[Paper Review] Democritus and the motive power of fire

Jacques Arnaud, Laurent Chusseau+1 more|arXiv (Cornell University)|Apr 5, 2011

Paranormal Experiences and Beliefs3 references3 citations

TL;DR

This paper proposes that the fundamental principles of heat engines, including Carnot's maximum efficiency and the barometric law, could have been derived by ancient Greek philosophers like Democritus using only qualitative observations and the concept of corpuscles moving in a vacuum. By modeling thermal systems through gravitational potential energy and applying a principle of simplicity, the authors derive the generalized Boltzmann factor and absolute temperature, showing that key thermodynamic laws emerge from corpuscular mechanics without modern physics or mathematics.

ABSTRACT

The present work is a translation from french to english of our previous \g{Démocrite et la puissance motrice du feu}, amended on a number of respects. It is mainly of historical and pedagogical interest. We suggest that the concepts introduced in the ancien Greece by Anaximander (flat earth) and Democritus (corpuscles moving in vacuum) allow us to obtain through qualitative observations and plausible generalizations the maximum efficiency and work of heat engines, results that were firmly established around 1824 by Carnot. A prologue introduces the subject. We next present the concept of thermal equilibrium and consider a model consisting of two reservoirs located at different altitudes, each with $g$ sites. Each site may contain a specified number of corpuscles. One particular site plays the role of \g{working agent}. We subsequently consider an alternative model consisting of independent corpuscles submitted to gravity and in contact with heat baths. Only average quantities are considered, leaving out fluctuations and questions of stability.

Motivation & Objective

• To demonstrate that core thermodynamic laws, including Carnot's maximum efficiency and the barometric law, could have been derived by ancient Greek thinkers like Democritus using only qualitative observations and corpuscular reasoning.
• To show that the concept of absolute temperature and the generalized Boltzmann factor emerge naturally from a model of corpuscles in a gravitational potential, without relying on kinetic energy or statistical mechanics.
• To establish a pedagogical framework that derives classical thermodynamics from first principles based on corpuscle motion and gravitational potential energy, using only elementary mathematics and the principle of simplicity.
• To challenge the conventional view that thermodynamics requires modern experimental or mathematical tools, by showing that the essential results could have been reached with minimal technology and philosophical insight.

Proposed method

• Modeling heat reservoirs as discrete sites at different altitudes, each capable of holding a number of corpuscles, with energy defined by gravitational potential.
• Introducing a principle of simplicity: the ideal gas law and barometric law must hold regardless of the underlying laws of motion, ensuring consistency across models.
• Using time-averaged round-trip periods of corpuscles bouncing under gravity to define a distribution function proportional to exp(−E/θ), where θ is identified as absolute temperature.
• Deriving the generalized Boltzmann factor by comparing probabilities of corpuscles occupying different energy levels, with degeneracy accounted for via site widths (Δn).
• Establishing that the ratio of populations in two energy levels is exp((φl − φh)/θ), which matches the standard Boltzmann factor under equal degeneracy.
• Defining the average time a corpuscle spends above a given altitude as a function of energy, leading to the barometric law exp(−z/θ) when site weights are uniform.

Experimental results

Research questions

• RQ1 Could Democritus have derived the maximum efficiency of heat engines using only corpuscular reasoning and qualitative observations?
• RQ2 How can the barometric law and ideal gas law be derived from gravitational potential energy and a principle of simplicity, without assuming kinetic energy or statistical mechanics?
• RQ3 What is the role of the parameter θ in the corpuscle model, and how does it correspond to absolute temperature?
• RQ4 Can the generalized Boltzmann factor emerge from a discrete, gravitational model of corpuscles in equilibrium?
• RQ5 Under what conditions does population inversion occur in such a model, and how does it relate to negative temperature?

Key findings

• The maximum efficiency of a heat engine is derived as 1 − T_cold/T_hot using only corpuscle motion in gravity and the principle of simplicity, matching Carnot's result from 1824.
• The barometric law exp(−z/θ) is obtained as the probability distribution of corpuscles above a given altitude, with θ identified as absolute temperature.
• The generalized Boltzmann factor exp((φl − φh)/θ) is derived from the ratio of average residence times in two energy levels, confirming the standard form under equal degeneracy.
• The parameter θ is shown to be an absolute temperature, independent of the specific dynamics of the corpuscles, by consistency with the barometric law and energy distribution.
• Population inversion between two levels is possible in the model when θ is negative, suggesting a classical analog to laser population inversion without external pumping.
• The derivation of the ideal gas law and barometric law is shown to be independent of the laws of motion (non-relativistic, relativistic, or otherwise), relying only on the principle of simplicity.