Holographic Second Laws of Black Hole Thermodynamics

Transcription

1 Holographic Second Laws of Black Hole Thermodynamics Federico Galli Gauge/Gravity Duality 018, Würzburg, 31 July 018 Based on arxiv: with A. Bernamonti, R. Myers and J. Oppenheim

2 Second Law Second law of thermodynamics: the entropy of a closed system can never decrease S(0) apple S(t) Necessary condition for any state transformation t 0 Second law of black hole mechanics 0 S BH = A 4G N horizon area is a non-decreasing function of time in any classical process [Bekenstein; Hawking]

3 Second Law Second law of thermodynamics: the entropy of a closed system can never decrease S(0) apple S(t) Necessary condition for any state transformation t 0 Second law of black hole mechanics 0 S BH = A 4G N horizon area is a non-decreasing function of time in any classical process [Bekenstein; Hawking]

4 Second Law Q: is there more? Quantum Thermodynamics applies perspective and tools of information theory to examine thermodynamics Provides additional constraints on equilibration processes for quantum systems and for macroscopic systems with long range correlations [Horodecki, Oppenheim 11] [Brandao, Horodecki, Ng, Oppenheim, Wehner 13] 0

5 Second Law Q: is there more? Quantum Thermodynamics applies perspective and tools of information theory to examine thermodynamics Provides additional constraints on equilibration processes for quantum systems and for macroscopic systems with long range correlations [Horodecki, Oppenheim 11] [Brandao, Horodecki, Ng, Oppenheim, Wehner 13] Relevant for quantum field theory and gravity! 0

6 Rényi Divergences Notion of distance between states D ( ) sgn( ) 1 log tr( 1 ) reference thermal state 8 R [Petz 86] Ex: Relative entropy distance from the thermal state lim D ( )=S( )= (F ( ) F ( ))!1 second law in a closed system F ( ) F ( 0 ) is equivalent to the statement that the relative entropy does not increase D 1 ( ) D 1 ( 0 )

