Abstract
A central focus thus far in this thesis has been the excess work required to drive a stochastic system out of thermodynamic equilibrium through a time-dependent external perturbation. This excess work is directly related to the entropy produced during the driving process, which conveniently allows excess work and entropy production to be used interchangeably to quantify dissipation. Given the common intuition of biological molecular machines as internally communicating work between components, it is tempting to extend this correspondence to the driving of one component of an autonomous system by another; however, no such relation between the internal excess work and entropy production exists. In this chapter we introduce the ‘transduced additional free energy rate’ between strongly coupled subsystems of an autonomous system, that is analogous to the excess power in systems driven by an external control parameter that receives no feedback from the system. We prove that this is a relevant measure of dissipation—in that it equals the (non-negative) steady-state entropy production rate due to the downstream subsystem—and demonstrate its advantages with a simple model system.
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Notes
- 1.
Material in this chapter also appears in Ref. [1].
- 2.
Because the entropy S (Sect. 2.5) is defined as the ensemble average of \(-\ln p_x\), we do not use angle brackets around entropy and entropy production terms here.
- 3.
This insight allows some intriguing interpretations in the context of the thermodynamics of sensing, where a system X collects information about an external and independent stochastic variable Y . Rearranging the second law with the information rate on the RHS of (9.6) yields a refined lower bound on the steady-state dissipation for the system in terms of the nostalgia [19, 20] or learning rate [21, 22].
- 4.
- 5.
Unlike the energy 𝜖 xy, the chemical potential is not a state function, and thus there is no unique chemical potential μ y for each state y. However, changes in chemical potential upon a transition \(\Delta \mu _{yy'}\) are well-defined for each transition.
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Large, S.J. (2021). Free Energy Transduction Within Autonomous Systems. In: Dissipation and Control in Microscopic Nonequilibrium Systems. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-85825-4_9
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