séminaire Histoire et Philosophie de la Physique

Jos Uffink (Université du Minnesota) -- The Problem of Irreversibility and  the Quantum Boltzmann Equation.

Quantum theory is time-reversal invariant, just as classical mechanics.  Nevertheless, in the field of condensed matter physics, a so-called Quantum Boltzmann Equation is derived from Quantum Field Theory, (see e.g.  Baym & Pethik (2004), Snoke et al. (2012), and Snoke (2020))--- much like Boltzmann (1872) famously derived his Boltzmann Equation from classical mechanics of dilute hard-sphere gases. In both cases, these equations imply irreversible behaviour of the system involved, and raise the question how such irreversible behaviour could be derived from a fundamentally time-reversal invariant theory. In the classical case, it is known that the question: "Which assumption in Boltzmann's derivation is responsible for breaking the time-reversal invariance symmetry?"   raised much debate (and misunderstanding) for more than a century after Boltzmann's presentation. In this talk, I will use this history as a backdrop to examine how the presented derivation of the Quantum Boltzmann Equation compares to its classical analogon.  
This talk is based on joint work in progress with Giovanni Valente.

 

 

 

Probabilities in classical statistical mechanics are standardly introduced because we don’t know the exact microstate of the system. This has led to three problems: (i) concerns about the probabilities being subjective or tied to us, (Albert 2000) (ii) concerns that there is a mismatch between the thermodynamic entropy defined in terms of the system’s individual state and the Gibbs entropy defined in terms of SM probabilities and (iii) concerns that adding these probabilities in is helping ourselves to too much when thinking about reduction (Sklar 1993). But the quantum case is radically different; it has its own source of probabilities (Wallace 2013). In this paper, I show how these quantum probabilities lead to the right statistical mechanical probabilities – the familiar microcanonical and canonical distributions, by relying on results from Popescu et al (2006). This gives a new perspective of the nature of SM probabilities – as emerging from entanglement - and allows us to solve the above problems. The key takeaway is that probabilities in SM don’t come from our lack of knowledge of the underlying states.