Thermodynamics provides a robust conceptual framework and set of laws that govern the exchange of energy and matter. Although these laws were originally articulated for macroscopic objects, nanoscale systems also exhibit “thermodynamic-like” behavior – for instance, biomolecular motors convert chemical fuel into mechanical work, and single molecules exhibit hysteresis when manipulated using optical tweezers. To what extent can the laws of thermodynamics be scaled down to apply to individual microscopic systems, and what new features emerge at the nanoscale? I will describe some of the challenges and recent progress – both theoretical and experimental – associated with addressing these questions. Along the way, my talk will touch on non-equilibrium fluctuations, “violations” of the second law, the thermodynamic arrow of time, nanoscale feedback control, strong system-environment coupling, and quantum thermodynamics. In two subsequent, classroom-style lectures I will explore these issues in greater depth, providing derivations and filling in details.
In this chalkboard lecture I will derive some of the theoretical results presented in Lecture 1. I will focus in particular on non-equilibrium fluctuation relations for work and free energy, and I will show how these can be obtained within various models of microscopic dynamics. I will discuss how these results reveal new features of the second law of thermodynamics at the nanoscale, especially relating to the probability to observe transient violations of the second law. I will also show that they provide a way of quantifying our ability to determine the thermodynamic arrow of time.
In my second chalkboard lecture I will focus on two broad topics. The first involves the thermodynamic costs and opportunities of information processing. I will discuss Maxwell’s demon and Landauer’s principle, and I will relate these issues to more recent work on fluctuation relations for feedback control. In the second portion of my talk I will discuss attempts to extend non-equilibrium work relations to the quantum realm, where the very definition of “quantum work” poses a challenge. I will show how such relations can be derived easily within the two-point measurement scheme for closed quantum systems, and I will discuss the difficulties associated with extending these results to open quantum systems.
This lecture series is part of the program Fluctuations in Nonequilibrium Systems: Theory and applications.