The quantum statistics of dynamic processes

Petr I. Arseev

Philip Taranto, Thomas J. Elliott, Simon Milz

In classical physics, memoryless dynamics and Markovian statistics are one and the same. This is not true for quantum dynamics, first and foremost because quantum measurements are invasive. Going beyond measurement invasiveness, here we derive a novel distinction between classical and quantum processes, namely the possibility of hidden quantum memory . While Markovian statistics of classical processes can always be reproduced by a memoryless dynamical model, our main result shows that this is not true in quantum mechanics: We first provide an example of quantum non-Markovianity whose manifestation depends on whether or not a previous measurement is performed – an impossible phenomenon for memoryless dynamics; we then strengthen this result by demonstrating statistics that are Markovian independent of how they are probed, but are nonetheless s t i l l incompatible with memoryless quantum dynamics. Thus, we establish the existence of Markovian statistics gathered by probing a quantum process that nevertheless f u n d a m e n t a l l y require memory for their creation.

N. G. van Kampen

Alessio Zaccone, Kostya Trachenko

For a system to qualify as a quantum fluid, quantum-statistical effects should operate in addition to quantum-mechanical ones. Here, we address the hitherto unexplored dynamical condition for the quantum-statistical effects to be manifested, and consider particle exchange events in the gaslike regime of fluid dynamics as a dynamical process with an intrinsic time scale. We subsequently propose a quantitative criterion of particle indistinguishability and associated quantum statistics to be inoperative at short time and emerge at long time. Experimentally verifiable, our predictions enable a systematic search for a transition between statistics-active and statistics-inactive regimes in quantum fluids.

Michael B. Weissman

There are three major sources of the 'randomness' underlying noise phenomena. These are the random outcomes of quantum 'measurement' processes, the random ensembles of statistical mechanics, and the algorithmic complexity of many dynamical processes. Here I dwell on the possible connections between the first two sources of randomness. It is often held that the empirical irreversibility of quantum measurement arises from statistical mechanics. I present somewhat speculative arguments that in fact the irreversible approach to statistical ensembles may be rooted in an irreversible quantum decoherence process.

Faqir Chand Auluck