we define for a driven system in contact with a single heat bath the four key thermodynamic quantities-internal energy, heat, work, and entropy-along a single "trajectory" for a causal model. The first law at the trajectory level and the second law on average is verified. We highlight the special case of Bayesian or "bare" measurements (incomplete information, but no average disturbance) which allows us to compare our theory with the literature and to derive a general inequality for the estimated free energy difference in Jarzynski-type experiments. An analysis of a recent Maxwell demon experiment using real-time feedback control is also given. As a mathematical tool, we prove a classical version of Stinespring's dilation theorem, which might be of independent interest.

Maxwell's Demons with Finite Size and Response Time.

Nearly all theoretical analyses of Maxwell's demon focus on its energetic and entropic costs of operation. Here, we focus on its rate of operation. In our model, a demon's rate limitation stems from its finite response time and gate area. We determine the rate limits of mass and energy transfer, as well as entropic reduction for four such demons: those that select particles according to (1)direction, (2)energy, (3)number, and (4)entropy. Last, we determine the optimal gate size for a demon with small, finite response time, and compare our predictions with molecular dynamics simulations with both ideal and nonideal gasses. Also, we study the conditions under which the demons are able to move both energy and particles in the chosen direction when attempting to only move one.

Work extraction, information-content and the Landauer bound in the continuous Maxwell Demon

In a recent paper we introduced a continuous version of the Maxwell demon (CMD) that is capable of extracting large amounts of work per cycle by repeated measurements of the state of the system Ribezzi-Crivellari and Ritort (2019 Nat. Phys.). Here we underline its main features such as the role played by the Landauer limit in the average extracted work, the continuous character of the measurement process and the differences between our continuous Maxwell demon and an autonomous Maxwell demon. We demonstrate the reversal of Landauer’s inequality depending on the thermodynamical and mechanical stability of the work extracting substance. We also emphasize the robustness of the Shannon definition of the information-content of the stored sequences in the limit where work extraction is maximal and fueled by the large information-content of rare events.

A Look at the Uncertainty of Measuring The Fundamental Constants and the Maxwell Demon from the Perspective of the Information Approach

This paper proposes a new framework for calculating the discrepancy of a model and the observed technological process or physical phenomenon. It offers powerful tools for all measurement methods applied in technology, engineering and experimental physics. Since the studies that validate and verificate the models of the phenomenon are still complex, they need to be combined into one total measure. Existing methods used in almost all literature up to the present time implicitly suggest that the use of supercomputers and the latest mathematical statistical methods allows achieving high accuracy very close to the boundaries of Heisenberg principle. To compare methodologies for improving models, we propose a new metric called comparative uncertainty. This allows us to prove that there is a limit to the achievable discrepancy between the model and the object under study.

Thermodynamics of Quantum Information Flows.

We report two results complementing the second law of thermodynamics for Markovian open quantum systems coupled to multiple reservoirs with different temperatures and chemical potentials. First, we derive a nonequilibrium free energy inequality providing an upper bound for a maximum power output, which for systems with inhomogeneous temperature is not equivalent to the Clausius inequality. Second, we derive local Clausius and free energy inequalities for subsystems of a composite system. These inequalities differ from the total system one by the presence of an information-related contribution and build the ground for thermodynamics of quantum information processing. Our theory is used to study an autonomous Maxwell demon.

Large work extraction and the Landauer limit in a continuous Maxwell demon

The relation between entropy and information dates back to the classical Maxwell demon (MD) paradox, a thought experiment proposed in 1867 by J. C. Maxwell to violate the second law of thermodynamics. A variant of the classical MD is the Szilard engine proposed by L. Szilard in 1926 in which the demon observes, at a given time, the compartment occupied by a single molecule in a vessel and extracts work by operating a pulley device. Here we introduce the Continuous Maxwell Demon (CMD), a device capable of extracting arbitrarily large amounts of work per cycle by repeated measurements of the state of a system, and experimentally test it in single DNA hairpin pulling experiments. In the CMD the demon monitors the state of the DNA hairpin (folded or unfolded) by observing it at equally spaced time intervals but extracts work only when the molecule changes state. We demonstrate that the average maximum work per cycle that can be extracted by the CMD is limited by the information-content of the stored sequences, in agreement with the second law. Work extraction efficiency is found to be maximal in the large information-content limit where work extraction is fuelled by rare events.

