The Thermodynamical Arrow of Time

  • H.-Dieter Zeh


The thermodynamical arrow of time is characterized by the increase of entropy according to the Second Law, in its phenomenological form written as
$$\frac{{dS}}{{dt}} = {\left\{ {\frac{{dS}}{{dt}}} \right\}_{ext}} + {\left\{ {\frac{{dS}}{{st}}} \right\}_{\operatorname{int} }}with d{S_{ext}} = \frac{{dQ}}{T}and{\left\{ {\frac{{dS}}{{dt}}} \right\}_{\operatorname{int} }} \geqslant 0$$
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 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.


Master Equation Liouville Equation Liouville Operator Macroscopic State Microscopic State 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • H.-Dieter Zeh
    • 1
  1. 1.Institut für Theoretische PhysikUniversität HeidelbergHeidelbergFed. Rep. of Germany

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