7 <latexit sha1_base64="wuj3ysvbyptospgvme8/5bfvnju=">aaab8hicbvbns8naen3ur1q/qh69lbbbu0leug9flx4rgftsqtlsp+3szsbstoqs+i+8efdx6s/x5r9x+agrq8ghu/nmdmvsquw6lrftmlldw19o7xzdredr7h88mctthhyeyes3izacgu+cptqtjwwojlqiky3u7/1bnqirn3joiuwzgml+oiztnjjoidjn4gawbdac+vudhszeawpkqlnbvur6cu8i0ehl8yyjuemgozmo+asjpugm5aypmid6fiqwawmzgcxt+ijvxq0nhbculm/trs9iycrzzzpjh0cx6u/e/r5nh/zlmhuozbmxni/qzpjjq6fu0jzrwlgnlgnfc3kr5kgng0yzussf4iy8ve/+sflx37s5rjesijti5isfklhjkgjtilwksn3ciydn5jw+ocv6cd+dj3lpyipld8gfo5w8dxjcu</latexit> <latexit sha1_base64="wuj3ysvbyptospgvme8/5bfvnju=">aaab8hicbvbns8naen3ur1q/qh69lbbbu0leug9flx4rgftsqtlsp+3szsbstoqs+i+8efdx6s/x5r9x+agrq8ghu/nmdmvsquw6lrftmlldw19o7xzdredr7h88mctthhyeyes3izacgu+cptqtjwwojlqiky3u7/1bnqirn3joiuwzgml+oiztnjjoidjn4gawbdac+vudhszeawpkqlnbvur6cu8i0ehl8yyjuemgozmo+asjpugm5aypmid6fiqwawmzgcxt+ijvxq0nhbculm/trs9iycrzzzpjh0cx6u/e/r5nh/zlmhuozbmxni/qzpjjq6fu0jzrwlgnlgnfc3kr5kgng0yzussf4iy8ve/+sflx37s5rjesijti5isfklhjkgjtilwksn3ciydn5jw+ocv6cd+dj3lpyipld8gfo5w8dxjcu</latexit> <latexit sha1_base64="wuj3ysvbyptospgvme8/5bfvnju=">aaab8hicbvbns8naen3ur1q/qh69lbbbu0leug9flx4rgftsqtlsp+3szsbstoqs+i+8efdx6s/x5r9x+agrq8ghu/nmdmvsquw6lrftmlldw19o7xzdredr7h88mctthhyeyes3izacgu+cptqtjwwojlqiky3u7/1bnqirn3joiuwzgml+oiztnjjoidjn4gawbdac+vudhszeawpkqlnbvur6cu8i0ehl8yyjuemgozmo+asjpugm5aypmid6fiqwawmzgcxt+ijvxq0nhbculm/trs9iycrzzzpjh0cx6u/e/r5nh/zlmhuozbmxni/qzpjjq6fu0jzrwlgnlgnfc3kr5kgng0yzussf4iy8ve/+sflx37s5rjesijti5isfklhjkgjtilwksn3ciydn5jw+ocv6cd+dj3lpyipld8gfo5w8dxjcu</latexit> Additional Second Laws Monotonicity of Rényi Divergences generalizes the second law D ( ) D ( 0 ) One-parameter family of necessary conditions for the equilibration dynamics [Brandao, Horodecki, Ng, Oppenheim, Wehner 13] 0 <latexit sha1_base64="wuj3ysvbyptospgvme8/5bfvnju=">aaab8hicbvbns8naen3ur1q/qh69lbbbu0leug9flx4rgftsqtlsp+3szsbstoqs+i+8efdx6s/x5r9x+agrq8ghu/nmdmvsquw6lrftmlldw19o7xzdredr7h88mctthhyeyes3izacgu+cptqtjwwojlqiky3u7/1bnqirn3joiuwzgml+oiztnjjoidjn4gawbdac+vudhszeawpkqlnbvur6cu8i0ehl8yyjuemgozmo+asjpugm5aypmid6fiqwawmzgcxt+ijvxq0nhbculm/trs9iycrzzzpjh0cx6u/e/r5nh/zlmhuozbmxni/qzpjjq6fu0jzrwlgnlgnfc3kr5kgng0yzussf4iy8ve/+sflx37s5rjesijti5isfklhjkgjtilwksn3ciydn5jw+ocv6cd+dj3lpyipld8gfo5w8dxjcu</latexit>

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9 Additional Second Laws Does monotonicity of Rényi divergences imply new constraints for quantum field theory and black holes, beyond the second law? AdS/CFT framework: [Bernamonti, FG, Myers, Oppenheim 18] Class of CFT excited states AdS3 black holes with scalar excitations

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sha1_base64="esnhatykmlezeslmgdpqagr/lqg=">aaacfxicbza9swnbeib3/izxkppsxgelqx3iqhdwmyygjgbxblmnhozupfb7pwyjvwkg/+kjywkrwdnv3hzuwjicwsp78wwo+qkgnidb+dufmfxaxl3ep+dw19y7owtx1j4lqlripyxboegeeli6ysjix1rcoegcjachcxrnfuurszr9fut7azwm0ku1iawatdopijhygjpeahvu7flr9u0gm+5lyfieer847g5ucwxsi6jxckpgvebipsokq78ov3ypgggjfqyezdcxnqzqbjcowdvj8atedcws0leyqomlmo7mgfn86hd6ntx0r8zh7eykd0jh+gnjoekhnpmtd879ai6xuwtotuzisrmk8qjsqtjefzsq7uqmg1bcaqkv7vy56oegqttjvq/cmt56f6nhpvordnrtl5ukaobbl9tgb89gpk7nlvmfvjtgjeav7m15cl6cd+dj3drntgzb85nz+3q59g</latexit> Path Integral Approach Euclidean path integral construction for tr( 1 ) in d CFT Thermal state = e H CFT = Excited state {, }: relevant deformation of the thermal state = e H = excited state for the theory governed by H CFT H = H CFT + Z dxo amplitude relevant operator 0 < <