Omnipresent Maxwell's demons orchestrate information management in living cells.

SummaryThe development of synthetic biology calls for accurate understanding of the critical functions that allow construction and operation of a living cell. Besides coding for ubiquitous structures, minimal genomes encode a wealth of functions that dissipate energy in an unanticipated way. Analysis of these functions shows that they are meant to manage information under conditions when discrimination of substrates in a noisy background is preferred over a simple recognition process. We show here that many of these functions, including transporters and the ribosome construction machinery, behave as would behave a material implementation of the information‐managing agent theorized by Maxwell almost 150 years ago and commonly known as Maxwell's demon (MxD). A core gene set encoding these functions belongs to the minimal genome required to allow the construction of an autonomous cell. These MxDs allow the cell to perform computations in an energy‐efficient way that is vastly better than our contemporary computers.

Quantum Information Remote Carnot Engines and Voltage Transformers.

A physical system out of thermal equilibrium is a resource for obtaining useful work when a heat bath at some temperature is available. Information Heat Engines are the devices which generalize the Szilard cylinders and make use of the celebrated Maxwell demons to this end. In this paper, we consider a thermo-chemical reservoir of electrons which can be exchanged for entropy and work. Qubits are used as messengers between electron reservoirs to implement long-range voltage transformers with neither electrical nor magnetic interactions between the primary and secondary circuits. When they are at different temperatures, the transformers work according to Carnot cycles. A generalization is carried out to consider an electrical network where quantum techniques can furnish additional security.

Phase filters for a novel kind of asymmetric transport – Scientific prospects and opportunities for possible applications

We present the concept of nonreciprocal interferometers. These two-way devices let particles pass in both directions, but in one direction break the phase of the particlesʼ wave functions. Such filters can be realized by using, for example, asymmetric quantum rings. Furthermore, we propose arrangements of these interferometers to obtain larger interferometers which are expected to exhibit a puzzling behavior that resembles Maxwell demon action. We indicate an opportunity to resolve this puzzle experimentally.

Maxwell’s demon and interactionism

Maxwell's demon is an imaginary being invented a century and a half ago by James Clarke Maxwell in order to illustrate the statistical nature of the Second Law of thermodynamics. It helped us reach a better understanding not only of that law but also of the relationship between statistical physics and thermodynamics. Since the 1910?s it has caused a flood of papers of scientists who have tried to save the Second Law from the threat of the demon and hence preclude the possibility of perpetuum mobile of the second kind. Nowadays, it helps us better understand the possibility of constructing an interactionist model of mental causation manifested through the violation of the Second Law by the mind.

Number of hidden states needed to physically implement a given conditional distribution

We consider the problem of how to construct a physical process over a finite state space X that applies some desired conditional distribution P to initial states to produce final states. This problem arises often in the thermodynamics of computation and nonequilibrium statistical physics more generally (e.g. when designing processes to implement some desired computation, feedback controller, or Maxwell demon). It was previously known that some conditional distributions cannot be implemented using any master equation that involves just the states in X. However, here we show that any conditional distribution P can in fact be implemented—if additional ‘hidden’ states not in X are available. Moreover, we show that it is always possible to implement P in a thermodynamically reversible manner. We then investigate a novel cost of the physical resources needed to implement a given distribution P: the minimal number of hidden states needed to do so. We calculate this cost exactly for the special case where P represents a single-valued function, and provide an upper bound for the general case, in terms of the non-negative rank of P. These results show that having access to one extra binary degree of freedom, thus doubling the total number of states, is sufficient to implement any P with a master equation in a thermodynamically reversible way, if there are no constraints on the allowed form of the master equation. (Such constraints can greatly increase the minimal needed number of hidden states.) Our results also imply that for certain P that can be implemented without hidden states, having hidden states permits an implementation that generates less heat.

