We discuss the thermodynamic aspects of a single qubit based device, powered by weak quantum measurements, and feedback controlled by a quantum Maxwell's demon. We discuss both discrete and time-continuous operation of the measurement based device at finite temperature of the reservoir. In the discrete example where a demon acquires information via discrete weak measurements, we find that the thermodynamic variables including the heat exchanged, extractable work, and the entropy produced are completely determined by an information theoretic measure of the demon's perceived arrow of time. We also discuss a realistic time-continuous operation of the device where the feedback is applied after a sequence of weak measurements. In the time-continuous limit, we derive the exact finite-time statistics of work, heat and entropy changes along individual quantum trajectories of the quantum measurement process, and relate them to the demon's arrow of time.
Why time is a one-way corridor? What's the origin of the arrow of time? We attribute the thermodynamic arrow of time as the direction of increasing quantum state complexity. Inspired by the work of Nielsen, Susskind and Micadei, we checked this hypothesis on both a simple two qubit and a three qubit quantum system. The result shows that in the two qubit system, the thermodynamic arrow of time always points in the direction of increasing quantum state complexity. For the three qubit system, the heat flow pattern among subsystems is closely correlated with the quantum state complexity of the sub…
Recently David Jennings and Terry Rudolph published two papers as reaction on Maccone's paper "Quantum Solution to the Arrow-of-Time Dilemma". In these papers, the authors suppose that second law of thermodynamics is not relevant for quantum systems. Unfortunately, these papers did not get relevant reply from Maccone. The reason of this is following. Both Maccone and the above-mentioned authors use thermodynamic law and thermodynamic-like terminology for non-thermodynamic systems, for example, microscopic system of three qubits. However, big size of a system (quantum or classic) is also not an…
We discuss quantum entanglement in the context of the thermodynamic arrow of time. We review the role of correlations in entropy-decreasing events and prove that the occurrence of a transformation between two thermodynamic states constitutes a new type of entanglement witness, one not defined as a separating plane in state space between separable and entangled states, but as a physical process dependent on the local initial properties of the states. Extending work by Partovi, we consider a general entangled multipartite system that allows large reversals of the thermodynamic arrow of time. We …
The mechanism by which thermodynamics sets the direction of time's arrow has long fascinated scientists. Here, we show that a machine learning algorithm can learn to discern the direction of time's arrow when provided with a system's microscopic trajectory as input. The performance of our algorithm matches fundamental bounds predicted by nonequilibrium statistical mechanics. Examination of the algorithm's decision-making process reveals that it discovers the underlying thermodynamic mechanism and the relevant physical observables. Our results indicate that machine learning techniques can be us…
In classical thermodynamics, heat cannot spontaneously pass from a colder system to a hotter system, which is called the thermodynamic arrow of time. However, if the initial states are entangled, the direction of the thermodynamic arrow of time may not be guaranteed. Here we take the thermofield double state at $0+1$ dimension as the initial state and assume its gravity duality to be the eternal black hole in AdS$_2$ space. We make the temperature difference between the two sides by changing the Hamiltonian. We turn on proper interaction between the two sides and calculate the changes in energ…
Microscopic physical laws are time-symmetric, hence, a priori there exists no preferential temporal direction. However, the second law of thermodynamics allows one to associate the "forward" temporal direction to a positive variation of the total entropy produced in a thermodynamic process, and a negative variation with its "time-reversal" counterpart. This definition of a temporal axis is normally considered to apply in both classical and quantum contexts. Yet, quantum physics admits also superpositions between forward and time-reversal processes, whereby the thermodynamic arrow of time becom…
In [Sch05a], it is argued that Boltzmann's intuition, that the psychological arrow of time is necessarily aligned with the thermodynamic arrow, is correct. Schulman gives an explicit physical mechanism for this connection, based on the brain being representable as a computer, together with certain thermodynamic properties of computational processes. [Haw94] presents similar, if briefer, arguments. The purpose of this paper is to critically examine the support for the link between thermodynamics and an arrow of time for computers. The principal arguments put forward by Schulman and Hawking will…
In this paper we lay out an argument that generically the psychological arrow of time should align with the thermodynamic arrow of time where that arrow is well-defined. This argument applies to any physical system that can act as a memory, in the sense of preserving a record of the state of some other system. This result follows from two principles: the robustness of the thermodynamic arrow of time to small perturbations in the state, and the principle that a memory should not have to be fine-tuned to match the state of the system being recorded. This argument applies even if the memory syste…
In this work we analyse the structure of the thermodynamic arrow of time, defined by transformations that leave the thermal equilibrium state unchanged, in classical (incoherent) and quantum (coherent) regimes. We note that in the infinite-temperature limit the thermodynamic ordering of states in both regimes exhibits a lattice structure. This means that when energy does not matter and the only thermodynamic resource is given by information, the thermodynamic arrow of time has a very specific structure. Namely, for any two states at present there exists a unique state in the past consistent wi…
It is shown in the framework of a harmonic system that the thermodynamical time arrow is induced by the environmental initial conditions in a manner similar to spontaneous symmetry breaking. The Closed Time Path formalism is introduced in classical mechanics to handle Green functions for initial condition problems by the action principle, in a systematic manner. The application of this scheme for quantum systems shows the common dynamical origin of the thermodynamical and the quantum time arrows. It is furthermore conjectured that the quantum-classical transition is strongly coupled.