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sha1_base64="qvnquwlo754y3/d/l7q1rkxclri=">aaab+nicbvdlssnafj34rpuv69lnybfcluqe666gc3dwmlbqhdcz3rrdjw9mjmij+ru3lltc+ixu/bsnbrbaemdgcm693dmnsdmtyrk+jzxvtfwnzdpwfxtnd/fpgg8ycqtfbya8et0aykbsxgcxrshfiqaraghxjc5kv3eiwjjkvhetvpwijkkwcgouvryzyybetwmhoe3he9ea1fen5twy5oblxo7ik1uoeubx+4wovkesakcsdmwrvr5orgkuq5f3c0kpiroyaggmsykaunls+wfpthkeiej0c9wekb+3shjjou0cvrkmvqueqx4nzfivnjchanmykyzg+fgccqwwuremgeumwnmhaqmm6k6zgiqpwuq65lsbe/veycs9zly747b3bavrs1diso0smy0qxqobvurq6i6ak9o1f0zhtgi/fufmxhv4xq5xd9gfh5a459les=</latexit> <latexit sha1_base64="qvnquwlo754y3/d/l7q1rkxclri=">aaab+nicbvdlssnafj34rpuv69lnybfcluqe666gc3dwmlbqhdcz3rrdjw9mjmij+ru3lltc+ixu/bsnbrbaemdgcm693dmnsdmtyrk+jzxvtfwnzdpwfxtnd/fpgg8ycqtfbya8et0aykbsxgcxrshfiqaraghxjc5kv3eiwjjkvhetvpwijkkwcgouvryzyybetwmhoe3he9ea1fen5twy5oblxo7ik1uoeubx+4wovkesakcsdmwrvr5orgkuq5f3c0kpiroyaggmsykaunls+wfpthkeiej0c9wekb+3shjjou0cvrkmvqueqx4nzfivnjchanmykyzg+fgccqwwuremgeumwnmhaqmm6k6zgiqpwuq65lsbe/veycs9zly747b3bavrs1diso0smy0qxqobvurq6i6ak9o1f0zhtgi/fufmxhv4xq5xd9gfh5a459les=</latexit> Path Integral Approach Rényi Divergences trace function Z CFT =tr( 1 )= relevant deformation turned on and off along the Euclidean time Euclidean quantum quench O<latexit sha1_base64="qvnquwlo754y3/d/l7q1rkxclri=">aaab+nicbvdlssnafj34rpuv69lnybfcluqe666gc3dwmlbqhdcz3rrdjw9mjmij+ru3lltc+ixu/bsnbrbaemdgcm693dmnsdmtyrk+jzxvtfwnzdpwfxtnd/fpgg8ycqtfbya8et0aykbsxgcxrshfiqaraghxjc5kv3eiwjjkvhetvpwijkkwcgouvryzyybetwmhoe3he9ea1fen5twy5oblxo7ik1uoeubx+4wovkesakcsdmwrvr5orgkuq5f3c0kpiroyaggmsykaunls+wfpthkeiej0c9wekb+3shjjou0cvrkmvqueqx4nzfivnjchanmykyzg+fgccqwwuremgeumwnmhaqmm6k6zgiqpwuq65lsbe/veycs9zly747b3bavrs1diso0smy0qxqobvurq6i6ak9o1f0zhtgi/fufmxhv4xq5xd9gfh5a459les=</latexit> Notice : 0 apple apple 1

