Time and thermodynamics extended discussion on “Time & clocks: A thermodynamic approach”

Calling Time on Digital Clocks

I explore two logical possibilities for the discretization of time, termed “instantaneous” and “smeared”. These are found by discretizing a continuous theory, and the resulting structure of configuration space and velocities are described. It is shown that results known in numerical methods for integration of dynamical systems preclude the existence of a system with fixed discrete time step whi...

Generating function approach to thermodynamics based on time averages

We derive the statistical-mechanical expressions obtained via the method of time averages [1,2] by considering a renewal stochastic process. Our approach is based on the introduction of a generating function for the n-th event occurrence. This involves weighting the probability distribution function ψn(t) for the n-th event taking place at time t by a factor zn. For identical independent events...

On the Thermodynamic Approach towards Time Series Analysis

A scheme is presented which allows for the computation of the topological pressure and power spectra associated with equilibrium measures from a given time series. Its convergence properties are demonstrated on numerical data sets obtained from the Lozi and the Henon map. Numerical evidence for sharp peaks in the power spectrum of the non{hyperbolic phase is given and supported by estimates usi...

Measuring Time and Comparing Clocks

Time, Internal Clocks and Movement

Tile ability of all animal to process temporal information has adaptive significance across different temporal ranges. The ability to encode and utilize temporal information allows an animal to predict and anticipate events. However, the lime scales var3.' widely. The predictable event might be based on information that changes over relatively long periods such as a year or a day. or over perio...