Wholeness as a Conceptual Foundation of Physical Theories

A description of physical reality in which wholeness is the foundation is discussed along with the motivation for such an attempt. As a possible mathematical framework within which a physical theory based on wholeness may be expressed, elementary embeddings along with the Wholeness Axiom are suggested. It is shown how features of wholeness such as wholeness being indescribable, more than the sum of parts, locally accessible and giving rise to a self-similar, or holographic, type of order are reflected in the mathematics. It is also shown how all the sets in the mathematical universe may be expressed as emerging from the dynamics of wholeness. Moreover, it is indicated how the mathematics may be further developed so as to connect up with a physical interpretation.Comment: 12 pages, 1 eps figure, submitted to "Physics Essays

Generalization of the Second Law for a Nonequilibrium Initial State

We generalize the second law of thermodynamics in its maximum work formulation for a nonequilibrium initial distribution. It is found that in an isothermal process, the Boltzmann relative entropy (H-function) is not just a Lyapunov function but also tells us the maximum work that may be gained from a nonequilibrium initial state. The generalized second law also gives a fundamental relation between work and information. It is valid even for a small Hamiltonian system not in contact with a heat reservoir but with an effective temperature determined by the isentropic condition. Our relation can be tested in the Szilard engine, which will be realized in the laboratory

Stochastic Equations in Black Hole Backgrounds and Non-equilibrium Fluctuation Theorems

We apply the non-equilibrium fluctuation theorems developed in the statistical physics to the thermodynamics of black hole horizons. In particular, we consider a scalar field in a black hole background. The system of the scalar field behaves stochastically due to the absorption of energy into the black hole and emission of the Hawking radiation from the black hole horizon. We derive the stochastic equations, i.e. Langevin and Fokker-Planck equations for a scalar field in a black hole background in the $\hbar \rightarrow 0$ limit with the Hawking temperature $\hbar \kappa/2 \pi$ fixed. We consider two cases, one confined in a box with a black hole at the center and the other in contact with a heat bath with temperature different from the Hawking temperature. In the first case, the system eventually becomes equilibrium with the Hawking temperature while in the second case there is an energy flow between the black hole and the heat bath. Applying the fluctuation theorems to these cases, we derive the generalized second law of black hole thermodynamics. In the present paper, we treat the black hole as a constant background geometry. Since the paper is also aimed to connect two different areas of physics, non-equilibrium physics and black holes physics, we include pedagogical reviews on the stochastic approaches to the non-equilibrium fluctuation theorems and some basics of black holes physics.Comment: 53 page

The thermodynamic meaning of negative entropy

Landauer's erasure principle exposes an intrinsic relation between thermodynamics and information theory: the erasure of information stored in a system, S, requires an amount of work proportional to the entropy of that system. This entropy, H(S|O), depends on the information that a given observer, O, has about S, and the work necessary to erase a system may therefore vary for different observers. Here, we consider a general setting where the information held by the observer may be quantum-mechanical, and show that an amount of work proportional to H(S|O) is still sufficient to erase S. Since the entropy H(S|O) can now become negative, erasing a system can result in a net gain of work (and a corresponding cooling of the environment).Comment: Added clarification on non-cyclic erasure and reversible computation (Appendix E). For a new version of all technical proofs see the Supplementary Information of the journal version (free access

Does a Computer have an Arrow of Time?

In [Sch05a], it is argued that Boltzmann's intuition, that the psychological arrow of time is necessarily aligned with the thermodynamic arrow, is correct. Schulman gives an explicit physical mechanism for this connection, based on the brain being representable as a computer, together with certain thermodynamic properties of computational processes. [Haw94] presents similar, if briefer, arguments. The purpose of this paper is to critically examine the support for the link between thermodynamics and an arrow of time for computers. The principal arguments put forward by Schulman and Hawking will be shown to fail. It will be shown that any computational process that can take place in an entropy increasing universe, can equally take place in an entropy decreasing universe. This conclusion does not automatically imply a psychological arrow can run counter to the thermodynamic arrow. Some alternative possible explana- tions for the alignment of the two arrows will be briefly discussed.Comment: 31 pages, no figures, publication versio

Second law, entropy production, and reversibility in thermodynamics of information

We present a pedagogical review of the fundamental concepts in thermodynamics of information, by focusing on the second law of thermodynamics and the entropy production. Especially, we discuss the relationship among thermodynamic reversibility, logical reversibility, and heat emission in the context of the Landauer principle and clarify that these three concepts are fundamentally distinct to each other. We also discuss thermodynamics of measurement and feedback control by Maxwell's demon. We clarify that the demon and the second law are indeed consistent in the measurement and the feedback processes individually, by including the mutual information to the entropy production.Comment: 43 pages, 10 figures. As a chapter of: G. Snider et al. (eds.), "Energy Limits in Computation: A Review of Landauer's Principle, Theory and Experiments

Physics from Wholeness : Dynamical Totality as a Conceptual Foundation for Physical Theories

Motivated by reductionism's current inability to encompass the quantum theory we explore an indivisible and dynamical wholeness as an underlying foundation for physics. After reviewing the role of wholeness in the quantum theory we set a philosophical background aiming at introducing an ontology, based on a dynamical wholeness. Equipped with the philosophical background we then propose a mathematical realization by representing the dynamics with a non-trivial elementary embedding from the mathematical universe to itself. By letting the embedding interact with itself through application we obtain a left-distributive universal algebra that is isomorphic to special braids. Via the connection between braids and quantum and statistical physics we show that a the mathematical structure obtained from wholeness yields known physics in a special case. In particular we point out the connections to algebras of observables, spin networks, and statistical mechanical models used in solid state physics, such as the Potts model. Furthermore we discuss the general case and there the possibility of interpreting the mathematical structure as a dynamics beyond unitary evolution, where entropy increase is involved