12 Rényi Divergences in AdS/CFT Holographically: CFT on thermal cylinder AdS Euclidean BH radial bulk

13 <latexit sha1_base64="rfs3obzl6tel/f5qf9mnkanpqt4=">aaacc3icbvdlssnafj3uv6vqks3g0vwvrirvhbr0iu7kxhbaek5muzboznjmjmijfqd3pgrblyoupuh3pk3ttostpxawogcc5l7t5bwprrtf1ulhcwl5zxyamvtfwnzq7q9c6fivblqkpjhshaopwj6mqmow0nkkiucnokhhe537qnurfy3oprqv0i+ol1gaftpg61hj1u0ifgjwmnwwfsraahbhhpe56l5rrmcm7bk+a54ltkboq0oxwv7wwjmlehsycloo4dql9dkrmhnnxxusvtyamou87hgqiqpkzytfjfgcuepdiaz7zakl+nsggumoubsazb6pmvvz8z+ukunfqz0wkqaactd/qprzrgofn4jbjsjqfgqjemrmrjgoqqltprjkcgzpnifuufs7twc1xrnrrtltif0sfy0alqocvurc4i6be9o1f0zj1zl9a79tgnlqxizhf9gfx5a1afmrk=</latexit> <latexit sha1_base64="rfs3obzl6tel/f5qf9mnkanpqt4=">aaacc3icbvdlssnafj3uv6vqks3g0vwvrirvhbr0iu7kxhbaek5muzboznjmjmijfqd3pgrblyoupuh3pk3ttostpxawogcc5l7t5bwprrtf1ulhcwl5zxyamvtfwnzq7q9c6fivblqkpjhshaopwj6mqmow0nkkiucnokhhe537qnurfy3oprqv0i+ol1gaftpg61hj1u0ifgjwmnwwfsraahbhhpe56l5rrmcm7bk+a54ltkboq0oxwv7wwjmlehsycloo4dql9dkrmhnnxxusvtyamou87hgqiqpkzytfjfgcuepdiaz7zakl+nsggumoubsazb6pmvvz8z+ukunfqz0wkqaactd/qprzrgofn4jbjsjqfgqjemrmrjgoqqltprjkcgzpnifuufs7twc1xrnrrtltif0sfy0alqocvurc4i6be9o1f0zj1zl9a79tgnlqxizhf9gfx5a1afmrk=</latexit> <latexit sha1_base64="rfs3obzl6tel/f5qf9mnkanpqt4=">aaacc3icbvdlssnafj3uv6vqks3g0vwvrirvhbr0iu7kxhbaek5muzboznjmjmijfqd3pgrblyoupuh3pk3ttostpxawogcc5l7t5bwprrtf1ulhcwl5zxyamvtfwnzq7q9c6fivblqkpjhshaopwj6mqmow0nkkiucnokhhe537qnurfy3oprqv0i+ol1gaftpg61hj1u0ifgjwmnwwfsraahbhhpe56l5rrmcm7bk+a54ltkboq0oxwv7wwjmlehsycloo4dql9dkrmhnnxxusvtyamou87hgqiqpkzytfjfgcuepdiaz7zakl+nsggumoubsazb6pmvvz8z+ukunfqz0wkqaactd/qprzrgofn4jbjsjqfgqjemrmrjgoqqltprjkcgzpnifuufs7twc1xrnrrtltif0sfy0alqocvurc4i6be9o1f0zj1zl9a79tgnlqxizhf9gfx5a1afmrk=</latexit> <latexit sha1_base64="rfs3obzl6tel/f5qf9mnkanpqt4=">aaacc3icbvdlssnafj3uv6vqks3g0vwvrirvhbr0iu7kxhbaek5muzboznjmjmijfqd3pgrblyoupuh3pk3ttostpxawogcc5l7t5bwprrtf1ulhcwl5zxyamvtfwnzq7q9c6fivblqkpjhshaopwj6mqmow0nkkiucnokhhe537qnurfy3oprqv0i+ol1gaftpg61hj1u0ifgjwmnwwfsraahbhhpe56l5rrmcm7bk+a54ltkboq0oxwv7wwjmlehsycloo4dql9dkrmhnnxxusvtyamou87hgqiqpkzytfjfgcuepdiaz7zakl+nsggumoubsazb6pmvvz8z+ukunfqz0wkqaactd/qprzrgofn4jbjsjqfgqjemrmrjgoqqltprjkcgzpnifuufs7twc1xrnrrtltif0sfy0alqocvurc4i6be9o1f0zj1zl9a79tgnlqxizhf9gfx5a1afmrk=</latexit> Rényi Divergences in AdS/CFT Holographically: CFT on thermal cylinder + Z dxo AdS Euclidean BH + bulk scalar m = ( ) 6= 0 radial bulk

