Related papers: Poincare Recurrence, Zermelo's Second Law Paradox,…
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…
Philosophers now seem to agree that frequentism is an untenable strategy to explain the meaning of probabilities. Nevertheless, I want to revive frequentism, and I will do so by grounding probabilities on typicality in the same way as the…
We study Poincar\'e recurrence from a purely geometrical viewpoint. We prove that the metric entropy is given by the exponential growth rate of return times to dynamical balls. This is the geometrical counterpart of Ornstein-Weiss theorem.…
Poincare recurrence theorem states that any finite system will come arbitrary close to its initial state after some very long but finite time. At the statistical level, this by itself does not represent a paradox, but apparently violates…
I argue that if a special science satisfies certain key assumptions that are familiar from physicalist accounts of the special sciences and from physics, then its causal regularities have an associated notion of entropy, and that this…
Here we deconstruct, and then in a reasoned way reconstruct, the concept of "entropy of a system," paying particular attention to where the randomness may be coming from. We start with the core concept of entropy as a COUNT associated with…
One of the important questions in statistical mechanics is how irreversibility (time's arrow) occurs when Newton equations of motion are time reversal invariant. One objection to irreversibility is based on Poincar\'e's recursion theorem: a…
Statistical mechanics descriptions of the second law of thermodynamics generally imply point-like particles driven by a dissipative overall mechanism for their simultaneous time-evolution. As the number of involved particles grows larger,…
Many physicists think that the maximum entropy formalism is a straightforward application of Bayesian statistical ideas to statistical mechanics. Some even say that statistical mechanics is just the general Bayesian logic of inductive…
We obtain a description of the Poincar\'e recurrences of chaotic systems in terms of the ergodic theory of transient chaos. It is based on the equivalence between the recurrence time distribution and an escape time distribution obtained by…
The second law of thermodynamics states that entropy increases (or does not change) by time in an isolated system. As microscopic physical laws are reversible, the origin of irreversibility is not straightforward. Although the outcome of a…
Since the work of Ferrenberg et al.[PRL 69, (1992)] some pseudo random number generators are known to yield wrong results in cluster Monte Carlo simulations. In this contribution the fundamental mechanism behind this failure is discussed.…
Unlike most other laws of nature, the second law of thermodynamics is of a statistical nature, according to Boltzmann, meaning that its reliability arises from the vast number of particles present in macroscopic systems. This means that…
If a measurement process is regarded as an irreversible process, then by Second law of thermodynamics the entropy should increase after any measurement process. By the same spirit a quantum system undergoing repeated measurement should show…
The celebrated Evans-Searles, respectively Gallavotti-Cohen, fluctuation theorem concerns certain universal statistical features of the entropy production rate of a classical system in a transient, respectively steady, state. In this paper,…
In statistical thermodynamics the 2nd law is properly spelled out in terms of conditioned probabilities. As such it makes the statement, that `entropy increases with time' without preferring a time direction. In this paper I try to explain…
The partial trace is commonly introduced in quantum mechanics as an algebraic operation used to define reduced states of composite systems. However, the probabilistic origin of this operation goes systematically unnoticed in the literature.…
Quantum superposition, a cornerstone of quantum mechanics, enables systems to exist in multiple states simultaneously, giving rise to probabilistic outcomes. In quantum information science, conditional entropy has become a key metric for…
For an ordinary thermodynamical system the Poincar\'{e} recurrence time is exponentially large in the Boltzmann entropy of the system. It turns out, that for a system with dynamical chaos it is determined by the Kolmogorov-Sinai entropy and…
The physical meaning of entropy is analyzed in the context of statistical, nuclear, atomic physics and cosmology. Only the microcanonical Boltzmann entropy leads to no contradictions in several simple, elementary and for thermodynamics…