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The purpose of this paper is to study the time average behavior of Markov chains with transition probabilities being kernels of completely continuous operators, and therefore to provide a sufficient condition for a class of Markov chains…
We develop the thermodynamics of non-Markovian generalized Langevin equations by embedding them in a high-dimensional Markovian representation involving auxiliary degrees of freedom. If the memory is linear and satisfies detailed balance…
In this article integro-differential Volterra equations whose convolution kernel depends on the vector variable are considered and a connection of these equations with a class of semi-Markov processes is established. The variable order…
We define common thermodynamic concepts purely within the framework of general Markov chains and derive Jarzynski's equality and Crooks' fluctuation theorem in this setup. In particular, we regard the discrete time case that leads to an…
Quantum thermodynamics studies how quantum systems and operations may be exploited as sources of work to perform useful thermodynamic tasks. In real-world conditions, the evolution of open quantum systems typically displays memory effects,…
Non-linear Hawkes processes with memory kernels given by the sum of Erlang kernels are considered. It is shown that their stability properties can be studied in terms of an associated class of piecewise deterministic Markov processes,…
Entropy production characterizes the thermodynamic irreversibility and reflects the amount of heat dissipated into the environment and free energy lost in nonequilibrium systems. According to the thermodynamic uncertainty relation, we…
Detecting broken time-reversibility at micro- and nanoscale is often difficult when experiments offer limited state resolution. We introduce a lumping method that builds an effective semi-Markov model able to reproduce exactly the full…
A Markov assumption considers a physical system memoryless to simplify its dynamics. Whereas memory effect or the non-Markovian phenomenon is more general in nature. In the quantum regime, it is challenging to define or quantify the…
Relative fluctuations of observables in discrete stochastic systems are bounded at all times by the mean dynamical activity in the system, quantified by the mean number of jumps. This constitutes a kinetic uncertainty relation that is…
The thermodynamic formalism, which was first developed for dynamical systems and then applied to discrete Markov processes, turns out to be well suited for continuous time Markov processes as well, provided the definitions are interpreted…
Stochastic thermodynamics is the field of study relating fluctuations in stochastic systems to thermodynamic quantities. The total entropy production (EP), is central to the thermodynamic classification of systems. Non-equilibrium systems…
The emergence of irreversibility in physical processes, despite the fundamentally reversible nature of quantum mechanics, remains an open question in physics. This thesis explores the intricate relationship between quantum mechanics and…
This paper deals with ergodic theorems for particular time-inhomogeneous Markov processes, whose the time-inhomogeneity is asymptotically periodic. Under a Lyapunov/minorization condition, it is shown that, for any measurable bounded…
Estimating entropy production from real observation data can be difficult due to finite resolution in both space and time and finite measurement statistics. We characterize the statistical error introduced by finite sample size and compare…
The accurate determination of transport coefficients in numerical simulations is becoming increasingly important in a wide range of applications. Here we consider the linear response in systems driven away from thermal equilibrium into a…
We study the asymptotic properties, in the weak sense, of regenerative processes and Markov renewal processes. For the latter, we derive both renewal-type results, also concerning the related counting process, and ergodic-type ones,…
In both classical and quantum thermodynamics, physical quantities are typically assigned objective values defined independently of our observations. We then refer to the 'work performed by a gas', or the 'entropy of the gas', regardless of…
Generalized empirical currents represent a vast class of thermodynamic observables of mesoscopic systems. Their fluctuations satisfy the thermodynamic uncertainty relations (TURs), as they can be bounded by the average entropy production.…
The deterministic analog of the Markov property of a time-homogeneous Markov process is the semigroup property of solutions of an autonomous differential equation. The semigroup property arises naturally when the solutions of a differential…