On Dissipation Bounds: Discrete Stochastic Control of Nonequilibrium Systems

Abstract

In the previous two chapters, we derived several methods of quantifying the excess work required to drive stochastic systems in novel ways that have been motivated in large part by the physics of biological molecular machines. While these two frameworks—stochastic and discrete driving protocols—individually provide interesting physical insights into how each driving mechanism affects the energy flows within nano-scale systems, it is the combination of both that most closely parallels the physical context of molecular machines. In this chapter, we explore the effects of consolidating these two theoretical frameworks into one. In addition, building upon recent work on the subject, we impose an external ‘cost of control’, to quantify the dissipation associated with generating time-asymmetric driving. Ultimately, we find that the nonequilibrium component of the average excess work is an additional contribution not captured in the scope of previous research. We study this theory within the context of a simple model system and find that, in all limits, the average excess work is lower bounded by a positive quantity. However, we also discuss the shortcomings of this approach—in particular how they relate to the local detailed-balance condition—and the associated implications for its utility in understanding the internal mechanics of molecular machines.