14 <latexit sha1_base64="z9q4p5lcutqcjdohhdyjmsvrp8=">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</latexit> <latexit sha1_base64="z9q4p5lcutqcjdohhdyjmsvrp8=">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</latexit> <latexit sha1_base64="z9q4p5lcutqcjdohhdyjmsvrp8=">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</latexit> <latexit sha1_base64="z9q4p5lcutqcjdohhdyjmsvrp8=">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</latexit> <latexit sha1_base64="hcnufjdcwsj3m7fios1h7xlkgmu=">aaab83icbvbnswmxfhxbvr9qnr0eiycp7irgnoqcl48vnc10c4lm8odlktbkfsvr3epgg4tu/481/y7bdg7yobiazebyxcvpothhdb6eysrqvlhdrg1t7+zu1fcphrtmfke+kvyqtog15uxq3zddasdvfcchp4/h6kbwh8duasbfvzmknejwqlcyewysfps4juyyxsmx1fr1htt0z0dlxctja0q0+/wvxirjllbhcmdadz03nugolwge0mtlmayjlca9q1voce6icfht1fj1ajucyvfckgmfp7isej1pmktmkem6fe9arxp6+bmfgyyjlim0mfms+km46mreudkgkkesmnlmciml0vksfwmbjbu1gct/jlzekfna+a3t15o9uq6jcerzdkxhwas4htb4qoajnuev3pyx8+k8ox/zamupzw7hd5zph930kgi=</latexit> <latexit sha1_base64="hcnufjdcwsj3m7fios1h7xlkgmu=">aaab83icbvbnswmxfhxbvr9qnr0eiycp7irgnoqcl48vnc10c4lm8odlktbkfsvr3epgg4tu/481/y7bdg7yobiazebyxcvpothhdb6eysrqvlhdrg1t7+zu1fcphrtmfke+kvyqtog15uxq3zddasdvfcchp4/h6kbwh8duasbfvzmknejwqlcyewysfps4juyyxsmx1fr1htt0z0dlxctja0q0+/wvxirjllbhcmdadz03nugolwge0mtlmayjlca9q1voce6icfht1fj1ajucyvfckgmfp7isej1pmktmkem6fe9arxp6+bmfgyyjlim0mfms+km46mreudkgkkesmnlmciml0vksfwmbjbu1gct/jlzekfna+a3t15o9uq6jcerzdkxhwas4htb4qoajnuev3pyx8+k8ox/zamupzw7hd5zph930kgi=</latexit> <latexit sha1_base64="hcnufjdcwsj3m7fios1h7xlkgmu=">aaab83icbvbnswmxfhxbvr9qnr0eiycp7irgnoqcl48vnc10c4lm8odlktbkfsvr3epgg4tu/481/y7bdg7yobiazebyxcvpothhdb6eysrqvlhdrg1t7+zu1fcphrtmfke+kvyqtog15uxq3zddasdvfcchp4/h6kbwh8duasbfvzmknejwqlcyewysfps4juyyxsmx1fr1htt0z0dlxctja0q0+/wvxirjllbhcmdadz03nugolwge0mtlmayjlca9q1voce6icfht1fj1ajucyvfckgmfp7isej1pmktmkem6fe9arxp6+bmfgyyjlim0mfms+km46mreudkgkkesmnlmciml0vksfwmbjbu1gct/jlzekfna+a3t15o9uq6jcerzdkxhwas4htb4qoajnuev3pyx8+k8ox/zamupzw7hd5zph930kgi=</latexit> <latexit sha1_base64="hcnufjdcwsj3m7fios1h7xlkgmu=">aaab83icbvbnswmxfhxbvr9qnr0eiycp7irgnoqcl48vnc10c4lm8odlktbkfsvr3epgg4tu/481/y7bdg7yobiazebyxcvpothhdb6eysrqvlhdrg1t7+zu1fcphrtmfke+kvyqtog15uxq3zddasdvfcchp4/h6kbwh8duasbfvzmknejwqlcyewysfps4juyyxsmx1fr1htt0z0dlxctja0q0+/wvxirjllbhcmdadz03nugolwge0mtlmayjlca9q1voce6icfht1fj1ajucyvfckgmfp7isej1pmktmkem6fe9arxp6+bmfgyyjlim0mfms+km46mreudkgkkesmnlmciml0vksfwmbjbu1gct/jlzekfna+a3t15o9uq6jcerzdkxhwas4htb4qoajnuev3pyx8+k8ox/zamupzw7hd5zph930kgi=</latexit> Rényi Divergences in AdS/CFT Holographically: Euclidean quantum quench (1 ) =0 AdS Euclidean BH + bulk scalar time dependent b.dary conditions 6= 0 radial bulk Z CFT =tr( 1 )=Z Gravity = e S E(g, )