We provide a dynamical proof of the second law of thermodynamics, along the lines of an argument of Penrose and Gibbs, making crucial use of the upper semicontinuity of the mean entropy proved by Robinson and Ruelle and Lanford and Robinson. An example is provided by a class of models of quantum spin systems introduced by Emch and Radin. Consequences regarding irreversibility and the time arrow, as well as possible extensions to quantum continuous systems are discussed.
In the understanding of the fundamental interactions, the origin of an arrow of time is viewed as problematic. However, quantum field theory has an arrow of causality, which tells us which time direction is the past lightcone and which is the future. This direction is tied to the conventions used in the quantization procedures. The different possible causal directions have related physics - in this sense they are covariant under time-reversal. However, only one causal direction emerges for a given set of conventions. This causal arrow tells us the direction that scattering reactions proceed. T…
According to the Second Law of thermodynamics, the evolution of physical systems has a preferred direction, that is characterized by some positive entropy production. Here we propose a direct way to measure the stochastic entropy produced while driving a quantum open system out of thermal equilibrium. The driving work is provided by a quantum battery, the system and the battery forming an autonomous machine. We show that the battery's energy fluctuations equal work fluctuations and check Jarzynski's equality. Since these energy fluctuations are measurable, the battery behaves as an embedded qu…
The crucial role of ambient correlations in determining thermodynamic behavior is established. A class of entangled states of two macroscopic systems is constructed such that each component is in a state of thermal equilibrium at a given temperature, and when the two are allowed to interact heat can flow from the colder to the hotter system. A dilute gas model exhibiting this behavior is presented. This reversal of the thermodynamic arrow is a consequence of the entanglement between the two systems, a condition that is opposite to molecular chaos and shown to be unlikely in a low-entropy envir…
In any physical theory that admits true indeterminism, the thermodynamic arrow of time can arise regardless of the system's initial conditions. Hence on such theories time's arrow emerges out of the basic physical interactions. The example of the GRW theory is studied in detail.
The familiar textbook quantum mechanics of laboratory measurements incorporates a quantum mechanical arrow of time --- the direction in time in which state vector reduction operates. This arrow is usually assumed to coincide with the direction of the thermodynamic arrow of the quasiclassical realm of everyday experience. But in the more general context of cosmology we seek an explanation of all observed arrows, and the relations between them, in terms of the conditions that specify our particular universe. This paper investigates quantum mechanical and thermodynamic arrows in a time-neutral fo…
Most attempts to argue for the second law of thermodynamics fail because (1) they use the unviable frequency theory of probability and (2) they do not explain why the arrow of time seen in experiments is aligned with the thermodynamic arrow of time. I use the decision theoretic interpretation of quantum probability from the many worlds interpretation of quantum mechanics to solve the probability problem. I then derive a correlation between the knowledge arrow of time and the entropy arrow of time using physical constraints on knowledge creation imposed by Popper's evolutionary theory of knowle…
In both thermodynamics and quantum mechanics the arrow of time is characterized by the statistical likelihood of physical processes. We characterize this arrow of time for the continuous quantum measurement dynamics of a superconducting qubit. By experimentally tracking individual weak measurement trajectories, we compare the path probabilities of forward and backward-in-time evolution to develop an arrow of time statistic associated with measurement dynamics. We compare the statistics of individual trajectories to ensemble properties showing that the measurement dynamics obeys both detailed a…
We present a quantum model for the motion of N point particles, implying nonlocal (i.e., superluminal) influences of external fields on the trajectories, that is nonetheless fully relativistic. In contrast to other models that have been proposed, this one involves no additional space-time structure as would be provided by a (possibly dynamical) foliation of space-time. This is achieved through the interplay of opposite microcausal and macrocausal (i.e., thermodynamic) arrows of time.
