Time is dispensable in thermodynamics

TL;DR

This paper demonstrates that time can be eliminated as a primitive concept in continuum thermodynamics by using axiomatic methods, redefining it through other primitive concepts, and exploring the implications of a time-independent formulation.

Contribution

It introduces a novel axiomatic approach to thermodynamics that removes the explicit need for time as a primitive concept, redefining it within the existing framework.

Findings

Time is dispensable in continuum thermodynamics.

Time can be defined from other primitive concepts.

Implications for physics and philosophy of time.

Abstract

We use Padoa's principle of independence of primitive symbols in axiomatic systems in order to show that time is dispensable in continuum thermodynamics, according to the axiomatic formulation of Gurtin and Williams. We also show how to define time by means of the remaining primitive concepts of Gurtin and Williams system. Finally, we introduce thermodynamics without any explicit reference to time and briefly discuss some physical and philosophical consequences of our main results.