Modeling Time’s Arrow

Jean Paul Van Bendegem

Nitay Hurvitz, Alon Kochol, Victor Fleurov +1 more

Measurement-induced phase transitions (MIPTs) in monitored quantum systems are typically diagnosed using entanglement-based measures. Here, we develop a complementary thermodynamic perspective based on the arrow of time (AoT), which arises from the intrinsic irreversibility of the quantum measurements driving these transitions. We study the AoT - defined as the logarithmic ratio of forward and backward trajectory probabilities - across a family of models exhibiting MIPTs. We find that, like entanglement entropy, the AoT is a nonlinear functional of the averaged density matrix; however, in contrast to entanglement, it is associated with a local operator. To determine whether the AoT exhibits critical behavior, we formulate and exactly solve a model of a random quantum circuit with non-projective measurements. This allows us to analytically demonstrate that the AoT displays nonanalytic behavior and identify its critical exponent. Our results establish the AoT as a novel diagnostic for phase transitions in monitored quantum systems.

Jacques Pienaar

Modern approaches to causal modeling give a central role to interventions, which require the active input of an observer and introduces an explicit `causal arrow of time'. Causal models typically adopt a mechanistic interpretation, according to which the direction of the causal arrow is intrinsic to the process being studied. Here we investigate whether the direction of the causal arrow might be a contribution from the observer, rather than an intrinsic property of the process. Working within a counterfactual and non-mechanistic interpretation of causal modeling developed in arXiv:1806.00895, we propose a definition of a `quantum observational scheme' that we argue characterizes the observer-invariant properties of a causal model. By restricting to quantum processes that preserve the maximally mixed state (unbiasedness) we find that the statistics is symmetric under reversal of the time-ordering. The resulting model can therefore accommodate the idea that the causal arrow is observer-dependent, indicating a route towards reconciling the causal arrow with time-symmetric laws of physics.

Luigi Accardi

J. G. Cramer

Agendanken experiment is proposed for distinguishing between two models accounting for the macroscopic arrow of time. The experiment involves the veloeity revesal of components of an isolated system, and the two models give contrasting predictions as to its behavior.

Tarek Halabi