A hypothetical formulation of quantum mechanics is presented so as to reconcile it with macro-realism. On the analogy drawn from thermodynamics, an objective description of wave packet reduction is postulated, in which a characteristic energy scale and a time scale are introduced to separate the quantum and classical conceptions.
The issue of irreversibility in a universe with time-reversal-symmetric laws is a central problem in physics. % , and, in particular, to statistical mechanics, information theory and quantum thermodynamics. In this letter, we discuss for the first time how irreversibility can emerge within the recently proposed constructor theory framework. Here irreversibility is expressed as the requirement that a task is possible, while its inverse is not. In particular, we demonstrate that this irreversibility is compatible with quantum theory's time reversal symmetric laws, by exploiting a specific model,…
The purpose of this comment is to show that a reinterpretation of the results from the Letter: "Physics and Metaphysics of Wigner's Friends: Even performed pre-measurements have no results" allows for reaching the conclusion "pre-measurements have no resul" [arXiv:2003.07464] based only on postulates of quantum mechanics without additional assumptions on irreversibility. Additionally, with supplementary reasoning based on Bell's theorem, one can show that unitary decoherence cannot be solely responsible for the quantum-to-classical transition, and an additional irreversibility model is require…
Within the general formalism of quantum theory irreversibility and the arrow of time in the evolution of various physical systems are studied. Irreversible behavior often manifests itself in the guise of entropy production. This motivates me to begin this paper with a brief review of quantum-mechanical entropy, a subject that Elliott Lieb has made outstanding contributions to, followed by an enumeration of examples of irreversible behavior and of an arrow of time analyzed in later sections. Subsequently, a derivation of the laws of thermodynamics from (quantum) statistical mechanics, and, in p…
We investigate the link between the irreversibility generated by a stationary dissipative process and the correlations established within a composite quantum system. We provide two equivalent expressions for the entropy generated in the non-equilibrium steady state of coupled quantum harmonic oscillators that allow for a simple interpretation of the onset of irreversibility. We then unveil a quantitative relation between the entropy production rate and correlations, both total and quantum, built between the two oscillators. In the small-coupling limit, the entropy production rate is shown to b…
The Loschmidt echo -- also known as fidelity -- is a very useful tool to study irreversibility in quantum mechanics due to perturbations or imperfections. Many different regimes, as a function of time and strength of the perturbation, have been identified. For chaotic systems, there is a range of perturbation strengths where the decay of the Loschmidt echo is perturbation independent, and given by the classical Lyapunov exponent. But observation of the Lyapunov decay depends strongly on the type of initial state upon which an average is done. This dependence can be removed by averaging the fid…
The concept of internal friction, a fully quantum mechanical phenomena, is investigated in a simple, experimentally accessible quantum system in which a spin-1/2 is driven by a transverse magnetic field in a quantum adiabatic process. The irreversible production of the waste energy due to the quantum friction is quantitatively analyzed in a forward-backward unitary transform of the system Hamiltonian by using the quantum relative entropy between the actual density matrix obtained in a parametric transformation and the one in a reversible adiabatic process. Analyzing the role of total transform…
Quantitative measure of disorder or randomness based on the entropy production characterizes thermodynamical irreversibility, which is relevant to the conventional second law of thermodynamics. Here we report, in a quantum mechanical fashion, the first theoretical prediction and experimental exploration of an information-theoretical bound on the entropy production. Our theoretical model consists of a simplest two-level dissipative system driven by a purely classical field, and under the Markovian dissipation, we find that such an information-theoretical bound, not fully validating quantum rela…
The wide-spread opinion is that original quantum mechanics is a reversible theory, but this statement is only true for undecomposed systems, that are those systems which sub-systems are out of consideration. Taking sub-systems into account, as it is by definition necessary for decomposed systems, the interaction Hamiltonians which are absent in undecomposed systems generate irreversibility. Thus, the following two-stage task arises: How to modify von Neumann's equation for undecomposed systems so that irreversibility appears, and how this modification affects decomposed systems ? The first ste…
