Clausius Inequality in the Philosophy and History of Physics

Jos Uffink rejected the existence of the arrow of time in classical thermodynamics, and his views turned out to be influential in the philosophy of physics. However, this position omits the connection between classical thermodynamics and continuum mechanics and is based on a simplistic view of equilibrium states. In this article, this issue is discussed with an example of a temperature field; we examine the relationship between the Fourier heat equation and classical thermodynamics in the 19th century. With this example the relationship of the Clausius inequality to time and transport equations of continuum mechanics is clarified. The question is raised whether it makes sense to carry out the axiomatization of classical thermodynamics without continuum mechanics.