Showing papers by "Vojkan Jaksic published in 2022"
TL;DR: In this paper , the authors studied the non-autonomous quantum dynamics of a translation-invariant spin or fermion system on the lattice and established a number of general structural results regarding such realizations.
Abstract: We study the slowly varying, non-autonomous quantum dynamics of a translation-invariant spin or fermion system on the lattice $$\mathbb {Z}^d$$ . This system is assumed to be initially in thermal equilibrium, and we consider realizations of quasi-static processes in the adiabatic limit. By combining the Gibbs variational principle with the notion of quantum weak Gibbs states introduced in Jakšić et al. (Approach to equilibrium in translation-invariant quantum systems: some structural results, in the present issue of Ann. H. Poincaré, 2023), we establish a number of general structural results regarding such realizations. In particular, we show that such a quasi-static process is incompatible with the property of approach to equilibrium studied in this previous work.
3 citations
TL;DR: In this paper , the universal typical-signal estimators of entropy and cross-entropy based on the asymptotics of recurrence and waiting times were introduced and studied in the context of one-sided shifts over finite alphabets.
Abstract: The universal typical-signal estimators of entropy and cross-entropy based on the asymptotics of recurrence and waiting times play an important role in information theory. Building on their construction, we introduce and study universal typical-signal estimators of entropy production in the context of nonequilibrium statistical mechanics of one-sided shifts over finite alphabets.
3 citations
TL;DR: In this article , the authors formulated the problem of approach to equilibrium in algebraic quantum statistical mechanics and studied some of its structural aspects, focusing on the relation between the zeroth law of thermodynamics (approach to equilibrium) and the second law (increase in entropy).
Abstract: We formulate the problem of approach to equilibrium in algebraic quantum statistical mechanics and study some of its structural aspects, focusing on the relation between the zeroth law of thermodynamics (approach to equilibrium) and the second law (increase in entropy). Our main result is that approach to equilibrium is necessarily accompanied by a strict increase in the specific (mean) energy and entropy. In the course of our analysis, we introduce the concept of quantum weak Gibbs state which is of independent interest.
3 citations
TL;DR: In this paper , lower decoupling was introduced to the study of the cross-entropy between two mutually independent stationary stochastic processes, and the validity of waiting-time estimation of cross entropy was considerably extended.
Abstract: We introduce conditions of lower decoupling to the study of waiting-time estimations of the cross entropy between two mutually independent stationary stochastic processes. Although similar decoupling conditions have been used in the literature on large deviations and statistical mechanics, they appear largely unexplored in information theory. Building on a result of Kontoyiannis, namely Theorem 4 in [Ko98], and replacing the ψ -mixing condition in this result with a lower decoupling condition, we considerably extend the validity of waiting-time estimation of cross entropy. MSC2020: Primary 37B20, 37M25, 94A15.
2 citations