Cosmological Solutions and Quantum Measurements in Conformal Vacuum Analogue

In a quantum measurement with post selection condition for transient short range observations with weak values as statistical ensembles in a time reversed scenario, vacuum energy fluctuations with entangled entropy and with its qubits of information can show transitions to action potentials for energy flows of an anomalous nature, so that superfluid state of vacuum as a quantum condensate system is relativistically transformed as an idealized cosmological fluid system with ultra high temperatures and vorticity, like in Blackhole analogous non singular metric of Einstein vacuum solutions of field equations. This can also explain quark gluon plasmic fluids in such metrics corresponding to quantum fluid vortex systems in a highly thermalised state. For short range and short lived observers, vacuum is measured as a quantum entangled system, with energy fluctuations in a strongly correlated state. This can have analogies with a spin coupled many body system of quantum particles corresponding to a fermionic superfluid as a scalar field with boson excitation and higher amplitude phonon modes. There is conformance with a system of strongly correlated quantum harmonic oscillators where the motion can be approximated to a Fourier Transform of KG equation as a generalised Klein Gordon one describing a quantized complex scalar field dynamics with a self interaction potential. The de Sitter vacuum invariant can be shown to correspond to a Black hole like metric in a non singular solution of field equations, with negative energy domains due to torsion tensor and Dirac Spinor minimal coupling. The geometrical vorticity with space time fluid state angular momentum of a large order can correspond to 2D quantum vortex flows in superfluids. The initial conditions of the hydrodynamic reveal negative energy and negative temperature domains prior to onset of quantum turbulence as the idealized fluid system expands and decays due to entropic effects, naturally. This can show time reversal behaviour with short lived local violations of the second law of thermodynamics, given an entropic lowering effect. However there is entanglement entropy with high mutual information due to strongly correlated state that might even imply negative conditional information. A situation thus locally exists for a time interval of a transient nature when quantum weak measurements by a nearby short range observer can manipulate quantum fluctuations like a supersystem in nature, having analogies to a quantum Maxwell demon translating high mutual information of strongly correlated quantum entangled states of conformal vacuum to action potentials for energy dissipation and work. Quantum mechanical indeterminism permits imposing post selection condition in such time reversed, scenario, so that fast thermalization can take place in a transition from negative temperature state to ultrahigh positive absolute hot conditions, as if a thermodynamic engine with higher than Carnot efficiencies is operating, locally and transiently.

Thermodynamics in Single-Electron Circuits and Superconducting Qubits

Classical and quantum electronic circuits provide ideal platforms to investigate stochastic thermodynamics, and they have served as a stepping stone to realize Maxwell's Demons with highly controllable protocols. In this article, we first review the central thermal phenomena in quantum nanostructures. Thermometry and basic refrigeration methods are described as enabling tools for thermodynamics experiments. Next, we discuss the role of information in thermodynamics that leads to the concept of Maxwell's Demon. Various Maxwell's Demons realized in single-electron circuits over the past couple of years are described. Currently, true quantum thermodynamics in superconducting circuits is a focus of attention, and we end the review by discussing the ideas and first experiments in this exciting area of research.

Extended quantum Maxwell demon acting over macroscopic distances

A quantum Maxwell demon is a device that can lower the entropy of a quantum system by providing it with purity. The functionality of such a quantum demon is rooted in a quantum mechanical SWAP operation exchanging mixed and pure states. We describe the setup and performance of a quantum Maxwell demon that purifies an energy-isolated system from a distance. Our cQED-based design involves two transmon qubits, where the mixed-state target qubit is purified by a pure-state demon qubit connected via an off-resonant transmission line; this configuration naturally generates an iSWAP gate. Although less powerful than a full SWAP gate, we show that assuming present-day performance characteristics of a cQED implementation, such an extended quantum Maxwell demon can purify the target qubit over macroscopic distances on the order of meters and tolerates elevated temperatures of the order of a few Kelvin in the transmission line.