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Developing a thermodynamic theory of computation is a challenging task at the interface of nonequilibrium thermodynamics and computer science. In particular, this task requires dealing with difficulties such as stochastic halting times, unidirectional (possibly deterministic) transitions, and restricted initial conditions, features common in real-world computers. Here, we present a framework which tackles all such difficulties by extending the martingale theory of nonequilibrium thermodynamics to generic nonstationary Markovian processes, including those with broken detailed balance and/or absolute irreversibility. We derive several universal fluctuation relations and second-law-like inequalities that provide both lower and upper bounds on the intrinsic dissipation (mismatch cost) associated with any periodic process—in particular, the periodic processes underlying all current digital computation. Crucially, these bounds apply even if the process has stochastic stopping times, as it does in many computational machines. We illustrate our results with exhaustive numerical simulations of deterministic finite automata processing bit strings, one of the fundamental models of computation from theoretical computer science. We also provide universal equalities and inequalities for the acceptance probability of words of a given length by a deterministic finite automaton in terms of thermodynamic quantities, and outline connections between computer science and stochastic resetting. Our results, while motivated from the computational context, are applicable far more broadly.
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Thermodynamic speed limits for mechanical work
Abstract Thermodynamic speed limits are a set of classical uncertainty relations that, so far, place global bounds on the stochastic dissipation of energy as heat and the production of entropy. Here, instead of constraints on these thermodynamic costs, we derive integral speed limits that are upper and lower bounds on a thermodynamic benefit—the minimum time for an amount of mechanical work to be done on or by a system. In the short time limit, we show how this extrinsic timescale relates to an intrinsic timescale for work, recovering the intrinsic timescales in differential speed limits from these integral speed limits and turning the first law of stochastic thermodynamics into a first law of speeds. As physical examples, we consider the work done by a flashing Brownian ratchet and the work done on a particle in a potential well subject to external driving.
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- Award ID(s):
- 1856250
- PAR ID:
- 10396220
- Publisher / Repository:
- IOP Publishing
- Date Published:
- Journal Name:
- Journal of Physics A: Mathematical and Theoretical
- Volume:
- 56
- Issue:
- 5
- ISSN:
- 1751-8113
- Page Range / eLocation ID:
- Article No. 05LT01
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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