Dependence of dissipation on the initial distribution over states

Kolchinsky, Artemy; Wolpert, David H.

doi:10.1088/1742-5468/aa7ee1

Cited by 42 publications

(53 citation statements)

References 58 publications

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“…Combining Eq. (37) with the definitions of EF and of cross entropy establishes the following set of equivalent ways of expressing the EF: 14 In [108], due to a Bayesian interpretation of q, the mismatch cost is instead called the "dissipation due to incorrect priors". Proposition 1.…”

Section: A Entropy Flow Entropy Production and Landauer Costmentioning

confidence: 99%

The stochastic thermodynamics of computation

Wolpert¹

2019

J. Phys. A: Math. Theor.

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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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Section: A Entropy Flow Entropy Production and Landauer Costmentioning

confidence: 99%

The stochastic thermodynamics of computation

Wolpert¹

2019

J. Phys. A: Math. Theor.

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139

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“…An interesting direction for future work would consider the related, but more difficult, problem of carrying out a logical map (i.e., a conditional probability distribution) T ij from initial states j to final states i, while using a limited set of energy functions and minimizing EP. In other words, this direction would analyze driving protocols which (1) implements some desired logical map T ij , (2) achieve vanishing EP on some particular initial distribution p(0) [37], and (3) only use energy functions from some limited set E. It is possible that this problem can be tackled by combining the "transfer" protocol used in Proposition 1 with the constructions developed in [17,38], which show how to implement a given logical map with time-inhomogeneous continuous-time master equation (while possibly using some number of auxiliary "hidden" states).…”

Section: Discussionmentioning

confidence: 99%

Entropy production given constraints on the energy functions

Kolchinsky

Wolpert

2021

Phys. Rev. E

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We consider the problem of driving a classical Markovian system from some initial distribution p(0) to some final distribution p(τ ), assuming that the driving protocols can only use some limited set of energy functions, E. Assuming no other constraints on the driving protocol, we derive a simple condition that guarantees that the transformation p(0) → p(τ ) can be carried out with vanishing entropy production. This condition is stated in terms of the smallest values of any components in {p(0), p(τ )}, together with a graph-theoretic property defined in terms of E. Our results show that a surprisingly small E is sufficient; for example, any transformation can be carried out so long as we can manipulate the energy of a single state. We also derive a lower bound on the entropy production given constraints on both the energy functions and the kinetics, which is formulated in terms of a convex optimization problem.

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“…Appealing to Eq. (4) again, we see that the minimum total work under time-symmetric driving must be 8 [5,33], and (ii) the cost of neglecting the local statistics of the manipulated memory [5,34].…”

Section: Time Symmetric Drivingmentioning

confidence: 99%

“…= μ 0 (000) + μ 0 (010) + μ 0 (100) + μ 0 (111) . (34) As a consequence, the initial correlation among the memory elements has a profound impact on the coefficient of minimal dissipation. The overall dissipation still diverges ∼ ln( −1 ), though, with increasing reliability as long as the implementation is time-symmetric.…”

Section: B Logic Gatesmentioning

confidence: 99%

Balancing error and dissipation in computing

Riechers

Boyd

Wimsatt

et al. 2020

Phys. Rev. Research

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Modern digital electronics support remarkably reliable computing, especially given the challenge of controlling nanoscale logical components that interact in fluctuating environments. However, we demonstrate that the high-reliability limit is subject to a fundamental error-energy-efficiency tradeoff that arises from time-symmetric control: requiring a low probability of error causes energy consumption to diverge as the logarithm of the inverse error rate for nonreciprocal logical transitions. The reciprocity (self-invertibility) of a computation is a stricter condition for thermodynamic efficiency than logical reversibility (invertibility), the latter being the root of Landauer's work bound on erasing information. Beyond engineered computation, the results identify a generic error-dissipation tradeoff in steady-state transformations of genetic information carried out by biological organisms. The lesson is that computational dissipation under time-symmetric control cannot reach, and is often far above, the Landauer limit. In this way, time-asymmetry becomes a design principle for thermodynamically efficient computing.

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Dependence of dissipation on the initial distribution over states

Cited by 42 publications

References 58 publications

The stochastic thermodynamics of computation

The stochastic thermodynamics of computation

Entropy production given constraints on the energy functions

Balancing error and dissipation in computing

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