Reversible dynamics is well-known to obey variational principles based on the action being the time integral of a Lagrangian with time-reversal symmetry. The purpose of the present paper is to find dissipative Lagrangians giving variational principles in dissipative dynamics with broken time-reversal symmetry. Conceptually the present theory insists on new Least Dissipation & Work Principles (LDWP) based on variational integrals weighted in time, in order to unify variational principles of physics including irreversible processes on many-body systems. This is also closely related to the present author's theory of entropy production in Kubo's scheme of transport phenomena and all nonlinear responses beyond. Through these investigations, we can understand the meaning (as a variational integral) of the action of reversible dynamics.

中文翻译：

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可逆动力学和不可逆动力学的统一变分理论-发现耗时的拉格朗日加权函数。

众所周知，可逆动力学遵循以时间为对称的拉格朗日时间积分作为作用的服从变分原理。本文的目的是找到耗散的拉格朗日方程，给出耗散动力学中具有离散时间反转对称性的变分原理。从概念上讲，本理论坚持基于时间加权变分积分的新的最小耗散和工作原理（LDWP），以统一包括多体系统上不可逆过程在内的物理学变分原理。这也与本作者的久保运输现象方案中的熵产生理论及以后的所有非线性响应密切相关。通过这些研究，我们可以了解可逆动力学作用的含义（作为变分积分）。