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We propose a thermodynamically consistent minimal model to study synchronization which is made of driven and interacting three-state units. This system exhibits at the mean-field level two bifurcations separating three dynamical phases: a…
We discuss the dynamics and thermodynamics of systems with weak long-range interactions. Generically, these systems experience a violent collisionless relaxation in the Vlasov regime leading to a (usually) non-Boltzmannian quasi stationary…
The development of a self-consistent thermodynamic theory of quantum systems is of fundamental importance for modern physics. Still, despite its essential role in quantum science and technology, there is no unifying formalism for…
The intermittent on-off switching of feedback control is considered as a major mechanism of postural stabilization during human quiet standing, which can be modeled by switched-type hybrid stochastic delay differential equations with…
Many biological systems can be described by finite Markov models. A general method for simplifying master equations is presented that is based on merging adjacent states. The approach preserves the steady-state probability distribution and…
A stabilized finite element method is introduced for the simulation of time-periodic creeping flows, such as those found in the cardiorespiratory systems. The new technique, which is formulated in the frequency rather than time domain,…
We discuss the conceptually different definitions used for the non-Markovianity of classical and quantum processes. The well-established definition for non-Markovianity of a classical stochastic process represents a condition on the…
The reduction of a continuous Markov process with multiple metastable states to a discrete rate process is investigated in the presence of slow time dependent parameters such as periodic external forces or slowly fluctuating barrier…
A positive rate of entropy production at steady state is a distinctive feature of truly non-equilibrium processes. Exact results, while being often limited to simple models, offer a unique opportunity to explore the thermodynamic features…
We show that classical thermodynamics has a formulation in terms of Hamilton-Jacobi theory, analogous to mechanics. Even though the thermodynamic variables come in conjugate pairs such as pressure/volume or temperature/entropy, the phase…
For Markov processes with absorption, we provide general criteria ensuring the existence and the exponential non-uniform convergence in total variation norm to a quasi-stationary distribution. We also characterize a subset of its domain of…
The foundations of statistical mechanics, namely how equilibrium hypothesis emerges microscopically from quantum theory, is explored through investigating the environment-induced quantum decoherence processes. Based on the recent results on…
$M_n(\mathbb{C})$ denotes the set of $n$ by $n$ complex matrices. Consider continuous time quantum semigroups $\mathcal{P}_t= e^{t\, \mathcal{L}}$, $t \geq 0$, where $\mathcal{L}:M_n(\mathbb{C}) \to M_n(\mathbb{C})$ is the infinitesimal…
Classical thermodynamics treats temperature as a state variable characterizing systems in equilibrium with idealized infinite reservoirs. We argue that this framing, while computationally exact, obscures an essential physical reality: any…
Markov models are widely used to describe processes of stochastic dynamics. Here, we show that Markov models are a natural consequence of the dynamical principle of Maximum Caliber. First, we show that when there are different possible…
We propose a method to approximate continuous-time, continuous-state stochastic processes by a discrete-time Markov chain defined on a nonuniform grid. Our method provides exact moment matching for processes whose first and second moments…
This PhD thesis deals with the Markov picture of developed turbulence from the theoretical point of view. The thesis consists of two parts. The first part introduces stochastic thermodynamics, the second part aims at transferring the…
This study investigates the asymptotic dynamics of solutions to the Fokker-Planck-Kolmogorov (FPK) equation, with a specific focus on ship roll stability in dynamic sea conditions. Utilizing a fourth-order filter, we conduct a thorough…
We show that apparently thermalized states still store relevant amounts of information about their past, information that can be tracked by experiments involving nonequilibrium processes. We provide a condition for the microcanonical…
We present an application of the theory of stochastic processes to model and categorize non-equilibrium physical phenomena. The concepts of uniformly continuous probability measures and modular evolution lead to a systematic hierarchical…