Related papers: Thermodynamic formalism and large deviation functi…
We present a formalism to describe slowly decaying systems in the context of finite Markov chains obeying detailed balance. We show that phase space can be partitioned into approximately decoupled regions, in which one may introduce…
In this article, we continue the program started in our previous article of exploring an important class of thermodynamic systems from a geometric point of view. In order to model the time evolution of systems verifying the two laws of…
By combining different ideas, a general and efficient protocol to deal with discontinuous phase transitions at low temperatures is proposed. For small $T$'s, it is possible to derive a generic analytic expression for appropriate order…
Building upon a thermodynamic formalism, we show that self-gravitating systems in hydrostatic equilibrium with a uniform density are maximal entropy states when submitted to perturbations which are slow on dynamical timescale. We coin this…
Expanding Thurston maps were introduced by M. Bonk and D. Meyer with motivation from complex dynamics and Cannon's conjecture from geometric group theory via Sullivan's dictionary. In this paper, we introduce subsystems of expanding…
Let (M,J) be a dynamical model of macroscopic systems and (N,K) a less microscopic model (i.e. a model involving less details) of the same macroscopic systems; M and N are manifolds, J are vector fields on M, and K are vector fields on N.…
We develop a flow renormalization approach for periodically-driven quantum systems, which reveals prethermal dynamical regimes and associated timescales via direct correspondence between real time and flow time behavior. In this formalism,…
We study hyperbolic attractors of some dynamical systems with apriori given countable Markov partitions. Assuming that contraction is stronger than expansion we construct new Markov rectangles such that their crossections by unstable…
This paper is devoted to study thermodynamic formalism for suspension flows defined over countable alphabets. We are mostly interested in the regularity properties of the pressure function. We establish conditions for the pressure function…
By considering general Markov stochastic dynamics and its coarse-graining, we study the framework of stochastic thermodynamics for the original and reduced descriptions corresponding to different scales. We are especially concerned with the…
The collective properties of small material systems considered as semidynamical systems revealing the Markov-type irreversible evolution, are investigated. It is shown that these material systems admit their treatment as thermodynamic…
Filtering is concerned with the sequential estimation of the state, and uncertainties, of a Markovian system, given noisy observations. It is particularly difficult to achieve accurate filtering in complex dynamical systems, such as those…
We present a class of stochastic processes in which the large deviation functions of time-integrated observables exhibit singularities that relate to dynamical phase transitions of trajectories. These illustrative examples include Brownian…
We distinguish a mechanical representation of the world in terms of point masses with positions and momenta and the chemical representation of the world in terms of populations of different individuals, each with intrinsic stochasticity,…
We develop a new thermodynamic formalism to investigate the transient behaviour of maps on the real line which are skew-periodic $\mathbb{Z}$-extensions of expanding interval maps. Our main focus lies in the dimensional analysis of the…
Thermodynamics of trajectories promises to make possible the thorough analysis of the dynamical properties of an open quantum system, a sought-after goal in modern physics. Unfortunately, calculation of the relevant quantities presents…
Countable Markov shifts, denoted by $\Sigma_A$ for a 0-1 infinite matrix $A$, are central objects in symbolic dynamics and ergodic theory. R. Exel and M. Laca introduced the corresponding operator algebras, a generalization of the…
This thesis is devoted to the theoretical study of slow thermodynamic processes in non-equilibrium stochastic systems. Its main result is a physically and mathematically consistent construction of relevant thermodynamic quantities in the…
An attempt toward the operational formulation of quantum thermodynamics is made by employing the recently proposed operations forming positive operator-valued measures for generating thermodynamic processes. The quantity of heat as well as…
Thermodynamical arguments are known to be useful in the construction of physically motivated Lyapunov functionals for nonlinear stability analysis of spatially homogeneous equilibrium steady states in thermodynamically isolated systems.…