Effect of Quantum Coherence on Landauer’s Principle

Landauer’s principle provides a fundamental lower bound for energy dissipation occurring with information erasure in the quantum regime. While most studies have related the entropy reduction incorporated with the erasure to the lower bound (entropic bound), recent efforts have also provided another lower bound associated with the thermal fluctuation of the dissipated energy (thermodynamic bound). The coexistence of the two bounds has stimulated comparative studies of their properties; however, these studies were performed for systems where the time-evolution of diagonal (population) and off-diagonal (coherence) elements of the density matrix are decoupled. In this paper, we aimed to broaden the comparative study to include the influence of quantum coherence induced by the tilted system–reservoir interaction direction. By examining their dependence on the initial state of the information-bearing system, we find that the following properties of the bounds are generically held regardless of whether the influence of the coherence is present or not: the entropic bound serves as the tighter bound for a sufficiently mixed initial state, while the thermodynamic bound is tighter when the purity of the initial state is sufficiently high. The exception is the case where the system dynamics involve only phase relaxation; in this case, the two bounds coincide when the initial coherence is zero; otherwise, the thermodynamic bound serves the tighter bound. We also find the quantum information erasure inevitably accompanies constant energy dissipation caused by the creation of system–reservoir correlation, which may cause an additional source of energetic cost for the erasure.     

Fidelity Mechanics: Analogues of the Four Thermodynamic Laws and Landauer’s Principle

Fidelity mechanics is formalized as a framework for investigating critical phenomena in quantum many-body systems. Fidelity temperature is introduced for quantifying quantum fluctuations, which, together with fidelity entropy and fidelity internal energy, constitute three basic state functions in fidelity mechanics, thus enabling us to formulate analogues of the four thermodynamic laws and Landauer’s principle at zero temperature. Fidelity flows, which are irreversible, are defined and may be interpreted as an alternative form of renormalization group flows. Thus, fidelity mechanics offers a means to characterize both stable and unstable fixed points: divergent fidelity temperature for unstable fixed points and zero-fidelity temperature and (locally) maximal fidelity entropy for stable fixed points. In addition, fidelity entropy behaves differently at an unstable fixed point for topological phase transitions and at a stable fixed point for topological quantum states of matter. A detailed analysis of fidelity mechanical-state functions is presented for six fundamental models—the quantum spin-1/2 XY model, the transverse-field quantum Ising model in a longitudinal field, the quantum spin-1/2 XYZ model, the quantum spin-1/2 XXZ model in a magnetic field, the quantum spin-1 XYZ model, and the spin-1/2 Kitaev model on a honeycomb lattice for illustrative purposes. We also present an argument to justify why the thermodynamic, psychological/computational, and cosmological arrows of time should align with each other, with the psychological/computational arrow of time being singled out as a master arrow of time.     

Beyond Causal Explanation: Einstein’s Principle Not Reichenbach’s

Our account provides a local, realist and fully non-causal principle explanation for EPR correlations, contextuality, no-signalling, and the Tsirelson bound. Indeed, the account herein is fully consistent with the causal structure of Minkowski spacetime. We argue that retrocausal accounts of quantum mechanics are problematic precisely because they do not fully transcend the assumption that causal or constructive explanation must always be fundamental. Unlike retrocausal accounts, our principle explanation is a complete rejection of Reichenbach’s Principle. Furthermore, we will argue that the basis for our principle account of quantum mechanics is the physical principle sought by quantum information theorists for their reconstructions of quantum mechanics. Finally, we explain why our account is both fully realist and psi-epistemic.     

Revisiting Born’s Rule through Uhlhorn’s and Gleason’s Theorems

In a previous article we presented an argument to obtain (or rather infer) Born’s rule, based on a simple set of axioms named “Contexts, Systems and Modalities" (CSM). In this approach, there is no “emergence”, but the structure of quantum mechanics can be attributed to an interplay between the quantized number of modalities that is accessible to a quantum system and the continuum of contexts that are required to define these modalities. The strong link of this derivation with Gleason’s theorem was emphasized, with the argument that CSM provides a physical justification for Gleason’s hypotheses. Here, we extend this result by showing that an essential one among these hypotheses—the need of unitary transforms to relate different contexts—can be removed and is better seen as a necessary consequence of Uhlhorn’s theorem.     

Schrödinger’s Ballot: Quantum Information and the Violation of Arrow’s Impossibility Theorem

We study Arrow’s Impossibility Theorem in the quantum setting. Our work is based on the work of Bao and Halpern, in which it is proved that the quantum analogue of Arrow’s Impossibility Theorem is not valid. However, we feel unsatisfied about the proof presented in Bao and Halpern’s work. Moreover, the definition of Quantum Independence of Irrelevant Alternatives (QIIA) in Bao and Halpern’s work seems not appropriate to us. We give a better definition of QIIA, which properly captures the idea of the independence of irrelevant alternatives, and a detailed proof of the violation of Arrow’s Impossibility Theorem in the quantum setting with the modified definition.     

