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Princeton, NJ, United States

Abe S.,Mie University | Abe S.,Institut Superieur des Materiaux et Mecaniques Avances du Mans | Abe S.,Inspire Inc. | Okuyama S.,Mie University
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2011

The similarity between quantum mechanics and thermodynamics is discussed. It is found that if the Clausius equality is imposed on the Shannon entropy and the analog of the quantity of heat, then the value of the Shannon entropy comes to formally coincide with that of the von Neumann entropy of the canonical density matrix, and pure-state quantum mechanics apparently transmutes into quantum thermodynamics. The corresponding quantum Carnot cycle of a simple two-state model of a particle confined in a one-dimensional infinite potential well is studied, and its efficiency is shown to be identical to the classical one. © 2011 American Physical Society.


Abe S.,Mie University | Abe S.,Institut Superieur des Materiaux et Mecaniques Avances du Mans | Abe S.,Inspire Inc.
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2011

In their work, Bender, Brody, and Meister have shown by employing a two-state model of a particle confined in the one-dimensional infinite potential well that it is possible to construct a quantum-mechanical analog of the Carnot engine through changes of both the width of the well and the quantum state in a specific manner. Here, a discussion is developed about realizing the maximum power of such an engine, where the width of the well moves at low but finite speed. The efficiency of the engine at the maximum power output is found to be universal independently of any of the parameters contained in the model. © 2011 American Physical Society.


Abe S.,Mie University | Abe S.,Institut Superieur des Materiaux et Mecaniques Avances du Mans | Abe S.,Inspire Inc.
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2010

Nonequilibrium complex systems are often effectively described by the mixture of different dynamics on different time scales. Superstatistics, which is "statistics of statistics" with two largely separated time scales, offers a consistent theoretical framework for such a description. Here, a theory is developed for log-normal superstatistics based on the fluctuation theorem for entropy changes as well as the maximum entropy method. This gives novel physical insight into log-normal statistics, other than the traditional multiplicative random processes. A comment is made on a possible application of the theory to the fluctuating energy dissipation rate in turbulence. © 2010 The American Physical Society.


Usha Devi A.R.,Bangalore University | Usha Devi A.R.,Inspire Inc. | Rajagopal A.K.,Inspire Inc. | Sudha,Kuvempu University | Sudha,University of Cambridge
Physical Review A - Atomic, Molecular, and Optical Physics | Year: 2011

Dynamical A and B maps have been employed extensively by Sudarshan and co-workers to investigate open-system evolution of quantum systems. A canonical structure of the A map is introduced here. It is shown that this canonical A map enables us to investigate whether the dynamics is completely positive (CP) or not completely positive (NCP) in an elegant way and, hence, it subsumes the basic results on open-system dynamics. Identifying memory effects in open-system evolution is gaining increasing importance recently and, here, a criterion of non-Markovianity, based on the relative entropy of the dynamical state is proposed. The relative entropy difference of the dynamical system serves as a complementary characterization-though not related directly-to the fidelity difference criterion proposed recently. Three typical examples of open-system evolution of a qubit, prepared initially in a correlated state with another qubit (environment), and evolving jointly under a specific unitary dynamics-which corresponds to a NCP dynamical map-are investigated by employing both the relative entropy difference and fidelity difference tests of non-Markovianity. The two-qubit initial states are chosen to be (i) a pure entangled state, (ii) the Werner state, which exemplifies both entangled and separable states of qubits, depending on a real parameter, and (iii) a separable mixed state. Both the relative entropy and fidelity criteria offer a nice display of how non-Markovianity manifests itself in all three examples. © 2011 American Physical Society.


Karthik H.S.,Raman Research Institute | Devi A.R.U.,Bangalore University | Devi A.R.U.,Inspire Inc. | Rajagopal A.K.,Inspire Inc. | And 2 more authors.
Physical Review A - Atomic, Molecular, and Optical Physics | Year: 2015

There has been a surge of research activity recently on the role of joint measurability of unsharp observables in nonlocal features, viz., violation of Bell inequality and EPR steering. Here, we investigate the entropic uncertainty relation for a pair of noncommuting observables (of Alice's system) when an entangled quantum memory of Bob is restricted to record outcomes of jointly measurable positive operator valued measures. We show that with this imposed constraint of joint measurability at Bob's end, the entropic uncertainties associated with Alice's measurement outcomes - conditioned by the results registered at Bob's end - obey an entropic steering inequality. Thus, Bob's nonsteerability is intrinsically linked to his inability to predict the outcomes of Alice's pair of noncommuting observables with better precision, even when they share an entangled state. As a further consequence, we prove that in the joint measurability regime, the quantum advantage envisaged for the construction of security proofs in quantum key distribution is lost. © 2015 American Physical Society.

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