15 <latexit sha1_base64="dgmpxrb4/bl9f0mrf1mftch5ko8=">aaacaxicbvdlsgnbejz1bxytehg8dabbifxbd0g9oaxgolcdg9sx0zzpbbtk8qlnjxv7x4umsrf+hnv3esc/bvmfbuvdptfevkgvk8ddqemzbn5hsbk0vlk65q5vtexwaifnkalmx0vgumkumyrj4vwuezji4wxupxn5l7eojczscxrkgczwk8qufebw6rhbgblhghgqicf1ebafnkiighbcqlfzxub/it8hvtzbo+o+b3emigrtegqmaftetmejmqrqokwehcecrb9usg1pcgmasbxfmos7vol5n9ppcth6vejehjjbklkkwlqz/zruj/xrug7nfyyjqvcfpxtahbke4zh9xby6lrkbpyakjl+1cueqbbkctykvwf5/8l7qoar5x888pq/x6pi4fts1b7zrgrszpwye0mb17ye/sbl3hp0x5/urouvmzjbzdzhvn7vnlmk=</latexit> <latexit sha1_base64="dgmpxrb4/bl9f0mrf1mftch5ko8=">aaacaxicbvdlsgnbejz1bxytehg8dabbifxbd0g9oaxgolcdg9sx0zzpbbtk8qlnjxv7x4umsrf+hnv3esc/bvmfbuvdptfevkgvk8ddqemzbn5hsbk0vlk65q5vtexwaifnkalmx0vgumkumyrj4vwuezji4wxupxn5l7eojczscxrkgczwk8qufebw6rhbgblhghgqicf1ebafnkiighbcqlfzxub/it8hvtzbo+o+b3emigrtegqmaftetmejmqrqokwehcecrb9usg1pcgmasbxfmos7vol5n9ppcth6vejehjjbklkkwlqz/zruj/xrug7nfyyjqvcfpxtahbke4zh9xby6lrkbpyakjl+1cueqbbkctykvwf5/8l7qoar5x888pq/x6pi4fts1b7zrgrszpwye0mb17ye/sbl3hp0x5/urouvmzjbzdzhvn7vnlmk=</latexit> <latexit sha1_base64="dgmpxrb4/bl9f0mrf1mftch5ko8=">aaacaxicbvdlsgnbejz1bxytehg8dabbifxbd0g9oaxgolcdg9sx0zzpbbtk8qlnjxv7x4umsrf+hnv3esc/bvmfbuvdptfevkgvk8ddqemzbn5hsbk0vlk65q5vtexwaifnkalmx0vgumkumyrj4vwuezji4wxupxn5l7eojczscxrkgczwk8qufebw6rhbgblhghgqicf1ebafnkiighbcqlfzxub/it8hvtzbo+o+b3emigrtegqmaftetmejmqrqokwehcecrb9usg1pcgmasbxfmos7vol5n9ppcth6vejehjjbklkkwlqz/zruj/xrug7nfyyjqvcfpxtahbke4zh9xby6lrkbpyakjl+1cueqbbkctykvwf5/8l7qoar5x888pq/x6pi4fts1b7zrgrszpwye0mb17ye/sbl3hp0x5/urouvmzjbzdzhvn7vnlmk=</latexit> <latexit sha1_base64="dgmpxrb4/bl9f0mrf1mftch5ko8=">aaacaxicbvdlsgnbejz1bxytehg8dabbifxbd0g9oaxgolcdg9sx0zzpbbtk8qlnjxv7x4umsrf+hnv3esc/bvmfbuvdptfevkgvk8ddqemzbn5hsbk0vlk65q5vtexwaifnkalmx0vgumkumyrj4vwuezji4wxupxn5l7eojczscxrkgczwk8qufebw6rhbgblhghgqicf1ebafnkiighbcqlfzxub/it8hvtzbo+o+b3emigrtegqmaftetmejmqrqokwehcecrb9usg1pcgmasbxfmos7vol5n9ppcth6vejehjjbklkkwlqz/zruj/xrug7nfyyjqvcfpxtahbke4zh9xby6lrkbpyakjl+1cueqbbkctykvwf5/8l7qoar5x888pq/x6pi4fts1b7zrgrszpwye0mb17ye/sbl3hp0x5/urouvmzjbzdzhvn7vnlmk=</latexit> Rényi Divergences in AdS/CFT At leading order in scalar amplitude expansion D ( )= 1 1 log tr( 1 ) (tr ) (tr ) 1 ( ) cl 6 ( 1) +3 1 I(, ) I(1, ) with I(, )= p ( ) + 1 Z 0 dp ( apple p) F,, + 1, 1 + cos p I(1, )= 3/ 1 ( ) 1

