Generalized Gibbs ensembles for time dependent processes

TL;DR

This paper develops a unified information-theoretic framework for describing finite classical and quantum systems evolving in time, introducing a generalized Gibbs ensemble with explicit time-dependent features.

Contribution

It introduces a variational principle-based approach to derive time-dependent density matrices with explicit flow components, extending Gibbs ensembles to non-equilibrium dynamics.

Findings

Derived a generalized Gibbs ensemble with time odd components.

Applied the framework to quantum Brownian motion and out-of-equilibrium processes.

Showed the approach captures dynamics across different time scales.

Abstract

An information theory description of finite systems explicitly evolving in time is presented for classical as well as quantum mechanics. We impose a variational principle on the Shannon entropy at a given time while the constraints are set at a former time. The resulting density matrix deviates from the Boltzmann kernel and contains explicit time odd components which can be interpreted as collective flows. Applications include quantum brownian motion, linear response theory, out of equilibrium situations for which the relevant information is collected within different time scales before entropy saturation, and the dynamics of the expansion.