arXiv subjects

Takahiro Sagawa

Publications and source records attributed to Takahiro Sagawa.

103 records · Page 6Linked to original sources

arXiv2011

Geometrical Expression of Excess Entropy Production

We derive a geometrical expression of the excess entropy production for quasi-static transitions between nonequilibrium steady states of Markovian jump processes, which can be exactly applied to nonlinear and nonequilibrium situations. The obtained expression is geometrical; the excess entropy production depends only on a trajectory in the parameter space, analogous to the Berry phase in quantum mechanics. Our results imply that vector potentials are needed to construct thermodynamics of nonequilibrium steady states.

cond-mat.stat-mech↗

arXiv2011

Hamiltonian Derivations of the Generalized Jarzynski Equalities under Feedback Control

In the presence of feedback control by "Maxwell's demon," the second law of thermodynamics and the nonequilibrium equalities such as the Jarzynski equality need to be generalized. In this paper, we derive the generalized Jarzynski equalities for classical Hamiltonian dynamics based on the Liouville's theorem, which is the same approach as the original proof of the Jarzynski equality [Phys. Rev. Lett. 78, 2690 (1997)]. The obtained equalities lead to the generalizations of the second law of thermodynamics for the Hamiltonian systems in the presence of feedback control.

cond-mat.stat-mech↗

arXiv2011

Uncertainty Relation Revisited from Quantum Estimation Theory

By invoking quantum estimation theory we formulate bounds of errors in quantum measurement for arbitrary quantum states and observables in a finite-dimensional Hilbert space. We prove that the measurement errors of two observables satisfy Heisenberg's uncertainty relation, find the attainable bound, and provide a strategy to achieve it.

quant-ph↗

arXiv2011

Quantum Szilard Engine

The Szilard engine (SZE) is the quintessence of Maxwell's demon, which can extract the work from a heat bath by utilizing information. We present the first complete quantum analysis of the SZE, and derive an analytic expression of the quantum-mechanical work performed by a quantum SZE containing an arbitrary number of molecules, where it is crucial to regard the process of insertion or removal of a wall as a legitimate thermodynamic process. We find that more (less) work can be extracted from the bosonic (fermionic) SZE due to the indistinguishability of identical particles.

quant-ph↗

arXiv2010

Information heat engine: converting information to energy by feedback control

In 1929, Leo Szilard invented a feedback protocol in which a hypothetical intelligence called Maxwell's demon pumps heat from an isothermal environment and transduces it to work. After an intense controversy that lasted over eighty years; it was finally clarified that the demon's role does not contradict the second law of thermodynamics, implying that we can convert information to free energy in principle. Nevertheless, experimental demonstration of this information-to-energy conversion has been elusive. Here, we demonstrate that a nonequilibrium feedback manipulation of a Brownian particle based on information about its location achieves a Szilard-type information-energy conversion. Under real-time feedback control, the particle climbs up a spiral-stairs-like potential exerted by an electric field and obtains free energy larger than the amount of work performed on it. This enables us to verify the generalized Jarzynski equality, or a new fundamental principle of "information-heat engine" which converts information to energy by feedback control.

cond-mat.stat-mech↗

arXiv2010

Generalized Jarzynski Equality under Nonequilibrium Feedback Control

The Jarzynski equality is generalized to situations in which nonequilibrium systems are subject to a feedback control. The new terms that arise as a consequence of the feedback describe the mutual information content obtained by measurement and the efficacy of the feedback control. Our results lead to a generalized fluctuation-dissipation theorem that reflects the readout information, and can be experimentally tested using small thermodynamic systems. We illustrate our general results by an introducing "information ratchet," which can transport a Brownian particle in one direction and extract a positive work from the particle.

cond-mat.stat-mech↗

arXiv2010

Optimal Measurement on Noisy Quantum Systems

We identify the optimal measurement for obtaining information about the original quantum state after the state to be measured has undergone partial decoherence due to noise. We quantify the information that can be obtained by the measurement in terms of the Fisher information and find its value for the optimal measurement. We apply our results to a quantum control scheme based on a spin-boson model.

quant-ph↗

arXiv2009

Minimal Energy Cost for Thermodynamic Information Processing: Measurement and Information Erasure

The fundamental lower bounds of the thermodynamic energy cost (work) needed for the measurement and the erasure of information are found. The lower bound for the erasure vindicates the "Landauer's principle" for a special case, but otherwise implies its breakdown, indicating that no unique relationship exists between logical reversibility and physical one. Our results constitute the second law of "information thermodynamics", in which the information content and thermodynamic variables are treated on an equal footing.

quant-ph↗

arXiv2009

Weak Value and Correlation Function

We show that there exists, in quantum theory, a close relationship between the weak value and the correlation function, which sheds new lights on the concept of the weak value.

quant-ph↗

arXiv2008

Second Law of Thermodynamics with Discrete Quantum Feedback Control

A new thermodynamic inequality is derived which leads to the maximum work that can be extracted from multi-heat baths with the assistance of discrete quantum feedback control. The maximum work is determined by the free-energy difference and a generalized mutual information content between the thermodynamic system and the feedback controller. This maximum work can exceed that in conventional thermodynamics and, in the case of a heat cycle with two heat baths, the heat efficiency can be greater than that of the Carnot cycle. The consistency of our results with the second law of thermodynamics is ensured by the fact that work is needed for information processing of the feedback controller.

quant-ph↗

arXiv2008

Accuracy matrix in generalized simultaneous measurement of a qubit system

We formulate the accuracy of quantum measurement for a qubit system in terms of a 3 by 3 matrix. This matrix, which we refer to as the accuracy matrix, can be calculated from a positive operator-valued measure (POVM) corresponding to the quantum measurement. Based on the accuracy matrix, we derive new trade-off relations between the measurement accuracy of two or three noncommuting observables of a qubit system. These trade-off relations offer a quantitative information-theoretic representation of Bohr's principle of complementarity. They can be interpreted as the uncertainty relations between measurement errors in simultaneous measurements, and also as the trade-off relations between the measurement error and back-action of measurement. A no-cloning inequality is derived from the trade-off relations. Furthermore, our formulation and the obtained results can be applied to analyze quantum state tomography. We also show that the accuracy matrix is closely related to the maximum-likelihood estimation and the Fisher information matrix for a finite number of samples; the accuracy matrix tells us how accurately we can estimate the probability distributions of observables of an unknown state by quantum measurement.

quant-ph↗

arXiv2007

Upper bound on our knowledge about noncommuting observables for a qubit system

A trade-off relation on our knowledge about two noncommuting observables of a qubit system in simultaneous measurement is formulated. The obtained inequality offers a quantitative information-theoretic representation of Bohr's principle of complementarity, and can be interpreted as a trade-off relation on the asymptotic accuracy of the maximum-likelihood estimation of the probability distributions of observables.

quant-ph↗

arXiv2007

Jarzynski Equality with Maxwell's Demon

We propose a new thermodynamic equality and several inequalities concerning the relationship between work and information for an isothermal process with Maxwell's demon. Our approach is based on the formulation a la Jarzynski of the thermodynamic engine and on the quantum information-theoretic characterization of the demon. The lower bound of each inequality, which is expressed in terms of the information gain by the demon and the accuracy of the demon's measurement, gives the minimum work that can be performed on a single heat bath in an isothermal process. These results are independent of the state of the demon, be it in thermodynamic equilibrium or not.

cond-mat.stat-mech↗