Hidden Dissipation and Irreversibility in Maxwell’s Demon

Maxwell’s demon is an entity in a 150-year-old thought experiment that paradoxically appears to violate the second law of thermodynamics by reducing entropy without doing work. It has increasingly practical implications as advances in nanomachinery produce devices that push the thermodynamic limits imposed by the second law. A well-known explanation claiming that information erasure restores second law compliance fails to resolve the paradox because it assumes the second law a priori, and does not predict irreversibility. Instead, a purely mechanical resolution that does not require information theory is presented. The transport fluxes of mass, momentum, and energy involved in the demon’s operation are analyzed and show that they imply “hidden” external work and dissipation. Computing the dissipation leads to a new lower bound on entropy production by the demon. It is strictly positive in all nontrivial cases, providing a more stringent limit than the second law and implying intrinsic thermodynamic irreversibility. The thermodynamic irreversibility is linked with mechanical irreversibility resulting from the spatial asymmetry of the demon’s speed selection criteria, indicating one mechanism by which macroscopic irreversibility may emerge from microscopic dynamics.     

Asymptotic Normality for Plug-In Estimators of Generalized Shannon’s Entropy

Shannon’s entropy is one of the building blocks of information theory and an essential aspect of Machine Learning (ML) methods (e.g., Random Forests). Yet, it is only finitely defined for distributions with fast decaying tails on a countable alphabet. The unboundedness of Shannon’s entropy over the general class of all distributions on an alphabet prevents its potential utility from being fully realized. To fill the void in the foundation of information theory, Zhang (2020) proposed generalized Shannon’s entropy, which is finitely defined everywhere. The plug-in estimator, adopted in almost all entropy-based ML method packages, is one of the most popular approaches to estimating Shannon’s entropy. The asymptotic distribution for Shannon’s entropy’s plug-in estimator was well studied in the existing literature. This paper studies the asymptotic properties for the plug-in estimator of generalized Shannon’s entropy on countable alphabets. The developed asymptotic properties require no assumptions on the original distribution. The proposed asymptotic properties allow for interval estimation and statistical tests with generalized Shannon’s entropy.     

A Refutation of Finite-State Language Models through Zipf’s Law for Factual Knowledge

We present a hypothetical argument against finite-state processes in statistical language modeling that is based on semantics rather than syntax. In this theoretical model, we suppose that the semantic properties of texts in a natural language could be approximately captured by a recently introduced concept of a perigraphic process. Perigraphic processes are a class of stochastic processes that satisfy a Zipf-law accumulation of a subset of factual knowledge, which is time-independent, compressed, and effectively inferrable from the process. We show that the classes of finite-state processes and of perigraphic processes are disjoint, and we present a new simple example of perigraphic processes over a finite alphabet called Oracle processes. The disjointness result makes use of the Hilberg condition, i.e., the almost sure power-law growth of algorithmic mutual information. Using a strongly consistent estimator of the number of hidden states, we show that finite-state processes do not satisfy the Hilberg condition whereas Oracle processes satisfy the Hilberg condition via the data-processing inequality. We discuss the relevance of these mathematical results for theoretical and computational linguistics.     

Wigner’s Friend Scenarios and the Internal Consistency of Standard Quantum Mechanics

Wigner’s friend scenarios involve an Observer, or Observers, measuring a Friend, or Friends, who themselves make quantum measurements. In recent discussions, it has been suggested that quantum mechanics may not always be able to provide a consistent account of a situation involving two Observers and two Friends. We investigate this problem by invoking the basic rules of quantum mechanics as outlined by Feynman in the well-known “Feynman Lectures on Physics”. We show here that these “Feynman rules” constrain the a priori assumptions which can be made in generalised Wigner’s friend scenarios, because the existence of the probabilities of interest ultimately depends on the availability of physical evidence (material records) of the system’s past. With these constraints obeyed, a non-ambiguous and consistent account of all measurement outcomes is obtained for all agents, taking part in various Wigner’s Friend scenarios.     

Generalized Landauer Bound for Information Processing: Proof and Applications

A generalized form of Landauer’s bound on the dissipative cost of classical information processing in quantum-mechanical systems is proved using a new approach. This approach sidesteps some prominent objections to standard proofs of Landauer’s bound—broadly interpreted here as a nonzero lower bound on the amount of energy that is irreversibly transferred from a physical system to its environment for each bit of information that is lost from the system—while establishing a far more general result. Specializations of our generalized Landauer bound for ideal and non-ideal information processing operations, including but not limited to the simplified forms for erasure and logical operations most familiar from the literature, are presented and discussed. These bounds, taken together, enable reconsideration of the links between logical reversibility, physical reversibility, and conditioning of operations in contexts that include but are far more general than the thermodynamic model systems that are most widely invoked in discussions of Landauer’s Principle. Because of the strategy used to prove the generalized bounds and these specializations, this work may help to illuminate and resolve some longstanding controversies related to dissipation in computation.     

