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Through the consideration of spherically symmetric gravitating systems consisting of perfect fluids with linear equation of state constrained to be in a finite volume, an account is given of the properties of entropy at conditions in which…
The irreversibility in a statistical system is traced to its probabilistic evolution, and the molecular chaos assumption is not its unique consequence as is commonly believed. Under the assumption that the rate of change of the each…
There is a relation between the irreversibility of thermodynamic processes as expressed by the breaking of time-reversal symmetry, and the entropy production in such processes. We explain on an elementary mathematical level the relations…
A microscopic understanding of the thermodynamic entropy in quantum systems has been a mystery ever since the invention of quantum mechanics. In classical physics, this entropy is believed to be the logarithm of the volume of phase space…
The 2nd law of thermodynamics yields an irreversible increase in entropy until thermal equilibrium is achieved. This irreversible increase is often assumed to require large and complex systems to emerge from the reversible microscopic laws…
In any spacetime, it is possible to have a family of observers following a congruence of timelike curves such that they do not have access to part of the spacetime. This lack of information suggests associating a (congruence dependent)…
One characterization of a chaotic system is the quick delocalization of quantum information (fast scrambling). One therefore expects that in such a system a state quickly becomes locally indistinguishable from its perturbations. In this…
The deep connection between entropy and information is discussed in terms of both classical and quantum physics. The mechanism of information transfer between systems via entanglement is explored in the context of decoherence theory. The…
Arguments about the conservation laws of energy and momentum in the micro-world being statistical or strict began in 1924, and conflicting viewpoints remain today. The former is mainly supported theoretically, but the latter has been proved…
I explore the possibility that the laws of physics might be laws of inference rather than laws of nature. What sort of dynamics can one derive from well-established rules of inference? Specifically, I ask: Given relevant information…
Our everyday descriptions of the universe are highly coarse-grained, following only a tiny fraction of the variables necessary for a perfectly fine-grained description. Coarse graining in classical physics is made natural by our limited…
The principle of entropy increase is not only the basis of statistical mechanics, but also closely related to the irreversibility of time, the origin of life, chaos and turbulence. In this paper, we first discuss the dynamic system…
Dissipative quantum systems are frequently described within the framework of the so-called "system-plus-reservoir" approach. In this work we assign their description to the Maximum Entropy Formalism and compare the resulting thermodynamic…
We rigorously show that the probability to have a specific trajectory of an externally perturbed classical open system satisfies a universal symmetry for Liouvillian reversible dynamics. It connects the ratio between the probabilities of…
The second law of thermodynamics can be expressed in terms of entropy production, which can be used to quantify the degree of irreversibility of a process. In this Chapter, we consider the standard scenario of open quantum systems, where a…
We extend classical coarse-grained entropy, commonly used in many branches of physics, to the quantum realm. We find two coarse-grainings, one using measurements of local particle numbers and then total energy, and the second using local…
We propose an approach to the realization of many-body quantum state distributions inspired by combined principles of thermodynamics and mesoscopic physics. Its essence is a maximum entropy principle conditioned by conservation laws. We go…
It has been suggested heuristically by Unruh and Wald, and independently by Page, that among systems with given energy and volume, thermal radiation has the largest entropy. The suggestion leads to the corresponding universal bound on…
While compactness is an essential assumption for many results in dynamical systems theory, for many applications the state space is only locally compact. Here we provide a general theory for compactifying such systems, i.e. embedding them…
All clocks, classical or quantum, are open non equilibrium irreversible systems subject to the constraints of thermodynamics. Using examples I show that these constraints necessarily limit the performance of clocks and that good clocks…