For decades, researchers have sought to understand how the irreversibility of the surrounding world emerges from the seemingly time symmetric, fundamental laws of physics. Quantum mechanics conjectured a clue that final irreversibility is set by the measurement procedure and that the time reversal requires complex conjugation of the wave function, which is overly complex to spontaneously appear in nature. Building on this Landau-Wigner conjecture, it became possible to demonstrate that time reversal is exponentially improbable in a virgin nature and to design an algorithm artificially reversin…
Wigner functions, allowing for a reformulation of quantum mechanics in phase space, are of central importance for the study of the quantum-classical transition. A full understanding of the quantum-classical transition, however, also requires an explanation for the absence of macroscopic superpositions to solve the quantum measurement problem. Stochastic reformulations of quantum mechanics based on spontaneous collapses of the wavefunction are a popular approach to this issue. In this article, we derive the dynamic equations for the four most important spontaneous collapse models - Ghirardi-Rim…
Recently probabilistic hysteresis in isolated Hamiltonian systems of ultracold atoms has been studied in the limit of large particle numbers, where a semiclassical treatment is adequate. The origin of irreversibility in these sweep experiments, where a control parameter is slowly (adiabatically) tuned back and forth, turned out to be a passage blue back and forth across a separatrix (integrable case) or a passage in and out of a chaotic sea in phase space (chaotic case). Here we focus on the full quantum mechanical description of the integrable system and show how the semiclassical results eme…
This paper discusses the relation between the decoherent histories approach to quantum mechanics that is based on coarse-grained decoherent histories of a closed system, and the approximate quantum mechanics of measured subsystems, as in the Copenhagen interpretation. We show how the a classical world used in such formulations is not to something to be postulated but rather explained by suitable sets of alternative histories of quasiclassical variables. We discuss the general definition of measurement, the collapse of the wave function, and irreversibility from the perspective of decoherent hi…
We study the irreversibility à la Maxwell from a quantum point of view, involving an arbitrarily large ensemble of independent particles, with a daemonic potential that is capable of inducing asymmetries in the evolution, exhibiting new perspectives on how Maxwell's apparent paradox is posed and resolved dynamically. In addition, we design an electromagnetic cavity, to which dielectrics are added, fulfilling the function of a daemon. Thereby, this physical system is capable of cooling and ordering incident electromagnetic radiation. This setting can be generalized to many types of waves, witho…
Error and Disturbance as Irreversibility with Applications: Unified Definition, Wigner--Araki--Yanase Theorem and Out-of-Time-Order Correlator
Graduate School of Information Science and Technology, Hokkaido University（北海道大学信息理工学院）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN（理化学研究所交叉理论数学科学中心（iTHEMS））；Department of Informatics, Faculty of Information Science and Electrical Engineering, Kyushu University（九州大学信息电气工程学院信息系）；JST, FOREST（日本科学技术振兴机构，FOREST计划）
I prove that, if a change happens in a closed quantum system so that its state is perfectly distinguishable from all past or future states, the Hamiltonian is $\widehat{H}=-i\hbar\frac{\partial\ }{\partialτ}$. A time operator $\widehatτ$ can be defined as its canonical conjugate. This Hamiltonian is usually rejected because it has no ground state, but I show that even a weaker form of irreversibility is inconsistent with a ground state. What is the right choice, that the world's Hamiltonian is $-i\hbar\frac{\partial\ }{\partialτ}$, or that changes are reversible?
By making use of a recently proposed framework for the inference of thermodynamic irreversibility in bosonic quantum systems, we experimentally measure and characterize the entropy production rates in the non-equilibrium steady state of two different physical systems -- a micro-mechanical resonator and a Bose-Einstein condensate -- each coupled to a high finesse cavity and hence also subject to optical loss. Key features of our setups, such as cooling of the mechanical resonator and signatures of a structural quantum phase transition in the condensate are reflected in the entropy production ra…
1/f noise at arbitrary low frequences is the way of existence of irreversibility in thermal motion governed by reversible laws of mechanics. This statement not once was confirmed in statistical mechanics beyond its traditional kinetical roughenings. Here we point out that in case of quantum statistical mechanics in principle it is sufficient to avoid such the roughening as the "Fermi golden rule". This means taking into account the time-energy uncertainty principle (time-frequency one in classical limit) and thus uncertainties in characteristics of real collisions and scatterings of particles …
