Smoothing out Boltzmannian Statistical Mechanics: On the Viability of an Alternative Partitioning of Phase Space Into Overlapping Worlds
摘要
A core method of the framework of Boltzmannian Statistical Mechanics (BSM) is the partitioning of phase space into non-overlapping macro regions, i.e., disjoint sets of micro states. Macro regions are of finite, non-zero volume, and stand in a one-to-one correspondence with different macro states. Given a finite volume of phase space to be partitioned, there is a finite number of macro regions in a partition. Macro states are specified via particular macro values, e.g., for temperature, volume and pressure of a gas. In general, macro states are defined and specified via particular macro values taken on by macro variables: following Werndl and Frigg (2015b, p. 1225), a system “can be characterized by a set \( \left\{{v}_1,\dots, {v}_k\right\} \) of macrovariables \( \left(k\in \mathbb{N}\right) \) . The \( {v}_i \) assume values in [macro value space] \( {\mathbbm{V}}_i \) , and capital letters \( {V}_i \) denote the values of \( {v}_i \) . A particular set of values \( \left\{{V}_1,\dots, {V}_k\right\} \) defines a macrostate \( {M}_{V_1,\dots, {V}_k} \) .”