Time Irreversibility

Cognitive Energy Cost of Informed Decisions ArXiv ID: 2310.15082 “View on arXiv” Authors: Unknown Abstract Time irreversibility in neuronal dynamics has recently been demonstrated to correlate with various indicators of cognitive effort in living systems. Using Landauer’s principle, which posits that time-irreversible information processing consumes energy, we establish a thermodynamically consistent measure of cognitive energy cost associated with belief dynamics. We utilize this concept to analyze a two-armed bandit game, a standard decision-making framework under uncertainty, considering exploitation, finite memory, and concurrent allocation to both game options or arms. Through exploitative, prediction-error-based belief dynamics, the decision maker incurs a cognitive energy cost. Initially, we observe the rise of dissipative structures in the steady state of the belief space due to time-reversal symmetry breaking at intermediate exploitative levels. To delve deeper into the belief dynamics, we liken it to the behavior of an active particle subjected to state-dependent noise. This analogy enables us to relate emergent risk aversion to standard thermophoresis, connecting two apparently unrelated concepts. Finally, we numerically compute the time irreversibility of belief dynamics in the steady state, revealing a strong correlation between elevated - yet optimized - cognitive energy cost and optimal decision-making outcomes. This correlation suggests a mechanism for the evolution of living systems towards maximally out-of-equilibrium structures. ...

Trend patterns statistics for assessing irreversibility in cryptocurrencies: time-asymmetry versus inefficiency ArXiv ID: 2307.08612 “View on arXiv” Authors: Unknown Abstract In this paper, we present a measure of time irreversibility using trend pattern statistics. We define the irreversibility index as the Kullback-Leibler divergence between the distribution of uptrends subsequences (increasing trends) and the corresponding downtrends subsequences distribution (decreasing trends) in a time series. We use this index to analyze the degree of irreversibility in log return series over time, specifically focusing on five cryptocurrencies: Bitcoin, Ethereum, Ripple, Litecoin, and Bitcoin Cash. Our analysis reveals a strong indication of irreversibility in all these cryptocurrencies and the characteristic evolves over time. We additionally evaluate the market efficiency for these cryptocurrencies based on a recently proposed information-theoretic measure. By comparing inefficiency and irreversibility, we explore the relationship between these statistical features. This comparison provides insight into the non-trivial relationship between inefficiency and irreversibility. ...