Algorithmic Approaches for Assessing Irreversibility in Time Series: Review and Comparison

The assessment of time irreversibility, i.e., of the lack of invariance of the statistical properties of a system under the operation of time reversal, is a topic steadily gaining attention within the research community. Irreversible dynamics have been found in many real-world systems, with alterations being connected to, for instance, pathologies in the human brain, heart and gait, or to inefficiencies in financial markets. Assessing irreversibility in time series is not an easy task, due to its many aetiologies and to the different ways it manifests in data. It is thus not surprising that several numerical methods have been proposed in the last decades, based on different principles and with different applications in mind. In this contribution we review the most important algorithmic solutions that have been proposed to test the irreversibility of time series, their underlying hypotheses, computational and practical limitations, and their comparative performance. We further provide an open-source software library that includes all tests here considered. As a final point, we show that “one size does not fit all”, as tests yield complementary, and sometimes conflicting views to the problem; and discuss some future research avenues.

The Problem of Engines in Statistical Physics

Engines are open systems that can generate work cyclically at the expense of an external disequilibrium. They are ubiquitous in nature and technology, but the course of mathematical physics over the last 300 years has tended to make their dynamics in time a theoretical blind spot. This has hampered the usefulness of statistical mechanics applied to active systems, including living matter. We argue that recent advances in the theory of open quantum systems, coupled with renewed interest in understanding how active forces result from positive feedback between different macroscopic degrees of freedom in the presence of dissipation, point to a more realistic description of autonomous engines. We propose a general conceptualization of an engine that helps clarify the distinction between its heat and work outputs. Based on this, we show how the external loading force and the thermal noise may be incorporated into the relevant equations of motion. This modifies the usual Fokker–Planck and Langevin equations, offering a thermodynamically complete formulation of the irreversible dynamics of simple oscillating and rotating engines.

The past shall not begin: Frozen seeds, extended presents and the politics of reversibility

The article analyzes the Svalbard Global Seed Vault (SGSV) as a specific security technology created to deal with the ecological threat of biodiversity loss. Built in 2008 inside the Arctic Circle, the SGSV serves as a backup for 1,700 agricultural gene banks around the world. If seed collections are lost due to natural disasters or human error, the gene banks can request copies of their varieties from Svalbard and restore their collections to continue the endeavour of plant breeding. The article focuses on the particular temporal politics expressed in the SGSV. Drawing on Niklas Luhmann’s reflections on time, it is argued that the SGSV opens up the possibility of reversing events by expanding the duration of the present. By separating seeds from their ecological connections on the one hand and controlling their metabolic processes through the use of cold on the other, an enduring temporal zone is created that allows modern society to control the unpredictable and irreversible dynamics of life and undo its emergent effects. The SGSV therefore materializes what is herein called the politics of reversibility.

Structure-preserving integrators for dissipative systems based on reversible– irreversible splitting

We study the optimal design of numerical integrators for dissipative systems, for which there exists an underlying thermodynamic structure known as GENERIC (general equation for the nonequilibrium reversible–irreversible coupling). We present a frame-work to construct structure-preserving integrators by splitting the system into reversible and irreversible dynamics. The reversible part, which is often degenerate and reduces to a Hamiltonian form on its symplectic leaves, is solved by using a symplectic method (e.g. Verlet) with degenerate variables being left unchanged, for which an associated modified Hamiltonian (and subsequently a modified energy) in the form of a series expansion can be obtained by using backward error analysis. The modified energy is then used to construct a modified friction matrix associated with the irreversible part in such a way that a modified degeneracy condition is satisfied. The modified irreversible dynamics can be further solved by an explicit midpoint method if not exactly solvable. Our findings are verified by various numerical experiments, demonstrating the superiority of structure-preserving integrators over alternative schemes in terms of not only the accuracy control of both energy conservation and entropy production but also the preservation of the conformal symplectic structure in the case of linearly damped systems.

Excitation dynamics of two level quantum systems coupled to Morse vibrations

Electronic excited states of a molecular aggregate coupled to Morse vibrations are analysed by a nonperturbative time dependent variational approach. General equations of motion for an electronically excited state are derived for electronic amplitudes, nuclear displacements and squeezing of the nuclear wave packets. Numerical simulations demonstrate that anharmonicities of vibrations lead to short-term irreversible dynamics, extra localization and transformation of stationary lowest-energy states.