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Recently a number of approaches has been developed to connect the microscopic dynamics of particle systems to the macroscopic properties of systems in nonequilibrium stationary states, via the theory of dynamical systems. This way a direct…
A microscopic definition of the thermodynamic entropy in an isolated quantum system must satisfy (i) additivity, (ii) extensivity and (iii) the second law of thermodynamics. We show that the diagonal entropy, which is the Shannon entropy in…
The entropy production rate is a key quantity in non-equilibrium thermodynamics of both classical and quantum processes. No universal theory of entropy production is available to date, which hinders progress towards its full grasping. By…
Multiscale thermodynamics is a theory of relations among levels of description. Energy and entropy are its two main ingredients. Their roles in the time evolution describing approach of a level (starting level) to another level involving…
To describe the nonequilibrium states of a system we introduce a new thermodynamic parameter - the lifetime of a system. The statistical distributions which can be obtained out of the mesoscopic description characterizing the behaviour of a…
A fundamental challenge is to understand nonequilibrium statistical mechanics starting from microscopic chaos in the equations of motion of a many-particle system. In this review we summarize recent theoretical advances along these lines.…
The problem of estimating entropy production from incomplete information in stochastic thermodynamics is essential for theory and experiments. Whereas a considerable amount of work has been done on this topic, arguably, most of it is…
In a first part the scope of classical thermodynamics and statistical mechanics is discussed in the broader context of formal dynamical systems, including computer programmes. In this context classical thermodynamics appears as a particular…
We explore the consequences of a deterministic microscopic thermostat-reservoir contact mechanism. With different temperature reservoirs at each end of a two-dimensional system, a heat current is produced and the system has an anomalous…
Understanding the thermodynamics of the duplication process is a fundamental step towards a comprehensive physical theory of biological systems. However, the immense complexity of real cells obscures the fundamental tensions between energy…
We obtain macroscopic isothermal thermodynamic transformations by space-time scalings of a microscopic Hamiltonian dynamics in contact with a heat bath. The microscopic dynamics is given by a chain of anharmonic oscillators subject to a…
The thermodynamic behavior of Markovian open quantum systems can be described at the level of fluctuations by using continuous monitoring approaches. However, practical applications require assessing imperfect detection schemes, where the…
We derive universal bounds for the finite-time survival probability of the stochastic work extracted in steady-state heat engines and the stochastic heat dissipated to the environment. We also find estimates for the time-dependent…
In analogy to Brownian computers we explicitly show how to construct stochastic models, which mimic the behaviour of a general purpose computer (a Turing machine). Our models are discrete state systems obeying a Markovian master equation,…
Conventional thermo-statistics address infinite homogeneous systems within the canonical ensemble. However, some 170 years ago the original motivation of thermodynamics was the description of steam engines, i.e. boiling water. Its essential…
Stochasticity is a key characteristic of intracellular processes such as gene regulation and chemical signalling. Therefore, characterising stochastic effects in biochemical systems is essential to understand the complex dynamics of living…
Entropy production is a fundamental concept that plays a crucial role in the second law of thermodynamics and the measure of irreversibility. It imposes rigorous constraints on the kinds of transformations allowed in thermodynamic…
We introduce an ambidextrous view of stochastic dynamical systems, comparing their forward-time and reverse-time representations and then integrating them into a single time-symmetric representation. The perspective is useful theoretically,…
Statistical thermodynamics delivers the probability distribution of the equilibrium state of matter through the constrained maximization of a special functional, entropy. Its elegance and enormous success have led to numerous attempts to…
Understanding the thermodynamic properties of many-body quantum systems and their emergence from microscopic laws is a topic of great significance due to its profound fundamental implications and extensive practical applications. Recent…