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We demonstrate that, for a quantum Markovian semigroup on a finite-dimensional Hilbert space, if it satisfies the standard quantum detailed balance condition, its generator admits a special representation that yields a vanishing entropy…
The uncertainty principle is an important principle in quantum theory. Based on this principle, it is impossible to predict the measurement outcomes of two incompatible observables, simultaneously. Uncertainty principle basically is…
We consider thermodynamic systems with finitely many degrees of freedom and subject to an external control action. We derive some basic results on the dependence of the relative entropy production rate on the controlling force. Applications…
We analyze and compare different measures for the degree of non-Markovianity in the dynamics of open quantum systems. These measures are based on the distinguishability of quantum states which is quantified, on the one hand, by the trace…
We investigate the irreversible entropy production of a qubit in contact with an environment modelled by a microscopic collision model both in Markovian and non-Markovian regimes. Our main goal is to contribute to the discussions on the…
The mechanism of irreversible dynamics in the mixing systems is constructed in the frames of the classical mechanics laws. The offered mechanism can be found only within the framework of the generalized Hamilton's formalism. The generalized…
Entropy production is a key quantity in any finite-time thermodynamic process. It is intimately tied with the fundamental laws of thermodynamics, embodying a tool to extend thermodynamic considerations all the way to non-equilibrium…
Based on a variational expression for the steady-state entropy production rate in overdamped Langevin dynamics, we derive concrete upper bounds on the entropy production rate in various physical settings. For particles in a thermal…
Dealing with a generic time-local non-Markovian master equation, we define current and power to be process-dependent as in classical thermodynamics. Each process is characterized by a symmetry transformation, a gauge of the master equation,…
In thermodynamics, entropy production and work quantify irreversibility and the consumption of useful energy, respectively, when a system is driven out of equilibrium. For quantum systems, these quantities can be identified at the…
The entropy change of a (non-equilibrium) Markovian ensemble is calculated from (1) the ensemble phase density $p(t)$ evolved as iterative map, $p(t) = \mathbb{M}(t) p(t- \Delta t)$ under detail balanced transition matrix $\mathbb{M}(t)$,…
This paper discusses the thermodynamic irreversibility realized in high-dimensional Hamiltonian systems with a time-dependent parameter. A new quantity, the irreversible information loss, is defined from the Lyapunov analysis so as to…
The dynamics of Markovian open quantum systems are described by Lindblad master equations, generating a quantum dynamical semigroup. An important concept for such systems is (Davies) irreducibility, i.e., the question whether there exist…
We examine the elements of the balance equation of entropy in open quantum evolutions and their response as we go from a Markovian to a non-Markovian situation. In particular, we look at the heat current and entropy production rate in the…
We prove a lower bound on the relative entropy between two finite-dimensional states in terms of their entropy difference and the dimension of the underlying space. The inequality is tight in the sense that equality can be attained for any…
There are several inequalities in physics which limit how well we can process physical systems to achieve some intended goal, including the second law of thermodynamics, entropy bounds in quantum information theory, and the uncertainty…
Let $(X_n)_{n=0}^\infty$ denote a Markov chain on a Polish space that has a stationary distribution $\varpi$. This article concerns upper bounds on the Wasserstein distance between the distribution of $X_n$ and $\varpi$. In particular, an…
We analyze underdamped Brownian motion in non-isothermal media with quadratic, linear, and piecewise-constant temperature profiles. Exact identities for entropy production and entropy extraction are derived, addressing whether a vanishing…
In this work we introduce a new system of partial differential equations as a simplified model for the evolution of reversible martensitic transformations under thermal cycling in low hysteresis alloys. The model is developed in the context…
The second law of thermodynamics states that entropy production cannot be negative. Recent developments concerning uncertainty relations in stochastic thermodynamics, such as thermodynamic uncertainty relations and speed limits, have…