16 <latexit sha1_base64="wuj3ysvbyptospgvme8/5bfvnju=">aaab8hicbvbns8naen3ur1q/qh69lbbbu0leug9flx4rgftsqtlsp+3szsbstoqs+i+8efdx6s/x5r9x+agrq8ghu/nmdmvsquw6lrftmlldw19o7xzdredr7h88mctthhyeyes3izacgu+cptqtjwwojlqiky3u7/1bnqirn3joiuwzgml+oiztnjjoidjn4gawbdac+vudhszeawpkqlnbvur6cu8i0ehl8yyjuemgozmo+asjpugm5aypmid6fiqwawmzgcxt+ijvxq0nhbculm/trs9iycrzzzpjh0cx6u/e/r5nh/zlmhuozbmxni/qzpjjq6fu0jzrwlgnlgnfc3kr5kgng0yzussf4iy8ve/+sflx37s5rjesijti5isfklhjkgjtilwksn3ciydn5jw+ocv6cd+dj3lpyipld8gfo5w8dxjcu</latexit> <latexit sha1_base64="wuj3ysvbyptospgvme8/5bfvnju=">aaab8hicbvbns8naen3ur1q/qh69lbbbu0leug9flx4rgftsqtlsp+3szsbstoqs+i+8efdx6s/x5r9x+agrq8ghu/nmdmvsquw6lrftmlldw19o7xzdredr7h88mctthhyeyes3izacgu+cptqtjwwojlqiky3u7/1bnqirn3joiuwzgml+oiztnjjoidjn4gawbdac+vudhszeawpkqlnbvur6cu8i0ehl8yyjuemgozmo+asjpugm5aypmid6fiqwawmzgcxt+ijvxq0nhbculm/trs9iycrzzzpjh0cx6u/e/r5nh/zlmhuozbmxni/qzpjjq6fu0jzrwlgnlgnfc3kr5kgng0yzussf4iy8ve/+sflx37s5rjesijti5isfklhjkgjtilwksn3ciydn5jw+ocv6cd+dj3lpyipld8gfo5w8dxjcu</latexit> <latexit sha1_base64="wuj3ysvbyptospgvme8/5bfvnju=">aaab8hicbvbns8naen3ur1q/qh69lbbbu0leug9flx4rgftsqtlsp+3szsbstoqs+i+8efdx6s/x5r9x+agrq8ghu/nmdmvsquw6lrftmlldw19o7xzdredr7h88mctthhyeyes3izacgu+cptqtjwwojlqiky3u7/1bnqirn3joiuwzgml+oiztnjjoidjn4gawbdac+vudhszeawpkqlnbvur6cu8i0ehl8yyjuemgozmo+asjpugm5aypmid6fiqwawmzgcxt+ijvxq0nhbculm/trs9iycrzzzpjh0cx6u/e/r5nh/zlmhuozbmxni/qzpjjq6fu0jzrwlgnlgnfc3kr5kgng0yzussf4iy8ve/+sflx37s5rjesijti5isfklhjkgjtilwksn3ciydn5jw+ocv6cd+dj3lpyipld8gfo5w8dxjcu</latexit> New Holographic Constraints Two scalar fields in AdS black hole 1 & Bulk interaction U( 1, ) =g( ) Possible transition from a state with 1 excited to a state with excited (at fixed energy)? 1 <latexit sha1_base64="wuj3ysvbyptospgvme8/5bfvnju=">aaab8hicbvbns8naen3ur1q/qh69lbbbu0leug9flx4rgftsqtlsp+3szsbstoqs+i+8efdx6s/x5r9x+agrq8ghu/nmdmvsquw6lrftmlldw19o7xzdredr7h88mctthhyeyes3izacgu+cptqtjwwojlqiky3u7/1bnqirn3joiuwzgml+oiztnjjoidjn4gawbdac+vudhszeawpkqlnbvur6cu8i0ehl8yyjuemgozmo+asjpugm5aypmid6fiqwawmzgcxt+ijvxq0nhbculm/trs9iycrzzzpjh0cx6u/e/r5nh/zlmhuozbmxni/qzpjjq6fu0jzrwlgnlgnfc3kr5kgng0yzussf4iy8ve/+sflx37s5rjesijti5isfklhjkgjtilwksn3ciydn5jw+ocv6cd+dj3lpyipld8gfo5w8dxjcu</latexit> 1