A profound quest of statistical mechanics is the origin of irreversibility - the arrow of time. New stimulants have been provided, thanks to unprecedented degree of control reached in experiments with isolated quantum systems and rapid theoretical developments of manybody localization in disordered interacting systems. The proposal of (many-body) eigenstate thermalization (ET) for these systems reinforces the common belief that either interaction or extrinsic randomness is required for thermalization. Here, we unveil a quantum thermalization mechanism challenging this belief. We find that, pro…
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…
Irreversibility is one of the most intriguing concepts in physics. While microscopic physical laws are perfectly reversible, macroscopic average behavior has a preferred direction of time. According to the second law of thermodynamics, this arrow of time is associated with a positive mean entropy production. Using a nuclear magnetic resonance setup, we measure the nonequilibrium entropy produced in an isolated spin-1/2 system following fast quenches of an external magnetic field and experimentally demonstrate that it is equal to the entropic distance, expressed by the Kullback-Leibler divergen…
In this paper we address the problem of the arrow of time from a cosmological point of view, rejecting the traditional entropic approach that defines the future direction of time as the direction of the entropy increase: from our perspective, the arrow of time has a global origin and it is an intrinsic, geometrical feature of space-time. Time orientability and existence of a cosmic time are necessary conditions for defining an arrow of time, which is manifested globally as the time-asymmetry of the universe as a whole, and locally as a time-asymmetric energy flux. We also consider arrows of ti…
The outcome of a single quantum experiment is unpredictable, except in a pure-state limit. The definite process that takes place in the apparatus may either be intrinsically random or be explainable from a deeper theory. While the first scenario is the standard lore, the latter implies that quantum mechanics is emergent. In that case, it is likely that one has to reconsider radiation by accelerated charges as a physical effect, which thus must be compensated by an energy input. Stochastic electrodynamics, for example, asserts that the vacuum energy arises from classical fluctuations with energ…
Theoretical achievements, as well as much controversy, surround multiverse theory. Various types of multiverses, with an increasing amount of complexity, were suggested and thoroughly discussed in literature by now. While these types are very different, they all share the same basic idea: our physical reality consists of more than just one universe. Each universe within a possibly huge multiverse might be slightly or even very different from the others. The quilted multiverse is one of these types, whose uniqueness arises from the postulate that every possible event will occur infinitely many …
The novelty of the Jean Pierre Badiali last scientific works stems to a quantum approach based on both (i) a return to the notion of trajectories (Feynman paths) and (ii) an irreversibility of the quantum transitions. These iconoclastic choices find again the Hilbertian and the von Neumann algebraic point of view by dealing statistics over loops. This approach confers an external thermodynamic origin to the notion of a quantum unit of time (Rovelli Connes' thermal time). This notion, basis for quantization, appears herein as a mere criterion of parting between the quantum regime and the thermo…
The existence of a non-thermodynamic arrow of time was demonstrated in a recent paper (Mod.Phys.Lett. A13, 1265 (1998)), in which a model of non-local Quantum Electrodynamics was formulated through the principle of gauge invariance. In this paper we show that the Cosmic Microwave Background Radiation is capable of making every particle of the universe (except those which are not acted upon by an electromagnetic field) follow this arrow of time.