Information Dark Energy Can Resolve the Hubble Tension and Is Falsifiable by Experiment

We consider the role information energy can play as a source of dark energy. Firstly, we note that if stars and structure had not formed in the universe, elemental bits of information describing the attributes of particles would have exhibited properties similar to the cosmological constant. The Landauer equivalent energy of such elemental bits would be defined in form and value identical to the characteristic energy of the cosmological constant. However, with the formation of stars and structure, stellar heated gas and dust now provide the dominant contribution to information energy with the characteristics of a dynamic, transitional, dark energy. At low redshift, z < ~1.35, this dark energy emulates the cosmological constant with a near-constant energy density, w = −1.03 ± 0.05, and an energy total similar to the mc² of the universe’s ∼10⁵³ kg of baryons. At earlier times, z > ~1.35, information energy was phantom, differing from the cosmological constant, Λ, with a CPL parameter difference of ∆w_o = −0.03 ± 0.05 and ∆w_a = −0.79 ± 0.08, values sufficient to account for the H₀ tension. Information dark energy agrees with most phenomena as well as Λ, while exhibiting characteristics that resolve many tensions and problems of ΛCDM: the cosmological constant problem; the cosmological coincidence problem; the H₀ tension, and the σ₈ tension. As this proposed dark energy source is not usually considered, we identify the expected signature in H(a) that will enable the role of information dark energy to be falsified by experimental observation.     

Gull’s Theorem Revisited

In 2016, Steve Gull has outlined has outlined a proof of Bell’s theorem using Fourier theory. Gull’s philosophy is that Bell’s theorem (or perhaps a key lemma in its proof) can be seen as a no-go theorem for a project in distributed computing with classical, not quantum, computers. We present his argument, correcting misprints and filling gaps. In his argument, there were two completely separated computers in the network. We need three in order to fill all the gaps in his proof: a third computer supplies a stream of random numbers to the two computers representing the two measurement stations in Bell’s work. One could also imagine that computer replaced by a cloned, virtual computer, generating the same pseudo-random numbers within each of Alice and Bob’s computers. Either way, we need an assumption of the presence of shared i.i.d. randomness in the form of a synchronised sequence of realisations of i.i.d. hidden variables underlying the otherwise deterministic physics of the sequence of trials. Gull’s proof then just needs a third step: rewriting an expectation as the expectation of a conditional expectation given the hidden variables.     

Entropy Based Student’s t-Process Dynamical Model

Volatility, which represents the magnitude of fluctuating asset prices or returns, is used in the problems of finance to design optimal asset allocations and to calculate the price of derivatives. Since volatility is unobservable, it is identified and estimated by latent variable models known as volatility fluctuation models. Almost all conventional volatility fluctuation models are linear time-series models and thus are difficult to capture nonlinear and/or non-Gaussian properties of volatility dynamics. In this study, we propose an entropy based Student’s t-process Dynamical model (ETPDM) as a volatility fluctuation model combined with both nonlinear dynamics and non-Gaussian noise. The ETPDM estimates its latent variables and intrinsic parameters by a robust particle filtering based on a generalized H-theorem for a relative entropy. To test the performance of the ETPDM, we implement numerical experiments for financial time-series and confirm the robustness for a small number of particles by comparing with the conventional particle filtering.     

Distinguishability and Disturbance in the Quantum Key Distribution Protocol Using the Mean Multi-Kings’ Problem

We introduce a quantum key distribution protocol using mean multi-kings’ problem. Using this protocol, a sender can share a bit sequence as a secret key with receivers. We consider a relation between information gain by an eavesdropper and disturbance contained in legitimate users’ information. In BB84 protocol, such relation is known as the so-called information disturbance theorem. We focus on a setting that the sender and two receivers try to share bit sequences and the eavesdropper tries to extract information by interacting legitimate users’ systems and an ancilla system. We derive trade-off inequalities between distinguishability of quantum states corresponding to the bit sequence for the eavesdropper and error probability of the bit sequence shared with the legitimate users. Our inequalities show that eavesdropper’s extracting information regarding the secret keys inevitably induces disturbing the states and increasing the error probability.     

