Organizers: Luigi Delle Site, Carsten Hartmann

Abstract:

The accurate calculation of (relative) free energies is one of the key problems in statistical mechanics. For example, the calculation of interface free energies in situations when there is strong coupling between subsystems can become computationally infeasible by standard thermodynamic integration or particle insertion methods. On the other hand, being able to quantify system-environment interactions is crucial to determine, e.g., the minimum size of a simulation box in a molecular dynamics simulation or to assess the degree on non-Markovianity under coarse-graining. This minisymposium aims at discussing both computational and theoretical challenges related to the micro-macro passage in particle systems. A particular focus will be on estimating thermodynamic potentials and quantifying finite size and memory effects.

Speakers:

11:30h: Martin Hanke (Johannes Gutenberg University)

Data driven parameterizations of multidimensional generalized Langevin equations

We present a numerical algorithm to construct a Markov model with an extended list of variables to parameterize the equation of motion of a multidimensional coarse-grained physical system, when memory effects are relevant. Our method uses autocorrelation data of the stationary velocities, but it avoids the inverse problem of finding the corresponding memory kernel from these data in a first step. Rather, the data are used to construct a Prony series approximation of the autocorrelation function, and the parameters of this Prony series provide the corresponding Markov model.

Numerical results for molecular dynamics data show a good match for parameterized models with five auxiliary variables for a one-dimensional, and twelve auxiliary variables for a two-dimensional system.

This is joint work with Maximilian Braun and Niklas Wolf.

12:00h: Christopher J. Stein (Technische Universität München)

Variational inference of free energy differences in strongly coupled open systems

The well-known Jarzynski equality allows us to calculate free energy differences from nonequilibrium work, but its standard derivation assumes microscopic reversibility and phase-space preservation—assumptions that fail for strongly coupled systems under non-Liouvillian driving. In this talk, I show these assumptions can be dropped.

I will present exact endpoint identities for free energy differences in strongly coupled open systems. The central object is the Hamiltonian-of-mean-force increment, whose exponential moments give both the free energy difference and the chi-squared overlap between endpoint states in the frozen-coupling regime. From this follow two additional results: a maximum-entropy reconstruction that infers the free energy difference and its uncertainty from sampled actions, and an exact finite-time inequality that bounds the free energy error—letting the estimate be qualified before the system fully equilibrates.

I close with a stringent test: a strongly coupled model driven by a phase-space-compressing ramp and underdamped relaxation. The standard Jarzynski estimator fails, while the endpoint identities recover the exact free energy difference. Our variational approach offers a route to systematically improve the estimate from finite samples and the finite-time criterion identifies when the estimate can be trusted.

12:30h: Johannes Zimmer (Technische Universität München)

Learning thermodynamic evolution from particles

In this talk, we will describe the thermodynamic framework provided by the so-called General Equation for Non-Equilibrium Reversible–Irreversible Coupling (GENERIC, also called metriplectic evolution) and discuss how the dissipative evolution can be inferred from microscopic to macroscopic scales. In particular, we will explain how the dissipative thermodynamic evolution operator can be learned from diffusive particle models via a fluctuation-dissipation result, in a model case with rigorous error estimates. We then sketch how this step can in principle be used to infer the other building blocks of the thermodynamic evolution.