Typicality, Irreversibility and the Status of Macroscopic Laws

Abstract

We discuss Boltzmann's explanation of the irreversible thermodynamic evolution of macroscopic systems on the basis of time-symmetric microscopic laws, providing a comprehensive presentation of what we call the typicality account. We then discuss the connection between this general scheme and the H-theorem, demonstrating the conceptual continuity between them. In our analysis, a special focus lies on the crucial role of typicality. Putting things in wider perspective, we go on to analyze the philosophical dimensions of this concept, explaining the connection between typicality and probability, and demonstrate its relevance for scientific reasoning, in particular for understanding the supervenience of macroscopic laws on microscopic laws. The second part of the paper responds to recent objections against the typicality account that have been raised in the philosophical literature. In particular, the concept of ergodicity, or a variant thereof, named "epsilon-ergodicity", which has been promoted by some authors as a crucial additional assumption on the dynamics, is shown to be of no use for its intended purpose. *

Typical: A Theory of Typicality and Typicality Explanation

“…14 For rigorous definitions of Γ, P , and µ, see Goldstein ([2001]) and Lazarovici and Reichert ([2015]).…”

“…For example, see(Frigg and Werndl [2012]) and(Goldstein [2001]). 2 For some discussion of typicality and explanation, see(Lazarovici and Reichert [2015]) and(Maudlin [2011]). …”

Arrow(s) of Time without a Past Hypothesis

“…The first point of view is largely motivated by the fact that our explanation of the thermodynamic arrow is based on a typicality reasoning (e.g. Lebowitz (1993), Goldstein (2001), Lazarovici and Reichert (2015)). Assuming a low-entropy initial macrostate of the universe, Boltzmann's analysis allows us to conclude that typical microstates relative to this macrostate will lead to a thermodynamic evolution of increasing entropy.…”

“…The point here is not that this makes it easier for a hypothetical creator of the universe, but that only the latter (microscopic) kind of fine-tuning gives rise to the worry that -given the huge number of microscopic degrees of freedom and the sensitivity of the evolution to variations of the initial data -atypical initial conditions could explain anything (and thus explain nothing; cf. Lazarovici and Reichert (2015)). Nonetheless, the necessity of a PH implies that our universe looks very different from a typical model of the fundamental laws of nature -and this is a fact that one can be legitimately worried about.…”

From the Universe to Subsystems: Why Quantum Mechanics Appears More Stochastic than Classical Mechanics

“…In any case, if we can establish that a certain fact or feature occurs for the vast majority of possible initial conditions -that is, in the last resort, for the overwhelming majority of possible universes described by a particular theory -, we can justifiably call it a prediction of that theory (see Lazarovici and Reichert (2015) for a detailed discussion). In order to make such an argument precise, we need a measure on phase space telling us what an "overwhelming majority" of initial conditions is.…”