The local balance laws for energy, momentum and entropy: how they came into being, and what was their destiny

TL;DR

This paper reviews the historical development of local balance laws for energy, momentum, and entropy, highlighting how their formulation evolved from global conservation principles to local continuity equations around the 19th to 20th century.

Contribution

It provides a historical analysis of how local balance laws for energy, momentum, and entropy were developed and their impact on physics education and understanding.

Findings

Local balance laws were formulated around the turn of the 20th century.

The development simplified the teaching of fundamental physical quantities.

Current physics language has remained largely unchanged since the laws' formulation.

Abstract

The historical process of the genesis of the extensive or substance-like quantities took place in two steps. First, global conservation or non-conservation was discovered. Only later did it become possible to formulate the balance locally in the form of a continuity equation. This process can be clearly seen in energy, momentum, and entropy. After a long and intricate history, the quantitative description of the local balance has been achieved for all of the three quantities in a surprisingly short period of time around the turn of the 19th to the 20th century. The new ideas could have simplified considerably the teaching of energy, momentum, and entropy. However, in all three cases, today's language of physics remained essentially the same as it was at the time when a local balancing was not yet possible.