Second-law-like inequalities with information and their interpretations

Horowitz, Jordan M.; Sandberg, Henrik

doi:10.1088/1367-2630/16/12/125007

Cited by 139 publications

(236 citation statements)

References 55 publications

(193 reference statements)

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“…As shown below, similar factors have been introduced before in the context of Fluctuation theorems with feedback [32,33] and on related second-law like inequalities with information [30,31].…”

Section: A Equilibrium Initial Conditionsmentioning

confidence: 92%

“…Due to the delay, the state variable x m obeys a nonmarkovian dynamics, and as a result, the error is correlated with the true work in a complex way. Linear Langevin systems with time delays have been studied extensively in the literature on feedback systems [30,31]. In that respect, our problem is simpler in that there is no feedback since the first equation in Eq.…”

Section: F Correlated Error Due To Finite Delay In Measurementsmentioning

confidence: 99%

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Thermodynamic inference based on coarse-grained data or noisy measurements

2016

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Fluctuation theorems have become an important tool in single molecule biophysics to measure free energy differences from non-equilibrium experiments. When significant coarse-graining or noise affect the measurements, the determination of the free energies becomes challenging. In order to address this thermodynamic inference problem, we propose improved estimators of free energy differences based on fluctuation theorems, which we test on a number of examples. The effect of the noise can be described by an effective temperature, which only depends on the signal to noise ratio, when the work is Gaussian distributed and uncorrelated with the error made on the work. The notion of effective temperature appears less useful for non-Gaussian work distributions or when the error is correlated with the work, but nevertheless, as we show, improved estimators can still be constructed for such cases. As an example of non-trivial correlations between the error and the work, we also consider measurements with delay, as described by linear Langevin equations.

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Section: A Equilibrium Initial Conditionsmentioning

confidence: 92%

Section: F Correlated Error Due To Finite Delay In Measurementsmentioning

confidence: 99%

Thermodynamic inference based on coarse-grained data or noisy measurements

2016

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“…But it is also stated that there is a strong connection between irreversibility and information gained or lost by the system, manifested in the physical consequences of the Szilard engine [3] and expressed in the Landauer principle of information erasure [4]. So a complete description of the entropy production following a thermodynamic transformation requires the account of the information flow [5] and the addition of information reservoirs, in addition to the traditional heat and chemical baths [6]. This is especially relevant in isolated quantum systems that equilibrate to complex equilibrium states [7] which store relevant information in sets of commuting constants of motion [8] or in the coherences between different subspaces of the system in the case of degenerate spectra [9,10].…”

Section: Introductionmentioning

confidence: 99%

Irreversible processes without energy dissipation in an isolated Lipkin-Meshkov-Glick model

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Relaño

2015

Phys. Rev. E

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For a certain class of isolated quantum systems, we report the existence of irreversible processes in which the energy is not dissipated. After a closed cycle in which the initial energy distribution is fully recovered, the expectation value of a symmetry-breaking observable changes from a value differing from zero in the initial state to zero in the final state. This entails the unavoidable loss of a certain amount of information and constitutes a source of irreversibility. We show that the von Neumann entropy of time-averaged equilibrium states increases in the same magnitude as a consequence of the process. We support this result by means of numerical calculations in an experimentally feasible system, the Lipkin-Meshkov-Glick model.

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“…Furthermore, unlike the information flow, transfer entropy is always non-negative. For a recent and detailed information-theoretic analysis on the use of transfer entropy rate and information flow to bound the extracted work during a thermodynamic process with feedback, we refer to [35].…”

Section: A the Liang-kleeman Approach: Thermodynamic Argumentsmentioning

confidence: 99%

Thermodynamic aspects of information transfer in complex dynamical systems

2016

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From the Horowitz-Esposito stochastic thermodynamical description of information flows in dynamical systems [J. M. Horowitz and M. Esposito, Phys. Rev. X4, 031015 (2014)], it is known that while the second law of thermodynamics is satisfied by a joint system, the entropic balance for the subsystems is adjusted by a term related to the mutual information exchange rate between the two subsystems. In this article, we present a quantitative discussion of the conceptual link between the Horowitz-Esposito analysis and the Liang-Kleeman work on information transfer between dynamical system components [X. S. Liang and R. Kleeman, Phys. Rev. Lett. 95, 244101 (2005)]. In particular, the entropic balance arguments employed in the two approaches are compared. Notwithstanding all differences between the two formalisms, our work strengthens the Liang-Kleeman heuristic balance reasoning by showing its formal analogy with the recent Horowitz-Esposito thermodynamic balance arguments.

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Second-law-like inequalities with information and their interpretations

Cited by 139 publications

References 55 publications

Thermodynamic inference based on coarse-grained data or noisy measurements

Thermodynamic inference based on coarse-grained data or noisy measurements

Irreversible processes without energy dissipation in an isolated Lipkin-Meshkov-Glick model

Thermodynamic aspects of information transfer in complex dynamical systems

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