On the Accessibility of States for Systems with Dissipative Dynamics

Zylka, Ch.

doi:10.1002/andp.19905020225

Cited by 4 publications

(3 citation statements)

References 7 publications

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“…[12]. In fact, the notion of continuous majorisation has a decades-long history and appears in a variety of research fields from thermodynamics and order theory [36,37], through plasma physics [38,39], to social sciences [40]. Moreover, the study in Ref.…”

Section: Region Cγ(p): Classical Memoryless Transformationsmentioning

confidence: 99%

Quantum advantage in simulating stochastic processes

Korzekwa,

Lostaglio

2020

Preprint

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We investigate the problem of simulating classical stochastic processes through quantum dynamics, and present three scenarios where memory/time quantum advantages arise. First, by introducing and analysing a quantum version of the embeddability problem for stochastic matrices, we show that quantum memoryless dynamics can simulate classical processes that necessarily require memory. Second, by extending the notion of space-time cost of a stochastic process P to the quantum domain, we prove an exponential advantage of the quantum cost of simulating P over the classical cost. Third, we demonstrate that the set of classical states accessible via Markovian master equations with quantum controls is larger than the set of those accessible with classical controls, leading, e.g., to an advantage in cooling protocols. To achieve this last point, we develop the notion of continuous thermo-majorisation, which strengthens the so-called "second laws" by including the typical constraint that the dynamics is (effectively) Markovian.

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Section: Region Cγ(p): Classical Memoryless Transformationsmentioning

confidence: 99%

Quantum advantage in simulating stochastic processes

Korzekwa,

Lostaglio

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…[37]. In fact, the notion of continuous majorization has a decadeslong history and appears in a variety of research fields from thermodynamics and order theory [38,39], through plasma physics [40,41], to social sciences [42]. Moreover, this notion was employed and studied in more detail in Ref.…”

Section: B Continuous Thermomajorizationmentioning

confidence: 99%

Continuous thermomajorization and a complete set of laws for Markovian thermal processes

Lostaglio

Korzekwa

2022

Phys. Rev. A

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The standard dynamical approach to quantum thermodynamics is based on Markovian master equations describing the thermalization of a system weakly coupled to a large environment, and on tools such as entropy production relations. Here we develop a framework overcoming the limitations that the current dynamical and information theory approaches encounter when applied to this setting. More precisely, we introduce the notion of continuous thermomajorization and employ it to obtain necessary and sufficient conditions for the existence of a Markovian thermal process transforming between given initial and final energy distributions of the system. These lead to a complete set of generalized entropy production inequalities including the standard one as a special case. Importantly, these conditions can be reduced to a finitely verifiable set of constraints governing nonequilibrium transformations under master equations. What is more, the framework is also constructive, i.e., it returns explicit protocols realizing any allowed transformation. These protocols use as building blocks elementary thermalizations, which we prove to be universal controls. Finally, we also present an algorithm constructing the full set of energy distributions achievable from a given initial state via Markovian thermal processes and provide a Mathematica implementation solving d = 6 on a laptop computer in minutes.

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“…[34]. In fact, the notion of continuous majorization has a decades-long history and appears in a variety of research fields from thermodynamics and order theory [35,36], through plasma physics [37,38], to social sciences [39]. Moreover, this notion was employed and studied in more detail in Ref.…”

Section: Definition 3 (Continuous Thermomajorization)mentioning

confidence: 99%

Continuous thermomajorization and a complete set of laws for Markovian thermal processes

Lostaglio,

Korzekwa

2021

Preprint

View full text Add to dashboard Cite

The standard dynamical approach to quantum thermodynamics is based on Markovian master equations describing the thermalization of a system weakly coupled to a large environment, and on tools such as entropy production relations. Here we introduce a new framework overcoming the limitations that the current dynamical and information theory approaches encounter when applied to this setting. More precisely, based on a newly introduced notion of continuous thermomajorization, we obtain necessary and sufficient conditions for the existence of a Markovian thermal process transforming between given initial and final energy distributions of the system. These lead to a complete set of generalized entropy production inequalities including the standard one as a special case. Importantly, these conditions can be reduced to a finitely verifiable set of constraints governing non-equilibrium transformations under master equations. What is more, the framework is also constructive, i.e., it returns explicit protocols realizing any allowed transformation. These protocols use as building blocks elementary thermalizations, which we prove to be universal controls. Finally, we also present an algorithm constructing the full set of energy distributions achievable from a given initial state via Markovian thermal processes and provide a Mathematica implementation solving d = 6 on a laptop computer in minutes.

show abstract

On the Accessibility of States for Systems with Dissipative Dynamics

Cited by 4 publications

References 7 publications

Quantum advantage in simulating stochastic processes

Quantum advantage in simulating stochastic processes

Continuous thermomajorization and a complete set of laws for Markovian thermal processes

Continuous thermomajorization and a complete set of laws for Markovian thermal processes

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