恒温器中的熵产生II
Entropy production in thermostats II
摘要：
我们证明了一个任意的Anosov高斯恒温器接近平衡时有正熵产生，除非外场$E$具有全局势。允许配置空间具有任何维度，并且也允许磁力。我们还证明了下面的非微扰结果。假设高斯恒温器对每个2-平面$σ$都满足\[K_{w}(σ)+{1/4}|E_σ|^2<0\]，其中$K_{w}$是相关Weyl联络的截面曲率，$E_σ$是$E$在$σ$上的正交投影。则任何SRB测度的熵产生都是正的，除非$E$具有全局势。对于曲面上的某些广义恒温器，也得到了一个相关的非微扰结果。
英文摘要：
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 \[K_{w}(σ)+{1/4}|E_σ|^2<0\] for every 2-plane $σ$, where $K_{w}$ is the sectional curvature of the associated Weyl connection and $E_σ$ 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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