Resource theory for work and heat

Sparaciari, Carlo; Oppenheim, Jonathan; Fritz, Tobias

doi:10.1103/physreva.96.052112

Cited by 65 publications

(121 citation statements)

References 56 publications

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“…Usually, notions of relative entropy are employed to capture asymptotic weakly correlated settings (thermodynamic limit), thus when acting on many uncorrelated copies of a system (see [28] for a recent discussion of asymptotic thermodynamics from the point of view of resource theories). Importantly, and in contrast, in our approach they emerge without having to invoke any thermodynamic limit, but rather follow from properties of monotones in the single-shot setting.…”

Section: Discussion and Outlookmentioning

confidence: 99%

Axiomatic Characterization of the Quantum Relative Entropy and Free Energy

Wilming

Gallego

Eisert

2017

Entropy

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Building upon work by Matsumoto, we show that the quantum relative entropy with full-rank second argument is determined by four simple axioms: (i) Continuity in the first argument; (ii) the validity of the data-processing inequality; (iii) additivity under tensor products; and (iv) super-additivity. This observation has immediate implications for quantum thermodynamics, which we discuss. Specifically, we demonstrate that, under reasonable restrictions, the free energy is singled out as a measure of athermality. In particular, we consider an extended class of Gibbs-preserving maps as free operations in a resource-theoretic framework, in which a catalyst is allowed to build up correlations with the system at hand. The free energy is the only extensive and continuous function that is monotonic under such free operations.

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Section: Discussion and Outlookmentioning

confidence: 99%

Axiomatic Characterization of the Quantum Relative Entropy and Free Energy

Wilming

Gallego

Eisert

2017

Entropy

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“…Then by Eq. (50), the 26 As an example, suppose the computational machine is a circuit, with the gates being the subsystems in question.…”

Section: Suppose We Have a Solitary Process Over A Subsystem A In Whimentioning

confidence: 99%

The stochastic thermodynamics of computation

Wolpert¹

2019

J. Phys. A: Math. Theor.

139

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One of the central concerns of computer science is how the resources needed to perform a given computation depend on that computation. Moreover, one of the major resource requirements of computers -ranging from biological cells to human brains to highperformance (engineered) computers -is the energy used to run them, i.e., the thermodynamic costs of running them. Those thermodynamic costs of performing a computation have been a long-standing focus of research in physics, going back (at least) to the early work of Landauer, in which he argued that the thermodynamic cost of erasing a bit in any physical system is at least kT ln [2].One of the most prominent aspects of computers is that they are inherently nonequilibrium systems. However, the research by Landauer and co-workers was done when non-equilibrium statistical physics was still in its infancy, requiring them to rely on equilibrium statistical physics. This limited the breadth of issues this early research could address, leading them to focus on the number of times a bit is erased during a computation -an issue having little bearing on the central concerns of computer science theorists.Since then there have been major breakthroughs in nonequilibrium statistical physics, leading in particular to the new subfield of "stochastic thermodynamics". These breakthroughs have allowed us to put the thermodynamic analysis of bit erasure on a fully formal (nonequilibrium) footing. They are also allowing us to investigate the myriad aspects of the relationship between statistical physics and computation, extending well beyond the issue of how much work is required to erase a bit.In this paper I review some of this recent work on the "stochastic thermodynamics of computation". After reviewing the salient parts of information theory, computer science theory, and stochastic thermodynamics, I summarize what has been learned about the entropic costs of performing a broad range of computations, extending from bit erasure to loop-free circuits to logically reversible circuits to information ratchets to Turing machines. These results reveal new, challenging engineering problems for how to design computers to have minimal thermodynamic costs. They also allow us to start to combine computer science theory and stochastic thermodynamics at a foundational level, thereby expanding both.dergoing arbitrary external driving. In particular, we can now decompose the time-derivative of the (Shannon) entropy of such a system into an "entropy production rate", quantifying the rate of change of the total entropy of the system and its environment, minus a "entropy flow rate", quantifying the rate of entropy exiting the system into its environment. Crucially, the entropy production rate is non-negative, regardless of the CTMC. So if it ever adds a nonzero amount to system entropy, its subsequent evolution cannot undo that increase in entropy. (For this reason it is sometimes referred to as irreversible entropy production.) This is the modern understanding of the second law of thermodynamics, for...

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“…", "What is heat?" [23,24,25,26,27,28,29], "What is entropy?" [7,4,8,9,32,34,33,30,15,31], "What is macroscopic?"…”

Section: Introductionmentioning

confidence: 99%

The fourth law of thermodynamics: steepest entropy ascent

Beretta

2020

Phil. Trans. R. Soc. A.

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When thermodynamics is understood as the science (or art) of constructing effective models of natural phenomena by choosing a minimal level of description capable of capturing the essential features of the physical reality of interest, the scientific community has identified a set of general rules that the model must incorporate if it aspires to be consistent with the body of known experimental evidence. Some of these rules are believed to be so general that we think of them as laws of Nature, such as the great conservation principles, whose ‘greatness’ derives from their generality, as masterfully explained by Feynman in one of his legendary lectures. The second law of thermodynamics is universally contemplated among the great laws of Nature. In this paper, we show that in the past four decades, an enormous body of scientific research devoted to modelling the essential features of non-equilibrium natural phenomena has converged from many different directions and frameworks towards the general recognition (albeit still expressed in different but equivalent forms and language) that another rule is also indispensable and reveals another great law of Nature that we propose to call the ‘fourth law of thermodynamics’. We state it as follows: every non-equilibrium state of a system or local subsystem for which entropy is well defined must be equipped with a metric in state space with respect to which the irreversible component of its time evolution is in the direction of steepest entropy ascent compatible with the conservation constraints. To illustrate the power of the fourth law, we derive (nonlinear) extensions of Onsager reciprocity and fluctuation–dissipation relations to the far-non-equilibrium realm within the framework of the rate-controlled constrained-equilibrium approximation (also known as the quasi-equilibrium approximation). This article is part of the theme issue ‘Fundamental aspects of nonequilibrium thermodynamics’.

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Resource theory for work and heat

Cited by 65 publications

References 56 publications

Axiomatic Characterization of the Quantum Relative Entropy and Free Energy

Axiomatic Characterization of the Quantum Relative Entropy and Free Energy

The stochastic thermodynamics of computation

The fourth law of thermodynamics: steepest entropy ascent

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