Abstract We use the Shannon (information) entropy to define an “entropic” temperature for 1D nonequilibrium system with heat flux. In contrast to the kinetic temperature, which is related to the average kinetic energy, the nonequilibrium entropic temperature is related to the changes in entropy and serves as a criterion for thermalization. However, the direction and value of the heat flux is controlled by the gradient of the kinetic temperature, whereas space-time evolution and the space-time evolution of the heat flux are governed by the hyperbolic heat conduction equation. The extended nonequilibrium variables, namely, entropy, entropic temperature, thermal conductivity, and heat capacity demonstrate a third-law-like behavior at high deviation from equilibrium when the heat flux tends to its maximum value, even at nonzero value of the kinetic temperature. The ratio of the heat flux to its maximum possible value plays a role of an order parameter – it varies from zero in the equilibrium (disordered) state to unity in the nonequilibrium (ordered) state.

中文翻译：

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一维双曲热传导的扩展非平衡变量

摘要 我们使用香农（信息）熵来定义具有热通量的一维非平衡系统的“熵”温度。与与平均动能有关的动力学温度相反，非平衡熵温度与熵的变化有关，并作为热化的标准。然而，热通量的方向和大小由动力学温度梯度控制，而热通量的时空演化和时空演化则由双曲热传导方程控制。扩展的非平衡变量，即熵、熵温度、热导率和热容量，当热通量趋于最大值时，在与平衡高度偏离时表现出类似第三定律的行为，即使在动力学温度的非零值下。热通量与其最大可能值的比率扮演着一个有序参数的角色——它从平衡（无序）状态的零到非平衡（有序）状态的统一。