Quantum thermodynamics

Vinjanampathy, Sai; Anders, Janet

doi:10.1080/00107514.2016.1201896

Cited by 909 publications

(847 citation statements)

References 219 publications

(354 reference statements)

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“…5 See e.g. [48][49][50] for discussion of the additional considerations To find the total work cost of a protocol, one typically integrates over a series of infinitesimal contributions.…”

Section: Corollary 11 (All Non-zero) If For Somementioning

confidence: 99%

Thermodynamics of complexity and pattern manipulation

et al. 2017

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Many organisms capitalize on their ability to predict the environment to maximize available free energy, and reinvest this energy to create new complex structures. This functionality relies on the manipulation of patterns-temporally ordered sequences of data. Here, we propose a framework to describe pattern manipulators -devices that convert thermodynamic work to patterns or vice versa -and use them to build a 'pattern engine that facilitates a thermodynamic cycle of pattern creation and consumption. We show that the least heat dissipation is achieved by the provably simplest devices; the ones that exhibit desired operational behaviour while maintaining the least internal memory. We derive the ultimate limits of this heat dissipation, and show that it is generally non-zero and connected with the patterns intrinsic crypticity -a complexity theoretic quantity that captures the puzzling difference between the amount of information the pattern's past behaviour reveals about its future, and the amount one needs to communicate about this past to optimally predict the future.The manipulation of patterns is as important to living organisms as it is for computation. Living things capitalize on structure in their environment for available energy, and use this energy to generate new complex structures. Similarly, a crucial task in the modern era of big data is to identify patterns in large data sets in order to make predictions about future events -often at great energetic cost. Here, we consider the thermodynamic costs intrinsic to this sort of pattern manipulation and ask: is there a preferred method by which this manipulation should be done? Our intuition is that simpler is better, a longstanding tenant of natural philosophy known as Occam's razor. To formalize this, we first qualify what is meant both by simpler and by better.In complexity science, computational mechanics formalizes what is simpler in the context of pattern manipulation [1][2][3]. The premise is that everything we observe in the environment can be considered to be a patterna temporal sequence of data exhibiting certain statistical structure. Much of science then deals with building models that can explain such statistics -machines that take information from past observations, and use it to generate statistically coinciding conditional future predictions. Given two machines that exhibit same pattern of behaviour, the one that stores less information from the past is considered simpler, the motivation being that it better isolates indicators of future behaviour. The simplest such machine then defines exactly how much memory is required to produce a given pattern, and thus * ajpgarner@nus.edu.sg † cqtmileg@nus.edu.sg quantifies the pattern's intrinsic structure. Known as statistical complexity, this measure has been applied to quantify structure in diverse contexts [4][5][6].Meanwhile in thermodynamics, better originally described heat engines that produce more work with less wasted heat. This carries through to modern thermodynamics: the best approach fo...

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“…5 See e.g. [48][49][50] for discussion of the additional considerations To find the total work cost of a protocol, one typically integrates over a series of infinitesimal contributions.…”

Section: Corollary 11 (All Non-zero) If For Somementioning

confidence: 99%

Thermodynamics of complexity and pattern manipulation

et al. 2017

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“…Resource theory is the study of possible transformations from one state to the other, by using "free states" and possibly non-free states that are considered as a resource [23,25,54]. The free states in TRT are the thermal states.…”

Section: Appendix IV -Resource Theory Monotonesmentioning

confidence: 99%

“…Thermodynamic resource theory states that under "Thermal operations" [23,54] the free energy is only one member of a whole monotone family [53]:…”

Section: Appendix IV -Resource Theory Monotonesmentioning

confidence: 99%

Additional energy-information relations in thermodynamics of small systems

Uzdin

2017

Phys. Rev. E

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The Clausius inequality (CI) form of the second law of thermodynamics relates information changes (entropy) to changes in the first moment of the energy (heat and indirectly also work). Are there similar relations between other moments of the energy distribution, and other information measures, or is the Clausius inequality a one of a kind instance of the energy-information paradigm? If there are additional relations, can they be used to make predictions on measurable quantities? Changes in the energy distribution beyond the first moment (average heat or work) are especially important in small systems which are often very far from thermal equilibrium. The generalized Clausius inequalities (GCI's), here derived, provide positive answers to the two questions above and add another layer to the fundamental connection between energy and information. To illustrate the utility of the new GCI's, we find scenarios where the GCI's yield tighter constraints on performance (e.g. in thermal machines) compared to the second law. To obtain the GCI's we use the Bregman divergence -a mathematical tool found to be highly suitable for energy-information studies. The quantum version of the GCI's provides a thermodynamic meaning to various quantum coherence measures. It is intriguing to fully map the regime of validity of the GCI's and extend the present results to more general scenarios including continuous systems and particles exchange with the baths.

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“…E denotes the average, over infinitely many trials, of the gas's internal energy; and S denotes the gas's statistical mechanical entropy [36]. The statistical mechanical entropy of a classical state has been cast in terms of the information-theoretic Shannon entropy [36,37].…”

Section: One-shot Statistical Mechanicsmentioning

confidence: 99%

“…The statistical mechanical entropy of a classical state has been cast in terms of the information-theoretic Shannon entropy [36,37]. The Shannon entropy of a discrete probability distribution P = {p i } is defined as…”

Section: One-shot Statistical Mechanicsmentioning

confidence: 99%

Toward Physical Realizations of Thermodynamic Resource Theories

Halpern

2016

Information and Interaction

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Conventional statistical mechanics describes large systems and averages over many particles or over many trials. But work, heat, and entropy impact the small scales that experimentalists can increasingly control, e.g., in single-molecule experiments. The statistical mechanics of small scales has been quantified with two toolkits developed in quantum information theory: resource theories and one-shot information theory. The field has boomed recently, but the theorems amassed have hardly impacted experiments. Can thermodynamic resource theories be realized experimentally? Via what steps can we shift the theory toward physical realizations? Should we care? I present eleven opportunities in physically realizing thermodynamic resource theories.

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Quantum thermodynamics

Cited by 909 publications

References 219 publications

Thermodynamics of complexity and pattern manipulation

Thermodynamics of complexity and pattern manipulation

Additional energy-information relations in thermodynamics of small systems

Toward Physical Realizations of Thermodynamic Resource Theories

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