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Stochastic Dynamics and Irreversibility
Erratic or irregular movements, which we call unpredictable or random, occur
spontaneously and are essential part of microscopic and macroscopic worlds. When
superimposed to the predictable movements, they make up the random fluctuations
sometimes called noise. Heat and temperature are macroscopic manifestations of
these fluctuations at the microscopic level, and statistical physics constitutes the
discipline that studies the systems affected by these fluctuations. According to this
discipline, the states of thermodynamic equilibrium are described by the BoltzmannGibbs distribution, from which we may obtain the thermodynamic properties and,
in particular, the phase transitions and critical phenomena. The states out of thermodynamic equilibrium, on the other hand, do not have such a general description.
However, there are very well known laws that describe out of equilibrium or near
equilibrium systems, such as the Fourier’s law, the Boltzmann H theorem, the
Onsager reciprocity relations and the dissipation-fluctuations theorems
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