Abstract
A general understanding of the thermodynamic costs of nonequilibrium processes would illuminate the design principles of efficient microscopic machines. Considerable effort has gone into finding and classifying the deterministic control protocols that drive a system rapidly between states at minimum energetic cost. But for autonomous microscopic systems—like molecular machines—driving processes are themselves stochastic. In this chapter we generalize a linear-response framework to incorporate such protocol variability, deriving a lower bound on the work that is realized at finite protocol duration, far from the quasistatic limit. We illustrate our findings in two model systems. Ultimately, this theoretical framework provides a thermodynamic rationale for rapid operation, independent of any functional incentives.
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Notes
- 1.
Material in this chapter also appears in Ref. [3].
- 2.
For a harmonic system, the forces are linear in position f ∝ x, and thus 〈δf(0)δf(t)〉∝〈δx(0)δx(t)〉. This implies that the force relaxation time and position relaxation time are equivalent.
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Large, S.J. (2021). Stochastic Control in Microscopic Nonequilibrium Systems. In: Dissipation and Control in Microscopic Nonequilibrium Systems. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-85825-4_6
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DOI: https://doi.org/10.1007/978-3-030-85825-4_6
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