Reliability of Financial Information from the Perspective of Benford’s Law

This study investigates the conformity to Benford’s Law of the information disclosed in financial statements. Using the first digit test of Benford’s Law, the study analyses the reliability of financial information provided by listed companies on an emerging capital market before and after the implementation of International Financial Reporting Standards (IFRS). The results of the study confirm the increase of reliability on the information disclosed in the financial statements after IFRS implementation. The study contributes to the existing literature by bringing new insights into the types of financial information that do not comply with Benford’s Law such as the amounts determined by estimates or by applying professional judgment.     

Enhancement of Cooperation and Reentrant Phase of Prisoner’s Dilemma Game on Signed Networks

We studied the prisoner’s dilemma game as applied to signed networks. In signed networks, there are two types of links: positive and negative. To establish a payoff matrix between players connected with a negative link, we multiplied the payoff matrix between players connected with a positive link by −1. To investigate the effect of negative links on cooperating behavior, we performed simulations for different negative link densities. When the negative link density is low, the density of the cooperator becomes zero because there is an increasing temptation payoff, b. Here, parameter b is the payoff received by the defector from playing the game with a cooperator. Conversely, when the negative link density is high, the cooperator density becomes almost 1 as b increases. This is because players with a negative link will suffer more payoff damage if they do not cooperate with each other. The negative link forces players to cooperate, so cooperating behavior is enhanced.     

Robust Test Statistics Based on Restricted Minimum Rényi’s Pseudodistance Estimators

The Rao’s score, Wald and likelihood ratio tests are the most common procedures for testing hypotheses in parametric models. None of the three test statistics is uniformly superior to the other two in relation with the power function, and moreover, they are first-order equivalent and asymptotically optimal. Conversely, these three classical tests present serious robustness problems, as they are based on the maximum likelihood estimator, which is highly non-robust. To overcome this drawback, some test statistics have been introduced in the literature based on robust estimators, such as robust generalized Wald-type and Rao-type tests based on minimum divergence estimators. In this paper, restricted minimum Rényi’s pseudodistance estimators are defined, and their asymptotic distribution and influence function are derived. Further, robust Rao-type and divergence-based tests based on minimum Rényi’s pseudodistance and restricted minimum Rényi’s pseudodistance estimators are considered, and the asymptotic properties of the new families of tests statistics are obtained. Finally, the robustness of the proposed estimators and test statistics is empirically examined through a simulation study, and illustrative applications in real-life data are analyzed.     

Proposal to Test a Transient Deviation from Quantum Mechanics’ Predictions for Bell’s Experiment

Quantum mechanics predicts correlations between measurements performed in distant regions of a spatially spread entangled state to be higher than allowed by intuitive concepts of Locality and Realism. These high correlations forbid the use of nonlinear operators of evolution (which would be desirable for several reasons), for they may allow faster-than-light signaling. As a way out of this situation, it has been hypothesized that the high quantum correlations develop only after a time longer than L/c has elapsed (where L is the spread of the entangled state and c is the velocity of light). In shorter times, correlations compatible with Locality and Realism would be observed instead. A simple hidden variables model following this hypothesis is described. It is based on a modified Wheeler–Feynman theory of radiation. This hypothesis has not been disproved by any of the experiments performed to date. A test achievable with accessible means is proposed and described. It involves a pulsed source of entangled states and stroboscopic record of particle detection during the pulses. Data recorded in similar but incomplete optical experiments are analyzed, and found consistent with the proposed model. However, it is not claimed, in any sense, that the hypothesis has been validated. On the contrary, it is stressed that a complete, specific test is absolutely needed.     

On Yaglom’s Law for the Interplanetary Proton Density and Temperature Fluctuations in Solar Wind Turbulence

In the past decades, there has been an increasing literature on the presence of an inertial energy cascade in interplanetary space plasma, being interpreted as the signature of Magnetohydrodynamic turbulence (MHD) for both fields and passive scalars. Here, we investigate the passive scalar nature of the solar wind proton density and temperature by looking for scaling features in the mixed-scalar third-order structure functions using measurements on-board the Ulysses spacecraft during two different periods, i.e., an equatorial slow solar wind and a high-latitude fast solar wind, respectively. We find a linear scaling of the mixed third-order structure function as predicted by Yaglom’s law for passive scalars in the case of slow solar wind, while the results for fast solar wind suggest that the mixed fourth-order structure function displays a linear scaling. A simple empirical explanation of the observed difference is proposed and discussed.     

Extending Kolmogorov’s Axioms for a Generalized Probability Theory on Collections of Contexts

Kolmogorov’s axioms of probability theory are extended to conditional probabilities among distinct (and sometimes intertwining) contexts. Formally, this amounts to row stochastic matrices whose entries characterize the conditional probability to find some observable (postselection) in one context, given an observable (preselection) in another context. As the respective probabilities need not (but, depending on the physical/model realization, can) be of the Born rule type, this generalizes approaches to quantum probabilities by Aufféves and Grangier, which in turn are inspired by Gleason’s theorem.