Molecules and the Eigenstate Thermalization Hypothesis

Abstract

We review a theory that predicts the onset of thermalization in a quantum mechanical coupled non-linear oscillator system, which models the vibrational degrees of freedom of a molecule. A system of N non-linear oscillators perturbed by cubic anharmonic interactions exhibits a many-body localization (MBL) transition in the vibrational state space (VSS) of the molecule. This transition can occur at rather high energy in a sizable molecule because the density of states coupled by cubic anharmonic terms scales as N3, in marked contrast to the total density of states, which scales as exp(aN), where a is a constant. The emergence of a MBL transition in the VSS is seen by analysis of a random matrix ensemble that captures the locality of coupling in the VSS, referred to as local random matrix theory (LRMT). Upon introducing higher order anharmonicity, the location of the MBL transition of even a sizable molecule, such as an organic molecule with tens of atoms, still lies at an energy that may exceed the energy to surmount a barrier to reaction, such as a barrier to conformational change. Illustrative calculations are provided, and some recent work on the influence of thermalization on thermal conduction in molecular junctions is also discussed.

Clusters of hairpins induce intrinsic transcription termination in bacteria

“…Cluster hairpins can, however, explain simple entropy-driven processes that may achieve efficient ITT. Such processes have been investigated in less complex systems for understanding the potential mechanisms at play 55 , 56 . If we assume RNAP:DNA:RNA hybrid and the immediate solvent environment as a quasi thermodynamic system inside the cell, the hybrid typically contributes to entropy change by its thermal fluctuations and translocation during transcription.…”

“…This entropy change can act as a perturbation and a trigger for conformational transitions along soft modes 55 of the RNAP complex. The perturbation may drive thermalization in the system leading to overcoming the transition barrier 56 for ITT to take place. The probability of such perturbations increases with the formation of more hairpins and thus increases the probability of stochastic ITT.…”

Asymmetric temperature equilibration with heat flow from cold to hot in a quantum thermodynamic system

“…It is very interesting to consider how the asymmetric temperature equilibration behavior might be observed in experiments or theoretical studies of real pure state total systems. One possibility is in the dynamics of gas phase molecules, which have recently been considered as promising laboratories for studying fundamental aspects of quantum thermodynamics [10,11,38]. Pure states of gas phase molecules are relatively easy to prepare and different molecules give access to a wide range of Hamiltonians.…”

Simulating quantum thermodynamics of a finite system and bath with variable temperature

“…Several investigators have proposed small molecules as laboratories for fundamental exploration of quantum thermodynamics and statistical mechanics. Leitner [10,11] has reviewed a method of using the eigenstate thermalization hypothesis to understand ergodicity and localization of energy within timedependent molecular systems. Pérez and Arce [9] performed simulations of dynamics on a potential energy surface of the molecule OCS, which has a long history as an exemplar of problems of classically chaotic molecular dynamics.…”

“…Molecular systems interacting with small baths are being investigated in calculations of entanglement dynamics and spectroscopic signals [7,8]. Recently [9][10][11], work on molecular "quantum chaos" is being conceptualized as a venue for the exploration of contemporary ideas about the foundations of quantum thermodynamics, to which we turn next.…”