Thermodynamic inequalities: motivation, foundations, and applications

In this talk, I will introduce the topic of thermodynamic inequalities. One motivation for studying inequalities is that they can provide universal constraints on what can and cannot happen in physical systems. From a more practical point of view, they can be used to estimate physical observables even in situations where no equality is available. I will highlight a few recent examples of thermodynamic inequalities in the form of uncertainty relations and speed limits.

In the main part of the talk, I will explain a general technique for deriving new inequalities, by starting from information-theoretic bounds and considering “virtual perturbations” of a physical system. I will show how this method can be used to derive and generalize the so-called “thermodynamic uncertainty relation”. An interesting application of such uncertainty relations is to estimate the dissipation in biological systems such as molecular motors.

The second main topic is how to relate inequalities to equalities. When using inequalities to estimate physical quantities, it is crucial to understand the conditions under which the inequality can be tight. One way to achieve this is to “promote” the inequality into an equality via a variational principle. On the one hand, this provides conditions for obtaining a tight bound. On the other hand, variational expressions can also serve as a starting point to derive new inequalities.