Irreversibility, stochasticity and non-locality in classical dynamics

Tomio Petrosky, Ilya Prigogine

M. Courbage

Basil J. Hiley, F. David Peat

It is a privilege to contribute to this volume honouring David Bohm. There is no need to enumerate his basic contributions to modern theoretical physics; these are well known to the scientific community. What IS however unique about David Bohm is his deep involvement in epistemological problems. In this perspective, there is probably no single concept more fundamental than time in its connection with cosmology. As Karl Popper beautifully writes 1: 'There is at least one philosophic problem in which all thinking men are interested. It is the problem of cosmology: the problem of understanding the world - including ourselves, and our knowledge, as part of the world.'

Luigi Accardi, Franco Fagnola, Roberto B. Quezada

We give a general definition of the local KMS condition and we prove its equivalence with a nonlinear Gibbs prescription. We discuss the irreversible $(H, \beta)$-KMS condition, its connections with the local KMS condition and we study the irreversible $(H, \beta)$-KMS condition for Markov generators of stochastic limit type. We introduce a definition of weighted detailed balance based on the notion of current decomposition and discuss invariant states with constant micro--currents. As an example, we construct a non-equilibrium steady state for a quantum spin chain coupled to two reservoirs at different temperatures and study its cycle dynamics and entropy production.

Xu-Cai Zhuang, Qing-Feng Xue, Qi Zhang +3 more

Abstract Entropy production plays a pivotal role in characterizing the inherent irreversibility of non-equilibrium quantum processes, and a thorough understanding of this concept holds immense potential for advancing the design of thermodynamically efficient quantum technologies. In this work, we demonstrate that the entropy production observed in multipartite open quantum systems, undergoing independent dissipations, arises from two sources: the local dynamics governing individual subsystems and the non-local correlations embedded within the system. The contributions of quantum correlations, as genuine quantum effects, to entropy production are identified explicitly. The revelation of the source of entropy production is substantiated by an analysis of its stochastic counterpart, derived from quantum trajectories. Furthermore, we propose an experimentally feasible scheme to isolate the contributions of both classical and quantum correlations to entropy production. The theoretical findings are simulated using an optical setup. Our work establishes a profound connection between thermodynamic and informational quantities, elucidating the source of irreversibility in the non-equilibrium process of multipartite quantum systems and the genuine quantum contribution therein.

Toru Ohira