# Two Types of Temporal Symmetry in the Laws of Nature

## TL;DR

This paper investigates how time symmetry in natural laws can lead to familiar time-related phenomena like the arrow of time.

## Contribution

The paper introduces symmetric and antisymmetric governing equations derived from time-symmetric boundary conditions.

## Key findings

- Symmetric and antisymmetric equations emerge from time-symmetric boundary conditions.
- Directional time properties arise from Markov bridges near boundaries without assuming a preferred time direction.
- Thermodynamic-like characteristics and causality emerge naturally from the mathematical framework.

## Abstract

This work explores the implications of assuming time symmetry and applying bridge-type, time-symmetric temporal boundary conditions to deterministic laws of nature with random components. The analysis, drawing on the works of Kolmogorov and Anderson, leads to two forms of governing equations, referred to here as symmetric and antisymmetric. These equations account for the emergence of characteristics associated with conventional thermodynamics, the arrow of time, and a form of antecedent causality. The directional properties of time arise from the mathematical structure of Markov bridges in proximity of the corresponding temporal boundary conditions, without requiring any postulates that impose a preferred direction of time.