This paper develops a generalization of Zubarev's nonequilibrium statistical operator method for the case of simultaneous inclusion of additive and nonlocal boundary functionals of trajectories. Using a unified thermodynamic approach, a three-parameter model of nonequilibrium systems is constructed, including the first-passage time, the dwell time above a given level, and the absolute extremum of the process. A correspondence is demonstrated between the maximum information entropy method for trajectories and the Donsker-Varadan large deviation formalism. Using the Doob`s h-transform, it is demonstrated that fixing extremal functionals of history induces efficient non-Markovian transport in the system with dynamic adaptation to historical records. Criteria for the applicability of the developed apparatus in the"large time"domain and the possibilities of its use for optimizing stochastic particle separation in periodic potentials are discussed.
This paper extends the formalism of stochastic path-space thermodynamics by systematically expanding the space of thermodynamic variables with a spectrum of boundary and relative functionals of random processes. Generalizing the approaches introduced in preprints arXiv:2607.24078 and arXiv:2609.08477, we investigate th...
We consider the theory of the fractional exclusion statistics (FES) by using both the Maximum Entropy Principle (MEP) and the Entropy Principle (EP) in the context of Rational Extended Thermodynamics (RET) with an arbitrary dimension
D
of phase space. To this purpose, we develop and apply a general approach for t...
M. Trovato, E. Distefano· Ricerche di Matematica· 0 citations
This paper is a modern review of C. B. Morrey's 1955 paper on the derivation of the equations of hydrodynamics from statistical mechanics. It has two main parts. First, assuming the existence of certain invariant N -particle phase distributions, Morrey derives formal balance laws for mass, momentum, and energy. Second,...
This review surveys diverse types of random motion within a unified framework, introducing essential mathematical tools, including special functions and fractional calculus, in a pedagogical manner. We focus on generalized random motions in one-dimensional space described by Fokker-Planck like equations, whose fundamen...
The collision operator for the Boltzmann equation is a nonlinear nonlocal operator. When lifted in the extended 2-particle space, it is viewed as the projection of a collisional linear operator. In this paper, we propose a particle method that samples the post-collision relative velocity directly from the Green's funct...
We study annealed current fluctuations in the two-dimensional symmetric simple exclusion process (SSEP) across a circular passive counting boundary. The initial average density is $\rho_1$ inside a disk of radius $R$ and $\rho_2$ outside, and the observable is the net decrease of the particle number in the disk over a...
Ting-Fei Li· 0 citations
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