## Imaginary Time 2

Another part of the analogy I started here, but this time using inverse temperature instead of imaginary time. It describes a thermometer where a mass changes position with temperature. I’m guessing this stuff only applies when the temperature is changing adiabatically.

Thermometer (unitless temperature): | ||

[1] | inverse temperature (unitless) | |

[m] | y coordinate | |

[kg/s^2 K] | spring constant * temp unit conversion | |

[m] | how position changes with (inverse) temperature | |

[kg m/s^2 K] | force per Kelvin | |

[kg m^2/s^2 K] | stretching energy per Kelvin | |

[kg m^2/s^2 K] | potential energy per Kelvin | |

[kg m^2/s^2 K] | entropy | |

Thermometer: | ||

[1/K] | inverse temperature | |

[m] | y coordinate | |

[kg/s^2 K^2 = bits/m^2 K] | how information density changes with temp | |

[m K] | how position changes with (inverse) temperature | |

[kg m/s^2 K = bits/m] | force per Kelvin | |

[kg m^2/s^2 = bits K] | stretching energy = change in stretching information with invtemp | |

[kg m^2/s^2 = bits K] | potential energy = change in potential information with invtemp | |

[bits] | entropy |

I assume that the dynamics of such a system would follow a path where is that a minimum-entropy path or a maximum?

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