# The Thermodynamical Arrow of Time

Chapter

## Abstract

The thermodynamical arrow of time is characterized by the increase of entropy according to the Second Law, in its phenomenological form written as
Here, S is the phenomenologically defined entropy of a bounded system, and dQ the total inward flow of heat through its boundary. The first term vanishes by definition for ‘thermodynamically closed’ systems. Since the whole universe may in this sense be considered as closed, its total entropy (or the mean entropy of a comoving volume element) should, according to this law, evolve towards an assumed maximum — the so-called

$$\frac{{dS}}{{dt}} = {\left\{ {\frac{{dS}}{{dt}}} \right\}_{ext}} + {\left\{ {\frac{{dS}}{{st}}} \right\}_{\operatorname{int} }}with d{S_{ext}} = \frac{{dQ}}{T}and{\left\{ {\frac{{dS}}{{dt}}} \right\}_{\operatorname{int} }} \geqslant 0$$

(3.1)

*wärmetod*(heat death). The phenomenological concepts used thereby are restricted to situations of partial equilibrium in which at least a local concept of temperature can be operationally defined.## Keywords

Master Equation Liouville Equation Liouville Operator Macroscopic State Microscopic State
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Preview

Unable to display preview. Download preview PDF.

## Reference

- Jancel, R. (1963):
*Foundations of Quantum and Classical Statistical Mechanics*(Pergamon Press)Google Scholar - Brillouin, L. (1962):
*Science and Information Theory*(Academic Press)Google Scholar - Denbigh, K.G. and Denbigh, J.S. (1985):
*Entropy in Relation to Incomplete Knowledge*(Cambridge University Press)Google Scholar - Bennett, C.H. (1987): Demons, Engines, and the Second Law. Sci. Am.
**257**, 108ADSCrossRefGoogle Scholar - Leff, H.S. and Rex, A.F. (1991):
*Maxwell’s Demon: Entropy*,*Information*,*Computing*(Princeton University Press)Google Scholar - Glansdorff, P. and Prigogine, I. (1971):
*Thermodynamic Theory of Structure*,*Stability and Fluctuation*(Wiley)Google Scholar - Haken, H. (1978):
*Synergetics*(Springer-Verlag)Google Scholar

## Copyright information

© Springer-Verlag Berlin Heidelberg 1992