Understanding Thermodynamic Singularities: Phase Transitions, Data, and Phenomena

Abstract

According to standard (quantum) statistical mechanics, the phenomenon of a phase transition, as described in classical thermodynamics, cannot be derived unless one assumes that the system under study is infinite. This is naturally puzzling since real systems are composed of a finite number of particles; consequently, a well-known reaction to this problem was to urge that the thermodynamic definition of phase transitions (in terms of singularities) should not be “taken seriously.” This article takes singularities seriously and analyzes their role by using the well-known distinction between data and phenomena, in an attempt to better understand the origin of the puzzle.

What Is the Paradox of Phase Transitions?

“…However, contra Bangu (2009), Callender (2001, Mainwood (2006), Jones (2006) and others, I contend that no contradiction arises by conjoining tenets 1-5. To see this, we must first distinguish between "concrete" phase transitions, on the one hand, and "abstract mathematical representations" of them, on the other hand.…”

“…Lebowitz 1999, S346;Liu 1999, S92;Morrison 2012, 143;Prigogine 1997, 45), which necessitate the development of new physical theory (Callender 2001, 550), and inducing a wide array of literature that argues to the contrary (e.g. Bangu 2009;Batterman 2005Batterman , 2011Butterfield 2011;Menon and Callender 2011;Norton 2011;Wayne 2009). …”

Thermal substances: a Neo-Aristotelian ontology of the quantum world

“…Phase transitions, such as those between the solid, liquid, gas states, and between conditions before and after the onset of coherent ferromagnetism or superconductivity in metals, require the use of infinite models (models involving the continuum limit): see Liu (1999), Ruetsche (2006) and Bangu (2009). Phase transitions are an important case of spontaneous symmetry breaking.…”

Infinite idealizations in physics

“…Recall that such phenomena are conventionally defined as singularities in the thermodynamic state functions of some system of interest, but said singularities can only arise when taking the infinite and idealized TDL. Accordingly, various essentialists have claimed that PT are irreducible emergent phenomena (e.g., Bangu, , , 2015a; Batterman, ; ; Lebowitz, , S346; Liu, , S92; Morrison, , 143; Prigogine, , 45; Humphreys, ). The idea here seems to be that PT are emergent because they are not reducible to (e.g., derivable from, or explainable by) statistical mechanics proper, i.e., statistical mechanics without the TDL.…”