The Power of Being Explicit: Demystifying Work, Heat, and Free Energy in the Physics of Computation

Ouldridge, Thomas E.; Brittain, Rory A.; Wolde, Pieter Rein ten

doi:10.37911/9781947864078.12

Cited by 3 publications

(5 citation statements)

References 57 publications

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“…Then the Landauer cost of that inputreinitialization could be reduced to zero, simply by using that offboard copy of x IN to change the state of the input variable of the device (which contains the same value x IN ) back to its initialized state. (This point is also emphasized in [101].) As a result, under standard accounting, the Landauer cost of the full cycle would be 0 − S( p 1 (X OUT )), i.e.…”

Section: Conventions That Are Usually Implicitmentioning

confidence: 94%

“…A necessary condition for a CTMC to be thermodynamically reversible when run on some q 0 is that if we run it forward on that initial distribution q 0 to produce q 1 , and then 'run the process backward', by changing the signs of all momenta and reversing the time-sequence of any driving by work reservoirs, we return to q 0 . (See [85,[99][100][101].) Moreover, it has recently been proven that for any π and initial distribution q 0 , we can always design a CTMC that implements π on any initial distribution, and in addition is thermodynamically reversible if the initial distribution is q 0 .…”

Section: Entropy Flow Entropy Production and Landauer Costmentioning

confidence: 99%

“…in [84,110], although the confusion seems to be absent in [154]). This confusion resulted in significant controversy, which lasted for over three decades in the philosophy of science community and even longer in the physics and computer science communities [101,103,111,112].…”

Section: Logical Versus Thermodynamic Reversibilitymentioning

confidence: 99%

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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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Section: Conventions That Are Usually Implicitmentioning

confidence: 94%

Section: Entropy Flow Entropy Production and Landauer Costmentioning

confidence: 99%

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The stochastic thermodynamics of computation

Wolpert¹

2019

J. Phys. A: Math. Theor.

139

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show abstract

“…This implies, at least for Markovian systems, the existence of steady-state probability currents in the state space, which change sign under time-reversal. When a thermodynamically consistent description is available, the average rate of entropy production can be related to the rate of energy or information exchange between the system, the heat bath(s) it is connected to, and any other thermodynamic entity involved in the dynamics, such as a measuring device [15][16][17]. Whilst the rate of energy dissipation is of immediate interest since it captures how 'costly' it is to sustain specific dynamics (e.g., the metabolism sustaining the development of an organism [18,19]), entropy production has also been found to relate non-trivially to the efficiency and precision of the corresponding process via uncertainty relations [3,20].…”

Section: Introductionmentioning

confidence: 99%

Entropy Production in Exactly Solvable Systems

Cocconi

Garcia-Millan

Zhen

et al. 2020

Entropy

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The rate of entropy production by a stochastic process quantifies how far it is from thermodynamic equilibrium. Equivalently, entropy production captures the degree to which global detailed balance and time-reversal symmetry are broken. Despite abundant references to entropy production in the literature and its many applications in the study of non-equilibrium stochastic particle systems, a comprehensive list of typical examples illustrating the fundamentals of entropy production is lacking. Here, we present a brief, self-contained review of entropy production and calculate it from first principles in a catalogue of exactly solvable setups, encompassing both discrete- and continuous-state Markov processes, as well as single- and multiple-particle systems. The examples covered in this work provide a stepping stone for further studies on entropy production of more complex systems, such as many-particle active matter, as well as a benchmark for the development of alternative mathematical formalisms.

show abstract

Section: Introductionmentioning

confidence: 99%

Entropy production in exactly solvable systems

Cocconi,

Garcia-Millan,

Zhen

et al. 2020

Preprint

View full text Add to dashboard Cite

The rate of entropy production by a stochastic process quantifies how far it is from thermodynamic equilibrium. Equivalently, entropy production captures the degree to which detailed balance and time-reversal symmetry are broken. Despite abundant references to entropy production in the literature and its many applications in the study of non-equilibrium stochastic particle systems, a comprehensive list of typical examples illustrating the fundamentals of entropy production is lacking. Here, we present a brief, self-contained review of entropy production and calculate it from first principles in a catalogue of exactly solvable setups, encompassing both discrete-and continuous-state Markov processes, as well as single-and multiple-particle systems. The examples covered in this work provide a stepping stone for further studies on entropy production of more complex systems, such as many-particle active matter, as well as a benchmark for the development of alternative mathematical formalisms.

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The Power of Being Explicit: Demystifying Work, Heat, and Free Energy in the Physics of Computation

Cited by 3 publications

References 57 publications

The stochastic thermodynamics of computation

The stochastic thermodynamics of computation

Entropy Production in Exactly Solvable Systems

Entropy production in exactly solvable systems

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