The thermodynamics of time

TL;DR

This paper explores the paradox of time in physics, proposing that minimal entropy production in quantum measurements of time is bounded by the number of clock ticks, with black holes achieving this bound.

Contribution

It introduces a resource-based perspective on the measurement of time, linking minimal entropy production to the number of clock ticks and black holes.

Findings

Minimal entropy production equals the number of clock ticks.

Black holes attain the lower bound of entropy production.

Time measurement imposes fundamental thermodynamic limits.

Abstract

The problem of time is a deep paradox in our physical description of the world. According to Aristotle's relational theory, time is a measure of change and does not exist on its own. In contrast, quantum mechanics, just like Newtonian mechanics, is equipped with a master clock that dictates the evolution of a system. This clock is infinitely precise and tacitly supplied free of charge from outside physics. Not only does this absolute time make it notoriously difficult to make a consistent theory of quantum gravity, it is also the underlying problem in establishing the second law. Indeed, contrary to our experience, the Wheeler-deWitt equation --a canonical quantization of general relativity-- predicts a static universe. Similarly, when simply concerned with the dynamics of a closed quantum system, there is no second law because the Von Neumann entropy is invariant under unitary transformations. Here we are mainly concerned with the latter problem and we show that it can be resolved by attributing a minimal amount of resources to the measurement of time. Although there is an absolute time in quantum mechanics, an observer can only establish a time by measuring a clock. For a local measurement, the minimal entropy production is equal to the number of ticks. This lower bound is attained by a black hole.