Question

Did Democritus predict atoms using Sharp Phase Transitions? How? Couldn't a classical field theory also have Sharp Phase Transitions?

One of Democritus' arguments in support of atomism was that atoms naturally explain the sharp phase boundaries observed in materials[citation needed], as when ice melts to water or water turns to steam.

Is this statement historically accurate? If so, did Democritus have an argument or explained his intuition on how exactly atoms explain sharp phase transitions?

A related question, would be how this relates to a a modern statistical mechanics viewpoint and If one really needs an atomistic description:

From a continuous model of matter like a classical field theory, could one arrive at a first order phase transition from first principles? I know you could just 'artificially' impose a phase transition, but I'm thinking of a procedure like taking the large-scale limit of a classical field theory and arriving at a new theory with phase transitions.

Answer 1

Democritus theorized that matter was made of indivisible particles called atomos, which rearrange to produce changes in matter, implying a formative understanding of phase transitions. Although he did not use the concept of sharp phase transitions, his ideas on change foreshadow modern interpretations in statistical mechanics. Classical field theories can describe phase transitions, but combining atomistic and continuous models offers a fuller explanation.

Step-by-step explanation:

Without experimental evidence, Democritus postulated over 2,500 years ago that matter was composed of indivisible and permanent particles, which he termed 'atomos'. He suggested that changes in matter's state occur when these atomos recombine or reconnect in various ways. Though he did not explicitly state how atoms explain sharp phase transitions like melting and boiling, his idea implies a fundamental change in the arrangement of atoms, which we now can relate to phase transitions in modern statistical mechanics.

Democritus further speculated that these atomos had different sizes, shapes, and masses, and believed that these were the only differing properties. He asserted that other properties, like color and taste, emerged from the atoms' arrangement rather than being inherent to the atoms themselves. Such hypotheses align with current understandings of atomic behavior and the emergence of macroscopic properties from the microscopic world.

Regarding the question of whether one needs an atomistic description to explain phase transitions, classical field theories can indeed capture first-order phase transitions through singularities or discontinuities in the free energy as a function of some order parameter. However, a complete understanding of the phase behavior of matter generally incorporates both atomistic and continuous descriptions, depending on the scale of interest.