Related papers: A brief introduction to observational entropy
The study considers advantages of the introduced measure of time based on the entropy change under irreversible processes (entropy production). Using the example of non-equilibrium expansion of an ideal gas in vacuum, such a measure is…
In this paper, we review the concept of entropy in connection with the description of quantum unstable systems. We revise the conventional definition of entropy due to Boltzmann and extend it so as to include the presence of complex-energy…
We present a relational framework in which temporal structure is not fundamental but emerges from correlations within a globally stationary quantum state. Each subsystem includes an internal clock, and conditional states evolve effectively…
The concept of {\em complexity} (as a quantity) has been plagued by numerous contradictory and confusing definitions. By explicitly recognising a role for the observer of a system, an observer that attaches meaning to data about the system,…
Boltzmann's entropy is slightly modified to make it suitable for discussing phase transitions in finite systems. As an example it is shown that the pendulum undergoes a second order phase transition when passing from a vibrational to a…
We define entropy invariants for abstract algebraic structures using an asymptotic Boltzmann formula.
We investigate an asymptotically spatially flat Robertson-Walker spacetime from two different perspectives. First, using von Neumann entropy, we evaluate the entanglement generation due to the encoded information in spacetime. Then, we work…
Quantum theory is applicable, in principle, to both the microscopic and macroscopic realms. It is therefore worthwhile to investigate whether it is possible to evolve a quantum-compatible view of the properties and states of macroscopic…
A possible mechanism of time is formulated by developing an idea of time replaced by quantum correlations, with the aid of modern quantum information theory. We invent a microscopic model, where correlations of a closed system are steadily…
Since its inception, quantum theory has been the subject of fierce interpretive controversy, which persists to this day. Disputed topics include the basic ontology and dynamics of the theory, the role (if any) of measurement, the meaning of…
Quantum mechanics is derived as an application of the method of maximum entropy. No appeal is made to any underlying classical action principle whether deterministic or stochastic. Instead, the basic assumption is that in addition to the…
Starting from a many-body classical system governed by a trace-form entropy we derive, in the stochastic quantization picture, a family of non linear and non-Hermitian Schroedinger equations describing, in the mean filed approximation, a…
We study the quantum entropy of systems that are described by general non-Hermitian Hamiltonians, including those which can model the effects of sinks or sources. We generalize the von Neumann entropy to the non- Hermitian case and find…
The Gibbs entropy of a macroscopic classical system is a function of a probability distribution over phase space, i.e., of an ensemble. In contrast, the Boltzmann entropy is a function on phase space, and is thus defined for an individual…
We present a general definition of entropy in the setting of pre-ordered semigroups, extending the notion of topological entropy. From our definition, we obtain the basic properties exhibited by various entropy-like theories encountered in…
The physical meaning of the operators is not reducible to the intrinsic relations of the quantum system, since unitary transformations can find other operators satisfying the exact same relations. The physical meaning is determined…
Statistical formulations of thermodynamic entropy, such as those by Boltzmann and Gibbs, were originally developed for classical systems and are well understood in that context. However, the foundational aspects of quantum statistical…
In both quantum mechanics and relativity theory, the concept of the observer plays a critical role. However, there is no consensus on the definition of observer in these theories. Following Einstein's thought experiments, one could ask:…
A generalized framework is developed which uses a set description instead of wavefunction to emphasize the role of the observer. Such a framework is found to be very effective in the study of the measurement problem and time's arrow.…
A new concept named nonsymmetric entropy which generalizes the concepts of Boltzman's entropy and shannon's entropy, was introduced. Maximal nonsymmetric entropy principle was proven. Some important distribution laws were derived naturally…