A relativistic Hamiltonian–Lagrangian formalism for a composite system submitted to conservative and non-conservative forces is developed. A block descending an incline with a frictional force, mechanical energy dissipation process, is described, obtaining an Euler–Lagrange equation including a Rayleigh’s dissipation function. A cannonball rising on an incline, process evolving with mechanical energy production, is described by an Euler–Lagrange equation including a Gibbs’ production function, with a chemical origin force. A matrix four-vector mechanical equation, considering processes’ mechanical and phenomenological aspects, is postulated. This relativistic Hamiltonian–Lagrangian four-vector formalism complements the Einstein–Minkowski–Lorentz four-vector fundamental equation formalism. By considering a process’ mechanical and thermodynamic description, temporal evolution equations, relating process’ Hamiltonian (mechanical energy) evolution and the involved thermodynamic potentials (entropy of the universe, Helmholtz free energy, Gibbs free enthalpy) variations, are obtained.

建立了服从保守和非保守势力的复合系统的相对论性哈密顿-拉格朗日形式主义。描述了一个通过摩擦力下降的块，即机械能耗散过程，从而获得了包含瑞利耗散函数的欧拉-拉格朗日方程。弹道上升时的炮弹，随着机械能的产生而发展，由包括吉布斯产生函数和化学原动力的欧拉-拉格朗日方程描述。考虑到过程的力学和现象学方面，提出了一个矩阵四向量力学方程。这种相对论的哈密顿-拉格朗日四向量形式主义是对爱因斯坦-闵可夫斯基-洛伦兹四向量基本方程形式主义的补充。