Condensed Matter Theory

Abstract:

Rényi entropies are conceptually valuable and experimentally relevant generalizations of the celebrated von Neumann entanglement entropy. After a quantum quench in a clean quantum many-body system they generically display a universal linear growth in time followed by saturation. While a finite subsystem is essentially at local equilibrium when the entanglement saturates, it is genuinely out of equilibrium in the growth phase. In particular, the slope of the growth carries vital information on the nature of the system’s dynamics, and its characterization is a key objective of current research. Here we show that the slope of Rényi entropies can be determined by means of a spacetime duality transformation. In essence, we argue that the slope coincides with the stationary density of entropy of the model obtained by exchanging the roles of space and time. Therefore, very surprisingly, the slope of the entanglement is expressed as an equilibrium quantity. We use this observation to find an explicit exact formula for the slope of Rényi entropies in all integrable models treatable by thermodynamic Bethe ansatz and evolving from integrable initial states. Interestingly, this formula can be understood in terms of a quasiparticle picture only in the von Neumann limit.

Abstract:

Enzymes are nano-scale machines that have evolved to drive chemical reactions out of equilibrium in the right place at the right time. Given the complexity and specificity of enzymatic function, the bottom-up design of enzymes presents a daunting task that is far more challenging than making passive molecules with specific binding affinities or building nano-scale mechanically active devices. We present a thermodynamically consistent model for the operation of such a fueled enzyme, which uses the energy from a favorable reaction to undergo non-equilibrium conformational changes that in turn catalyze a chemical reaction on an attached substrate molecule. We show that enzymatic function can emerge through a bifurcation upon appropriate implementation of momentum conservation on the effective reaction coordinates of the low-dimensional description of the enzyme, and thanks to a generically present dissipative coupling. Our results can complement the recently developed strategies for de novo enzyme design based on machine learning approaches

Abstract:

In the version of the article initially published, the declaration of no competing interests was missing, and has now been inserted in the HTML and PDF versions of the article.