Stochastic Thermodynamics

Abstract

The modern theory of spontaneous fluctuations close to equilibrium was outlined in the classic papers of ONSAGER and MACHLUP /1/. In their theory, the fluctuations are described as stationary, Gaussian continuous Markov processes. The amplitude of the fluctuations (or rather of the random “forces” producing them) is calculated from the Boltzmann relation between the probability $P({\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{x}})$ for an equilibrium macrostate ${{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{x}}}$ and the corresponding entropy $S({\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{x}})$:

$$P({\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{x}}) \sim \exp \left[ {\frac{{S({\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{x}})}}{{{k_{B}}}}} \right]$$

Bevoegdverklaard Navorser N.F.W.O. België