Abstract
Microscopic physical laws are time-symmetric, hence, a priori there exists no preferential temporal direction. However, the second law of thermodynamics allows one to associate the “forward” temporal direction to a positive variation of the total entropy produced in a thermodynamic process, and a negative variation with its “time-reversal” counterpart. This definition of a temporal axis is normally considered to apply in both classical and quantum contexts. Yet, quantum physics admits also superpositions between forward and time-reversal processes, whereby the thermodynamic arrow of time becomes quantum-mechanically undefined. In this work, we demonstrate that a definite thermodynamic time’s arrow can be restored by a quantum measurement of entropy production, which effectively projects such superpositions onto the forward (time-reversal) time-direction when large positive (negative) values are measured. Finally, for small values (of the order of plus or minus one), the amplitudes of forward and time-reversal processes can interfere, giving rise to entropy-production distributions featuring a more or less reversible process than either of the two components individually, or any classical mixture thereof.
Highlights
Microscopic physical laws are time-symmetric, a priori there exists no preferential temporal direction
Attempts to uphold with physical arguments the evidence of the time flow are being made on multiple fronts, mainly on the basis of empirical observations: we see that entropy in the universe increases, that the universe expands, that causes always precede their effects
We will show that, when the measured dissipative work equals βWdiss ≫ 1, the superposition is effectively projected onto the forward process, whereas when βWdiss ≪ −1, it is effectively projected onto the time-reversal one, recovering a definite thermodynamic arrow of time
Summary
Microscopic physical laws are time-symmetric, a priori there exists no preferential temporal direction. The second law of thermodynamics allows one to associate the “forward” temporal direction to a positive variation of the total entropy produced in a thermodynamic process, and a negative variation with its “time-reversal” counterpart This definition of a temporal axis is normally considered to apply in both classical and quantum contexts. We demonstrate that a definite thermodynamic time’s arrow can be restored by a quantum measurement of entropy production, which effectively projects such superpositions onto the forward (time-reversal) time-direction when large positive (negative) values are measured. Applied to the notion of thermodynamic time’s arrow, this implies that quantum mechanics can allow the superposition of thermodynamic processes (namely, dynamic processes wherein a system of interest exchanges either heat, work, or both with other systems, the environment and/or external agents) producing opposite variations in the entropy This raises the question of how a well-defined thermodynamic arrow of time can be established in the quantum framework when such superpositions are in place. In the case of interference, the probabilities take on values that cannot be obtained by any classical (convex) mixture of the forward and the time-reversal processes
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