Related papers: High order derivatives of Boltzmann microcanonical…
In this paper, we present an energy method for the system of Boltzmann equations in the multicomponent mixture case, based on a micro-macro decomposition. More precisely, the perturbation of a solution to the Boltzmann equation around a…
In this paper we explore the general conditions in order that a 2-dimensional natural Hamiltonian system possess a second invariant which is a polynomial in the momenta and is therefore Liouville integrable. We examine the possibility that…
A vast concourse of events and phenomena occur in nature that may be interrelated by a entropy-maximization technique that provides a comprehensible explanation of a range of physical problems, integrating in a new framework the universal…
At the core of optimal control theory is the Pontryagin maximum principle - the celebrated first order necessary optimality condition - whose solutions are called extremals and which are obtained through a function called Hamiltonian, akin…
We develop a geometric theory of phase transitions (PTs) for Hamiltonian systems in the microcanonical ensemble. This theory allows to reformulate Bachmann's classification of PTs for finite-size systems in terms of geometric properties of…
We study stochastic thermodynamics of over-damped Brownian motion in a flowing fluid. Unlike some previous works, we treat the effects of the flow field as a non-conservational driving force acting on the Brownian particle. This allows us…
A pedagogical approach for deriving the statistical mechanical partition function, in a manner that emphasizes the key role of entropy in connecting the microscopic states to thermodynamics, is introduced. The connections between the…
Relativistic hydrodynamics of classic plasmas is derived from the microscopic model in the limit of ideal plasmas. The chain of equations is constructed step by step starting from the concentration evolution. It happens that the energy…
The multiplicative Hamiltonian flow on the phase space for a system with 1 degree of freedom was constituted from infinite hierarchy Hamiltonian flows. A new type of canonical transformation associated with the multiplicative Hamiltonian…
Gyrocenter dynamics of charged particles plays a fundamental role in plasma physics. In particular, accuracy and conservation of energy are important features for correctly performing long-time simulations. For this purpose, we here propose…
We derive the second-order hydrodynamic equation for reactive multi-component systems from the relativistic Boltzmann equation. In the reactive system, particles can change their species under the restriction of the imposed conservation…
The entropy of a thermally isolated system should not decrease after a quench or external driving. For a classical system following Hamiltonian dynamics, we show how this statement emerges for a large system in the sense that the extensive…
An analytical method to compute thermodynamic properties of a given Hamiltonian system is proposed. This method combines ideas of both dynamical systems and ensemble approaches to thermodynamics, providing de facto a possible alternative to…
To go beyond Gaussian approximation to the Hohenberg-Kohn free energy playing the key role in the density functional theory (DFT), the density functional \textit{integral} representation would be relevant, because field theoretical approach…
A simple extension of the Lattice Boltzmann equation is proposed, which permits to handle reactive flow dynamics in the limit of fast chemistry at virtually no extra-cost with respect to the purely hydrodynamic scheme.
New Lagrangians, depending on the field strengths and the electric and magnetic sources are found, which lead to the Maxwell equations. One new feature is that the equations of motion are obtained by varying the Lagrangian with respect to…
Boltzmann's entropy is slightly modified to make it suitable for discussing phase transitions in finite systems. As an example it is shown that the pendulum undergoes a second order phase transition when passing from a vibrational to a…
Microcanonical thermodynamics allows the application of statistical mechanics both to finite and even small systems and also to the largest, self-gravitating ones. However, one must reconsider the fundamental principles of statistical…
The finite-size Tomonaga-Luttinger Hamiltonian with an arbitrary potential is mapped onto a non-interacting Fermi gas with renormalized potential. This is done by means of flow equations for Hamiltonians and is valid for small…
In hydrodynamics the existence of an entropy current with non-negative divergence is related to the existence of a time-independent solution in a static background. Recently there has been a proposal for how to construct an entropy current…