Abstract
We show that an arbitrary Anosov Gaussian thermostat close to equilibrium has positive entropy poduction unless the external field E has a global potential. The configuration space is allowed to have any dimension and magnetic forces are also allowed. We also show the following non-perturbative result. Suppose a Gaussian thermostat satisfies \(K_w(\sigma)+\frac14|E_\sigma|^2<0\) for every 2-plane σ, where K w is the sectional curvature of the associated Weyl connection and \(E_\sigma\) is the orthogonal projection of E onto σ. Then the entropy production of any SRB measure is positive unless E has a global potential. A related non-perturbative result is also obtained for certain generalized thermostats on surfaces.
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Dairbekov, N.S., Paternain, G.P. Entropy Production in Thermostats II. J Stat Phys 127, 887–914 (2007). https://doi.org/10.1007/s10955-007-9301-5
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DOI: https://doi.org/10.1007/s10955-007-9301-5