Contents
What is an ergodic system?
Ergodicity is a property of the system; it is a statement that the system cannot be reduced or factored into smaller components. Ergodic theory is the study of systems possessing ergodicity. Ergodic systems occur in a broad range of systems in physics and in geometry.
What does the ergodic theorem state?
In physics and thermodynamics, the ergodic hypothesis says that, over long periods of time, the time spent by a system in some region of the phase space of microstates with the same energy is proportional to the volume of this region, i.e., that all accessible microstates are equiprobable over a long period of time.
Is the answer to the ergodicity problem always yes?
At a crucial place in the foundations of economics, it is assumed that the answer is always yes — a pernicious error. To make economic decisions, I often want to know how fast my personal fortune grows under different scenarios. This requires determining what happens over time in some model of wealth.
What does ergodicity mean in growth rate optimization?
Growth rate optimization is now sometimes called ‘ergodicity economics’. This doesn’t mean that ergodicity is assumed — quite the opposite: it refers to doing economics by asking explicitly whether something is ergodic, which is often not the case.
Why is the ergodicity problem in economics invisible?
The consequences are numerous, but over the centuries their root cause has become invisible in the growing formalism. Observed behaviour deviates starkly from model predictions. Paired with a firm belief in its models, this has led to a narrative of human irrationality in large parts of economics.
How is ergodicity used in equilibrium statistical mechanics?
In systems with transient behaviour, that may require defining P ( ω) as the t → ∞ limit of a time dependent density function P ( ω; t ). Famously, ergodicity is assumed in equilibrium statistical mechanics, which successfully describes the thermodynamic behaviour of gases. However, in a wider context, many observables don’t satisfy equation ( 1 ).