Time-arrow $s=+/-$, intrinsic to a concrete physical system, is associated with the direction of information loss $ΔI$ displayed by the random evolution of the given system. When the information loss tends to zero the intrinsic time-arrow becomes uncertain. We propose the heuristic relationship $1/[1+exp(-sΔI)]$ for the probability of the intrinsic time-arrow. The main parts of the present work are trying to confirm this heuristic equation. The probability of intrinsic time arrow is defined by Bayesian inference from the observed random process. From irreversible thermodynamic systems, the pro…
This paper is a natural continuation of our previous paper arXiv:1011.4173 . We illustrated earlier that in classical Hamilton mechanics, for overwhelming majority of real chaotic macroscopic systems, alignment of their thermodynamic time arrows occurs because of their low interaction. This fact and impossibility to observe entropy decrease at introspection explain the second law of thermodynamics. The situation in quantum mechanics is even a little bit easier: all closed systems of finite volume are periodic or nearly periodic. The proof in quantum mechanics is in many respects similar to the…
Uncovering the origin of the arrow of time remains a fundamental scientific challenge. Within the framework of statistical physics, this problem was inextricably associated with the second law of thermodynamics, which declares that entropy growth proceeds from the system's entanglement with the environment. It remains to be seen, however, whether the irreversibility of time is a fundamental law of nature or whether, on the contrary, it might be circumvented. Here we show that, while in nature the complex conjugation needed for time reversal is exponentially improbable, one can design a quantum…
Voting is a game with a no-go theorem. New proofs of Arrow's impossibility theorem are given based on quantum information theory. We show that the Arrowian dictator is equivalent to the perfect cloning circuit. We present \textit{Gedankenexperiment} of voting and Bell-like inequalities of voting. We provide the thermodynamic interpretation of voting with Landauer's principle.
The arrow of time dilemma: the laws of physics are invariant for time inversion, whereas the familiar phenomena we see everyday are not (i.e. entropy increases). I show that, within a quantum mechanical framework, all phenomena which leave a trail of information behind (and hence can be studied by physics) are those where entropy necessarily increases or remains constant. All phenomena where the entropy decreases must not leave any information of their having happened. This situation is completely indistinguishable from their not having happened at all. In the light of this observation, the se…
In order to describe the quantum electrodynamic measurement process in a relativistic observer-participant manner, an operator symmetry of "microscopic observer-participation" called Measurement Color (MC) is incorporated into the field theoretic structure of Quantum Electrodynamics (QED) in the Heisenberg Picture. It is found that the resultant Measurement Color Quantum Electrodynamics (MC-QED) contains a microscopic quantum electrodynamic arrow of time that emerges dynamically, independent of any thermodynamic or cosmological assumptions. This occurs because the photon has a negative time pa…
We provide a new perspective on the close relationship between entanglement and time. Our main focus is on bipartite entanglement, where this connection is foreshadowed both in the positive partial transpose criterion due to Peres [A. Peres, Phys. Rev. Lett., 77, 1413 (1996)] and in the classification of quantum within more general non-signalling bipartite correlations [M. Frembs and A. Döring, arXiv:2204.11471]. Extracting the relevant common features, we identify a necessary and sufficient condition for bipartite entanglement in terms of a compatibility condition with respect to time orienta…
Recent research on the thermodynamic arrow of time, at the microscopic scale, has questioned the universality of its direction. Theoretical studies showed that quantum correlations can be used to revert the natural heat flow (from the hot body to the cold one), posing an apparent challenge to the second law of thermodynamics. Such an "anomalous" heat current was observed in a recent experiment (arXiv:1711.03323), by employing two spin systems initially quantum correlated. Nevertheless, the precise relationship between this intriguing phenomenon and the initial conditions that allow it is not f…
One of the stunning consequences of quantum correlations in thermodynamics is the reversal of the arrow of time, recently shown experimentally in [K. Micadei, et al., Nat. Commun. 10:2456 (2019)], and manifesting itself by a reversal of the heat flow (from the cold system to the hot one). Here, we show that contrary to what could have been expected, heat flow reversal can happen without reversal of the arrow of time. Moreover, contrasting with previous studies, no initial correlations between system and bath is required. Instead, the heat flow reversal only relies on internal quantum coherence…
