相关论文: On the Coupling of Hamilton's Principle and Thermo…

Causal variational principles, which are the analytic core of the physical theory of causal fermion systems, are found to have an underlying Hamiltonian structure, giving a formulation of the dynamics in terms of physical fields in…

We consider the canonical ensemble of $N$ particles admitting a strange Hamiltonian description. Each of the particles obeys a set of Newtonian equation of motion, which can also be described by the standard canonical Hamiltonian mechanics.…

The field-dependent equilibrium thermodynamics is derived with two methods: either by using the potential formalism either by the statistical method. Therefore, Pontrjagin's extremum principle of control theory is applied to an extended…

We introduce the idea of weakly coherent collisional models, where the elements of an environment interacting with a system of interest are prepared in states that are approximately thermal, but have an amount of coherence proportional to a…

Stochastic field theories are often constructed phenomenologically, without a systematic assessment of thermodynamic consistency or local detailed balance. This may hinder a physical description of irreversibility at the field-theoretic…

The most common physical formalisms are the Lagrangian formalism and the Hamiltonian formalism. From the superficial point of view, they are one and the same, but rewritten in other terms. However, it seems that the Hamiltonian formalism…

The purpose of this paper is two-fold. First, to make clear (and de-mystify) the basic concepts of classical thermodynamics, and thus to enable the integration of thermodynamics within systems modeling and control. Second, to demonstrate…

Applications of variational methods are typically restricted to conservative systems. Some extensions to dissipative systems have been reported too but require ad hoc techniques such as the artificial doubling of the dynamical variables.…

We consider the entropy production of a strongly coupled bipartite system. The total entropy production can be partitioned into various components, which we use to define local versions of the Second Law that are valid without the usual…

We develop a method for systematically constructing Lagrangian functions for dissipative mechanical, electrical and, mechatronic systems. We derive the equations of motion for some typical mechatronic systems using deterministic principles…

We revisit the concavity property of the thermodynamic entropy in order to formulate a general proof of the minimum energy principle as well as of other equivalent extremum principles that are valid for thermodynamic potentials and…

In this paper we obtain new estimates of the Hadamard fractional derivatives of a function at its extreme points. The extremum principle is then applied to show that the initial-boundary-value problem for linear and nonlinear…

It is shown that a given non-autonomous system of two first-order ordinary differential equations can be expressed in Hamiltonian form. The derivation presented here allow us to obtain previously known results such as the infinite number of…

A methodology is proposed for formulating dynamic equations in thermo-piezoelectric and dissipative media from the first principle of energy conservation. The results are in agreement with those from Hamiltonian principle. Our formulations…

A new form of governing equations is derived from Hamilton's principle of least action for a constrained Lagrangian, depending on conserved quantities and their derivatives with respect to the time-space. This form yields conservation laws…

The usual canonical Hamiltonian or Lagrangian formalism of classical mechanics applied to macroscopic systems describes energy conserving adiabatic motion. If irreversible diabatic processes are to be included, then the law of increasing…

In purely non-dissipative systems, Lagrangian and Hamiltonian reduction have proven to be powerful tools for deriving physical models with exact conservation laws. We have discovered a hint that an analogous reduction method exists also for…

We put forth the idea that Hamilton's equations coincide with deterministic and reversible evolution. We explore the idea from five different perspectives (mathematics, measurements, thermodynamics, information theory and state mapping) and…

In this work, a methodology is proposed for formulating general dynamical equations in mechanics under the umbrella of the principle of energy conservation. It is shown that Lagrange's equation, Hamilton's canonical equations, and…

In two recent papers necessary and sufficient conditions for a given system of second-order ordinary differential equations to be of Lagrangian form with additional dissipative forces were derived. We point out that these conditions are not…