The Thermodynamical Arrow of Time

Abstract

The thermodynamical arrow of time is characterized by the increase of entropy according to the Second Law. This law was first postulated by Rudolf Clausius in 1865 as a consequence of Carnot’s theorem of 1824 when combined with the just established equivalence of heat with other forms of energy (the First Law of thermodynamics). It can be written in a general form by means of a sum of external and internal changes of entropy as

$$ \frac{{dS}} {{dt}} = \left\{ {\frac{{dS}} {{dt}}} \right\}_{ext} + \left\{ {\frac{{dS}} {{dt}}} \right\}_{int} , $$

where

$$ dS_{ext} = \frac{{dQ}} {T} and \left\{ {\frac{{dS}} {{dt}}} \right\}_{int} \geqslant 0. $$

((3.1))

Here, S is phenomenologically defined as the entropy of a bounded system — thereby exploiting reversible processes with (dS/dt)_int = 0, while dQ is the reversible (infinitely slow) inward heat flux through the system’s complete boundary during a time interval dt. (See also the local form (3.39) of the Second Law on p. 60.)