In a quantum universe with a strong arrow of time, it is standard to postulate that the initial wave function started in a particular macrostate--the special low-entropy macrostate selected by the Past Hypothesis. Moreover, there is an additional postulate about statistical mechanical probabilities according to which the initial wave function is a "typical" choice in the macrostate (the Statistical Postulate). Together, they support a probabilistic version of the Second Law of Thermodynamics: typical initial wave functions will increase in entropy. Hence, there are two sources of randomness in…
The relationship between 'information' and 'time' is explored in order to look for a 'solution' to the 'Problem of Time'. 'Time' is found to be the result of the conversion of energy into 'information'. The 'time' number or label we assign to 'events' can be manufactured by processing information 'flowing' from a Feynman Clock (FC), via a 'signal', to a Feynman Detector (FD) in causal networks. Macroscopic arrows of time are built from the irreversible Quantum Arrow of Time (QAT) associated with unstable or excited states of quantum systems. The QAT is shown to be connected to the thermodynami…
We investigate the statistical arrow of time for a quantum system being monitored by a sequence of measurements. For a continuous qubit measurement example, we demonstrate that time-reversed evolution is always physically possible, provided that the measurement record is also negated. Despite this restoration of dynamical reversibility, a statistical arrow of time emerges, and may be quantified by the log-likelihood difference between forward and backward propagation hypotheses. We then show that such reversibility is a universal feature of non-projective measurements, with forward or backward…
A legend tells that once Loschmidt asked Boltzmann on what happens to his statistical theory if one inverts the velocities of all particles, so that, due to the reversibility of Newton's equations, they return from the equilibrium to a nonequilibrium initial state. Boltzmann only replied ``then go and invert them''. This problem of the relationship between the microscopic and macroscopic descriptions of the physical world and time-reversibility has been hotly debated from the XIXth century up to nowadays. At present, no modern computer is able to perform Boltzmann's demand for a macroscopic nu…
We demonstrate that irreversibility arises from the principle of microscopic reversibility and the presence of memory in the time evolution of a single copy of a system driven by a protocol. We introduce microscopic reversibility by using the concept of protocol- and pathway-dependent thermodynamic function, as defined in J.R. Arias-Gonzalez, arXiv:1511.08017 [cond-mat.stat-mech], and memory by using the concept of non-Markovianity, as in J.R. Arias-Gonzalez, arXiv:1511.06139 [cond-mat.stat-mech]. We define work as the change in free energy and heat as the change in entropy for micoscopic, ind…
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…
Leggett Garg inequalities (LGIs) test the incompatibility between the notion of macrorealism and quantum mechanics. For unitary dynamics, the optimal quantum violation of an LGI is constrained by the Lüders bound. However, the LGIs does not provide the necessary and sufficient for macrorealism. A suitably formulated set of no-signaling in time (NSIT) conditions along with the arrow-of-time (AOT) condition provides the same. In this paper, we study two formulations in the three-time LG scenario, viz., the standard LGIs and the recently formulated variant of LGIs when the system evolves under $\…
All the laws of physics are time-reversible. Time arrow emerges only when ensembles of classical particles are treated probabilistically, outside of physics laws, and the entropy and the second law of thermodynamics are introduced. In quantum physics, no mechanism for a time arrow has been proposed despite its intrinsic probabilistic nature. In consequence, one cannot explain why an electron in an excited state will "spontaneously" transition into a ground state as a photon is created and emitted, instead of continuing in its reversible unitary evolution. To address such phenomena, we introduc…
We study entropy production (EP) in processes involving repeated quantum measurements of finite quantum systems. Adopting a dynamical system approach, we develop a thermodynamic formalism for the EP and study fine aspects of irreversibility related to the hypothesis testing of the arrow of time. Under a suitable chaoticity assumption, we establish a Large Deviation Principle and a Fluctuation Theorem for the EP.
The first paper: We describe principles of new cybernetics and use these principles for resolution of basic physical paradoxes. It demonstrates universality of the principles of new cybernetics. The second paper: recent letter by Maccone presents a solution based on the existing laws of quantum mechanics to the arrow-of-time dilemma. He argues that all phenomena in which the entropy decreases must not leave any information (in the observer's memory) of their having occurred because the observer is a part of the whole system. Maccone concludes that quantum mechanics is necessary to his argument…
