高斯恒温器中的熵产生

恒温器中的熵产生II

Entropy production in thermostats II

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。

Estimates of the Derivative of the Entropy of Gaussian Thermostats

We consider a variation of an Anosov geodesic flow by Gaussian Thermostats and we obtain estimates of the derivative of the entropy map at the geodesic flow. In particular, we prove that the entropy of the geodesic flow is a local maximum for the entropy map.

Fluctuation of the entropy production for the Lorentz gas under small external forces

In this paper we study the physical and statistical properties of the periodic Lorentz gas with finite horizon driven to a non-equilibrium steady state by the combination of non-conservative external forces and deterministic thermostats. A version of this model was introduced by Chernov, Eyink, Lebowitz, and Sinai and subsequently generalized by Chernov and the third author. Non-equilibrium steady states for these models are SRB measures and they are characterized by the positivity of the steady state entropy production rate. Our main result is to establish that the entropy production, in this…

Entropy production and folding of the phase space in chaotic dynamics

We study the entropy production of Gibbs (equilibrium) measures for chaotic dynamical systems with folding of the phase space. The dynamical chaotic model is that generated by a hyperbolic non-invertible map $f$ on a general basic (possibly fractal) set $Λ$; the non-invertibility creates new phenomena and techniques than in the diffeomorphism case. We prove a formula for the \textit{entropy production}, involving an asymptotic logarithmic degree, with respect to the equilibrium measure $μ_ϕ$ associated to the potential $ϕ$. This formula helps us calculate the entropy production of the measure …