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We revisit the Ornstein-Uhlenbeck (OU) process as the fundamental mathematical description of linear irreversible phenomena, with fluctuations, near an equilibrium. By identifying the underlying circulating dynamics in a stationary process…
Small systems in contact with a heat bath evolve by stochastic dynamics. Here we show that, when one such small system is weakly coupled to another one, it is possible to infer the presence of such weak coupling by observing the violation…
Within the general formalism of quantum theory irreversibility and the arrow of time in the evolution of various physical systems are studied. Irreversible behavior often manifests itself in the guise of entropy production. This motivates…
An essential quantity in quantum information theory is the von Neumann entropy which depends entirely on the quantum density operator. Once known, the density operator reveals the statistics of observables in a quantum process, and the…
We derive an integral fluctuation theorem (FT) in a general setup of cavity quantum electrodynamics systems. In the derivation, a key difficulty lies in a diverging behavior of entropy change arising from the zero-temperature limit of an…
Hermiticity is usually treated as a foundational axiom of quantum mechanics, guaranteeing real spectra and unitary time evolution. In this work we argue that Hermiticity is more naturally understood as a symmetry law arising from the global…
The renewed interest in the foundations of quantum statistical mechanics in recent years has led us to study John von Neumann's 1929 article on the quantum ergodic theorem. We have found this almost forgotten article, which until now has…
We take the view that the standard von Neumann definition, in which the entropy $S^{vN}$ of a pure state is zero, is in evident conflict with the statement of the second law that the entropy of the universe $S_{univ}$ increases in…
Stochastic entropy production, which quantifies the difference between the probabilities of trajectories of a stochastic dynamics and its time reversals, has a central role in nonequilibrium thermodynamics. In the theory of probability, the…
For quantum spin systems in any spatial dimension with a local, translation-invariant Hamiltonian, we prove that asymptotic state convertibility from a quantum state to another one by a thermodynamically feasible class of quantum dynamics,…
This paper introduces several new classes of mathematical structures that have close connections with physics and with the theory of dynamical systems. The most general of these structures, called indivisible stochastic processes,…
Thermal behavior in subsystems of closed quantum systems is commonly attributed to dynamical chaos, quantum ergodicity, canonical typicality, or the eigenstate thermalization hypothesis, suggesting a fundamentally statistical origin of…
The classic Birkhoff- von Neumann theorem states that the set of doubly stochastic matrices is the convex hull of the permutation matrices. In this paper, we study a generalisation of this theorem in the type $II_1$ setting. Namely, we…
The combined law of thermodynamics derived by Gibbs laid the foundation of thermodynamics though only applicable to systems without internal processes. Gibbs further derived the classical statistical thermodynamics in terms of the…
The time-dependent variational principle using generalized Gaussian trial functions yields a finite dimensional approximation to the full quantum dynamics and is used in many disciplines. It is shown how these 'semi-quantum' dynamics may be…
We study the validity of Bekenstein's entropy bound for a charged black hole in the context of nonlinear electrodynamics. Bekenstein's inequalities are commonly understood as universal relations between the entropy, the charge, the…
Active systems evade the rules of equilibrium thermodynamics by constantly dissipating energy at the level of their microscopic components. This energy flux stems from the conversion of a fuel, present in the environment, into sustained…
In this Thesis, several results in quantum information theory are collected, most of which use entropy as the main mathematical tool. *While a direct generalization of the Shannon entropy to density matrices, the von Neumann entropy behaves…
In classical Hamiltonian theories, entropy may be understood either as a statistical property of canonical systems, or as a mechanical property, that is, as a monotonic function of the phase space along trajectories. In classical mechanics,…
Modified gravity theory is known to violate Birkhoff's theorem. We explore a key consequence of this violation, the effect of distant matter in the Universe on the motion of test particles. We find that when a particle is accelerated, a…