Classical emulation of quantum-coherent thermal machines

Abstract

The performance enhancements observed in various models of continuous quantum thermal machines have been linked to the buildup of coherences in a preferred basis. But, is this connection always an evidence of 'quantum-thermodynamic supremacy'? By force of example, we show that this is not the case. In particular, we compare a power-driven three-level continuous quantum refrigerator with a four-level combined cycle, partly driven by power and partly by heat. We focus on the weak driving regime and find the four-level model to be superior since it can operate in parameter regimes in which the three-level model cannot, it may exhibit a larger cooling rate, and, simultaneously, a better coefficient of performance. Furthermore, we find that the improvement in the cooling rate matches the increase in the stationary quantum coherences exactly. Crucially, though, we also show that the thermodynamic variables for both models follow from a classical representation based on graph theory. This implies that we can build incoherent stochastic-thermodynamic models with the same steady-state operation or, equivalently, that both coherent refrigerators can be emulated classically. More generally, we prove this for any N-level weakly driven device with a 'cyclic' pattern of transitions. Therefore, even if coherence is present in a specific quantum thermal machine, it is often not essential to replicate the underlying energy conversion process.

Non-Markovian dynamics of a quantum heat engine: out-of-equilibrium operation and thermal coupling control

“…This has crucial consequences: first, the engine's operation must be understood as a specific mode of the cyclic dynamics of an open quantum system with the coupling/de-coupling processes to/from thermal reservoirs being integral parts of the time evolution; second, thermal coupling strength and thermal times  k T B at low temperatures T may match characteristic scales of the work medium. The latter requires a non-perturbative treatment beyond standard weak-coupling approaches [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31] to include medium-reservoir quantum correlations and non-Markovian effects [32][33][34][35][36][37][38]. The former implies the introduction of two distinct sources of work.…”

Thermodynamics from indistinguishability: Mitigating and amplifying the effects of the bath

“…The above phenomena have promising applications, detailed in Section "Applications", regarding thermal machines, refrigeration operations, battery charging, state protection, and also contribute to the aforementioned ongoing debate [13,[40][41][42] on genuine quantum effects in thermodynamics. In particular, we detail the large indistinguishability-induced power enhancements that can be reached in cyclic thermal machines.…”

Certifying Quantum Signatures in Thermodynamics and Metrology via Contextuality of Quantum Linear Response

“…[1][2][3][4][5][6][7][8][9][10], and references therein), followed by recent experimental effort [11]. However, similar signatures can be observed in classical engines as well [12,13]. Hence, such claims should be backed by a no-go theorem that (i) defines a precise notion of nonclassicality and (ii) shows that this notion leads to statistical predictions incompatible with the corresponding quantum statistics.…”

“…For example, T T ðλ 0 jλÞ may be generated by a rate equation among a discrete set of λ's, as in the classical model described in Ref. [13]. Or, in Hamiltonian dynamics, λ ¼ ðx; pÞ and, after time t, T T ½x 0 ;p 0 jxð0Þ;pð0Þ ¼ δ½x 0 − xðtÞδ½p 0 − pðtÞ, where xðtÞ; pðtÞ is the solution of Hamilton's equations with initial conditions xð0Þ; pð0Þ.…”