Related papers: Geometry of Thermodynamic Processes
Classical mechanical systems are modeled by a symplectic manifold $(M,\omega)$, and their symmetries, encoded in the action of a Lie group $G$ on $M$ by diffeomorphisms that preserves $\omega$. These actions, which are called "symplectic",…
A deeper understanding of nonequilibrium phenomena is needed to reveal the principles governing natural and synthetic molecular machines. Recent work has shown that when a thermodynamic system is driven from equilibrium then, in the linear…
We use so-called geometrical approach in description of transition from regular motion to chaotic in Hamiltonian systems with potential energy surface that has several local minima. Distinctive feature of such systems is coexistence of…
We develop a geometric foundation of microcanonical thermodynamics in which entropy and its derivatives are determined from the geometry of phase space, rather than being introduced through an a priori ensemble postulate. Once the minimal…
In this work, we conduct a systematic study of Hamiltonian and quasi-Hamiltonian systems within the framework of nondecomposable generalized Poisson geometry. Our focus lies on the interplay between the algebraic structure of…
Theory of the first-order phase transition in contact statistical manifold has been proposed to describe interface systems. The theory has not limitations of known Van der Waals-like phase transitions theories. Based on this approach,…
In this paper, we introduce the notion of port-Lagrangian systems in nonequilibrium thermodynamics, which is constructed by generalizing the notion of port-Lagrangian systems for nonholonomic mechanics proposed in Yoshimura and Marsden…
We formulate a geometric framework in which physical laws emerge from restricted access to microscopic information. Measurement constraints are modeled as a gauge symmetry acting on density operators, inducing a gauge-reduced space of…
We discuss the relevance of geometric concepts in the theory of stochastic differential equations for applications to the theory of non-equilibrium thermodynamics of small systems. In particular, we show how the Eells-Elworthy-Malliavin…
We examine "dynamical similarities" in the Lagrangian framework. These are symmetries of an intrinsically determined physical system under which observables remain unaffected, but the extraneous information is changed. We establish three…
In this paper, we investigate the reduction process of a contact Lagrangian system whose Lagrangian is invariant under a group of symmetries. We give explicit coordinate expressions of the resulting reduced differential equations, the…
Nondegeneracy conditions need to be imposed in K.A.M. theorems to insure that the set of diophantine tori has a large measure. Although they are usually expressed in action coordinates, it is possible to give a geometrical formulation using…
We investigate the topologies of random geometric complexes built over random points sampled on Riemannian manifolds in the so-called "thermodynamic" regime. We prove the existence of universal limit laws for the topologies; namely, the…
We present the development of the approach to thermodynamics based on measurement. First of all, we recall that considering classical thermodynamics as a theory of measurement of extensive variables one gets the description of thermodynamic…
We explore the idea that non-equilibrium steady states breaking detailed balance are obtained by deforming trajectories (lines in space-time) that have been sampled in a reference system with stochastic dynamics obeying detailed balance,…
In some previous papers, a geometric description of Lagrangian Mechanics on Lie algebroids has been developed. In the present paper, we give a Hamiltonian description of Mechanics on Lie algebroids. In addition, we introduce the notion of a…
We explore a particular approach to the analysis of dynamical and geometrical properties of autonomous, Pfaffian non-holonomic systems in classical mechanics. The method is based on the construction of a certain auxiliary constrained…
We investigate the consequences of reparametrizations in the geometric description of thermodynamics analyzing the effects on the thermodynamic phase space. It is known that the contact and Riemannian structures of the thermodynamic phase…
A new approach based on a statistical operator is presented, which allows to take into account the inhomogeneous particle distribution induced by gravitational interaction. This method uses the saddle point procedure to find the dominant…
The statistical mechanical description of small systems staying in thermal equilibrium with an environment can be achieved by means of the Hamiltonian of mean force. In contrast to the reduced density matrix of an open quantum system, or…