Related papers: Computability at zero temperature
It is shown that in quantum gravity at finite temperature, the effective potential evaluated in the tadpole approximation can have a local minimum below a certain critical temperature. However, when the leading higher order thermal loop…
We prove that the maximum speed and the entropy of a one-tape Turing machine are computable, in the sense that we can approximate them to any given precision $\epsilon$. This is contrary to popular belief, as all dynamical properties are…
It is shown that the von Neumann entropy, a measure of quantum entanglement, does have its classical counterpart in thermodynamic systems, which we call partial entropy. Close to the critical temperature the partial entropy shows perfect…
We assume that markovian dynamics on a finite graph enjoys a gauge symmetry under local scalings of the probability density, derive the transformation law for the transition rates and interpret the thermodynamic force as a gauge potential.…
Residual entropy, which reflects the degrees of freedom in a system at absolute zero temperature, is crucial for understanding quantum and classical ground states. Despite its key role in explaining low-temperature phenomena and ground…
A definition of entropy via the Kolmogorov algorithmic complexity is discussed. As examples, we show how the meanfield theory for the Ising model, and the entropy of a perfect gas can be recovered. The connection with computations are…
In a previous paper, the author introduced the idea of intrinsic density --- a restriction of asymptotic density to sets whose density is invariant under computable permutation. We prove that sets with well-defined intrinsic density (and…
Local temperature defined by a local canonical state of the respective subsystem, does not always exist in quantum many body systems. Here, we give some examples of how this breakdown of the temperature concept on small length scales might…
We numerically determine the entropy for heat-conducting states, which is connected to the so-called excess heat considered as a basic quantity for steady-state thermodynamics in nonequilibrium. We adopt an efficient method to estimate the…
Considering an arbitrary, varying equation of the state parameter, the thermodynamic properties of the dark energy fluid in a semiclassical loop quantum cosmology scenario, which we consider the inverse volume modification, is studied. The…
Attempts to understand zero temperature phase transitions have forced physicists to consider a regime where the standard paradigms of condensed matter physics break down [1-4]. These quantum critical systems lack a simple description in…
Irreversible thermodynamics of simple fluids have been connected recently to the theory of dynamical systems and some interesting assumptions have been made about the nature of the associated invariant measures. We show that the tests of…
In this paper we study the computability of the stable and unstable manifolds of a hyperbolic equilibrium point. These manifolds are the essential feature which characterizes a hyperbolic system. We show that (i) locally these manifolds can…
The quantum thermodynamic property of the fractional damping system is investigated extensively. A fractional power-law decaying entropy function is revealed which presents another evidence for the validity of the third law of…
One of the most intriguing features of string thermodynamics is thermal duality, which relates the physics at temperature T to the physics at inverse temperature 1/T. Unfortunately, the traditional definitions of thermodynamic quantities…
We devise a hierarchy of computational algorithms to enumerate the microstates of a system comprising N independent, distinguishable particles. An important challenge is to cope with integers that increase exponentially with system size,…
We consider blocks of quantum spins in a chain at thermal equilibrium, focusing on their properties from a thermodynamical perspective. Whereas in classical systems the temperature behaves as an intensive magnitude, a deviation from this…
Brolin-Lyubich measure $\lambda_R$ of a rational endomorphism $R:\riem\to\riem$ with $\deg R\geq 2$ is the unique invariant measure of maximal entropy $h_{\lambda_R}=h_{\text{top}}(R)=\log d$. Its support is the Julia set $J(R)$. We…
We generalize several results of the classical theory of Thermodynamic Formalism by considering a compact metric space $M$ as the state space. We analyze the shift acting on $M^\mathbb{N}$ and consider a general a-priori probability for…
Recent investigations into the physical nature of information and fundamental limits to information transmission have revealed questions such as the possibility of superluminal data transfer or not; and whether reversible computation…