Beyond Thermodynamic Uncertainty Relations: nonlinear response, error-dissipation trade-offs, and speed limits

TL;DR

This paper develops new bounds on nonlinear responses and speed limits in stochastic systems, linking thermodynamics, information theory, and system complexity, with applications to memory reliability and transition times.

Contribution

It introduces a master inequality unifying various thermodynamic uncertainty relations and derives novel bounds on system response, speed limits, and thermodynamic costs.

Findings

Derived a lower bound of 2.8 k_BT per Shannon bit for memory writing.

Established new speed limits for Markov processes based on thermodynamic and kinetic quantities.

Linked system complexity to fragility and robustness against perturbations.

Abstract

From a recent geometric generalization of Thermodynamic Uncertainty Relations (TURs) we derive novel upper bounds on the nonlinear response of an observable of an arbitrary system undergoing a change of probabilistic state. Various relaxations of these bounds allow to recover well known bounds such as (strengthenings of) Cramer-Rao's and Pinsker's inequalities. In particular we obtain a master inequality, named Symmetric Response Intensity Relation, which recovers several TURs as particular cases. We employ this set of bounds for three physical applications. First, we derive a trade-off between thermodynamic cost (dissipated free energy) and reliability of systems switching instantly between two states, such as one-bit memories. We derive in particular a lower bound of $2.8 k_BT$ per Shannon bit to write a bit in such a memory, a bound distinct from Landauer's one. Second, we obtain a new family of classic speed limits which provide lower bounds for non-autonomous Markov processes on the time needed to transition between two probabilistic states in terms of a thermodynamic quantity (e.g. non-equilibrium free energy) and a kinetic quantity (e.g. dynamical activity). Third, we provide an upper bound on the nonlinear response of a system based solely on the `complexity' of the system (which we relate to a high entropy and non-uniformity of the probabilities). We find that `complex' models (e.g. with many states) are necessarily fragile to some perturbations, while simple systems are robust, in that they display a low response to arbitrary perturbations.