Stationary engines in and beyond the linear response regime at the Carnot efficiency

The condition for stationary engines to attain the Carnot efficiency in and beyond the linear response regime is investigated. We find that this condition for finite-size engines is significantly different from that for macroscopic engines in the thermodynamic limit. For the case of finite-size engines, the tight-coupling condition in the linear response regime directly implies the attainability of the Carnot efficiency beyond the linear response regime. Contrary to this, for the case of macroscopic engines in the thermodynamic limit, there are three types of mechanisms to attain the Carnot efficiency. One mechanism allows engines to attain the Carnot efficiency only in the linear response limit, while other two mechanisms enable engines to attain the Carnot efficiency beyond the linear response regime. These three mechanisms are classified by introducing tight-coupling window.Comment: 11 pages, 7 figure

Anomalous System Size Dependence of Large Deviation Functions for Local Empirical Measure

We study the large deviation function for the empirical measure of diffusing particles at one fixed position. We find that the large deviation function exhibits anomalous system size dependence in systems that satisfy the following conditions: (i) there exists no macroscopic flow, and (ii) their space dimension is one or two. We investigate this anomaly by using a contraction principle. We also analyze the relation between this anomaly and the so-called long-time tail behavior on the basis of phenomenological arguments.Comment: 14 page

Connection between quantum-many-body scars and the AKLT model from the viewpoint of embedded Hamiltonians

We elucidate the deep connection between the PXP model, which is a standard model of quantum many-body scars, and the AKLT Hamiltonian. Using the framework of embedded Hamiltonians, we establish the connection between the PXP Hamiltonian and the AKLT Hamiltonian, which clarifies the reason why the PXP Hamiltonian has nonthermal energy eigenstates similar to the AKLT state. Through this analysis, we find that the presence of such nonthermal energy eigenstates reflects the symmetry in the AKLT Hamiltonian.Comment: 11 pages, no figur

Attainability of Carnot Efficiency with Autonomous Engines

The maximum efficiency of autonomous engines with finite chemical potential difference is investigated. We show that without a particular type of singularity autonomous engines cannot attain the Carnot efficiency. In addition, we demonstrate that a special autonomous engine with the singularity attains the Carnot efficiency even if it is macroscopic. Our results clearly illustrate that the singularity plays a crucial role for the maximum efficiency of autonomous engines.Comment: 11 pages, 8 figure

Finite-time thermodynamic uncertainty relation do not hold for discrete-time Markov process

Discrete-time counterpart of thermodynamic uncertainty relation (conjectured in P. Pietzonka, et.al., arXiv:1702.07699 (2017)) with finite time interval is considered. We show that this relation do not hold by constructing a concrete counterexample to this. Our finding suggests that the proof of thermodynamic uncertainty relation with finite time interval, if true, should strongly rely on the fact that the time is continuous.Comment: 3 page

Fundamental relation between entropy production and heat current

We investigate the fundamental relation between entropy production rate and the speed of energy exchange between a system and baths in classical Markov processes. We establish the fact that quick energy exchange inevitably induces large entropy production in a quantitative form. More specifically, we prove two inequalities on instantaneous quantities: One is applicable to general Markov processes induced by heat baths, and the other is applicable only to systems with the local detailed-balance condition but is stronger than the former one. We demonstrate the physical meaning of our result by applying to some specific setups. In particular, we show that our inequalities are tight in the linear response regime.Comment: 31 pages, no figur

Incompatibility between Carnot efficiency and finite power in Markovian dynamics

In Markovian dynamics with the local detailed balance condition, we decompose the total entropy production rate into microscopic transitions. By applying this decomposition to the heat to work conversion process, we rigorously show that the Carnot efficiency implies zero power for any heat engine, even with broken time-reversal symmetry beyond the linear response regime. Moreover, we propose a trade-off relationship between the entropy production rate and the heat flow between the system and bath.Comment: 6 pages, 1 figure. This paper has been withdrawn by authors to resubmit a new revised paper arxiv:1605.0035

Constructing Concrete Hard Instances of the Maximum Independent Set Problem

We provide a deterministic construction of hard instances for the maximum independent set problem (MIS). The constructed hard instances form an infinite graph sequence with increasing size, which possesses similar characteristics to sparse random graphs and in which MIS cannot be solved efficiently. We analytically and numerically show that all algorithms employing cycle-chain refutation, which is a general refutation method we introduce for capturing the ability of many known algorithms, cannot upper bound the size of the maximum independent set tightly.Comment: 9 pages, 5 figure

Information-theoretical bound of the irreversibility in thermal relaxation processes

We establish that entropy production, which is crucial to the characterization of thermodynamic irreversibility, is obtained through a variational principle involving the Kulback-Leibler divergence. A simple application of this representation leads to an information-theoretical bound on entropy production in thermal relaxation processes; this is a stronger inequality than the conventional second law of thermodynamics. This bound is also interpreted as a constraint on the possible path of a thermal relaxation process in terms of information geometry. Our results reveal a hidden universal law inherent to general thermal relaxation processes.Comment: 10 pages, 5 figures (accepted to Phys. Rev. Lett

Systematic Construction of Counterexamples to the Eigenstate Thermalization Hypothesis

We propose a general method to embed target states into the middle of the energy spectrum of a many-body Hamiltonian as its energy eigenstates. Employing this method, we construct a translationally-invariant local Hamiltonian with no local conserved quantities, which does not satisfy the eigenstate thermalization hypothesis. The absence of eigenstate thermalization for target states is analytically proved and numerically demonstrated. In addition, numerical calculations of two concrete models also show that all the energy eigenstates except for the target states have the property of eigenstate thermalization, from which we argue that our models thermalize after a quench even though they does not satisfy the eigenstate thermalization hypothesis.Comment: 9 pages, 3 figure