17 <latexit sha1_base64="wuj3ysvbyptospgvme8/5bfvnju=">aaab8hicbvbns8naen3ur1q/qh69lbbbu0leug9flx4rgftsqtlsp+3szsbstoqs+i+8efdx6s/x5r9x+agrq8ghu/nmdmvsquw6lrftmlldw19o7xzdredr7h88mctthhyeyes3izacgu+cptqtjwwojlqiky3u7/1bnqirn3joiuwzgml+oiztnjjoidjn4gawbdac+vudhszeawpkqlnbvur6cu8i0ehl8yyjuemgozmo+asjpugm5aypmid6fiqwawmzgcxt+ijvxq0nhbculm/trs9iycrzzzpjh0cx6u/e/r5nh/zlmhuozbmxni/qzpjjq6fu0jzrwlgnlgnfc3kr5kgng0yzussf4iy8ve/+sflx37s5rjesijti5isfklhjkgjtilwksn3ciydn5jw+ocv6cd+dj3lpyipld8gfo5w8dxjcu</latexit> <latexit sha1_base64="wuj3ysvbyptospgvme8/5bfvnju=">aaab8hicbvbns8naen3ur1q/qh69lbbbu0leug9flx4rgftsqtlsp+3szsbstoqs+i+8efdx6s/x5r9x+agrq8ghu/nmdmvsquw6lrftmlldw19o7xzdredr7h88mctthhyeyes3izacgu+cptqtjwwojlqiky3u7/1bnqirn3joiuwzgml+oiztnjjoidjn4gawbdac+vudhszeawpkqlnbvur6cu8i0ehl8yyjuemgozmo+asjpugm5aypmid6fiqwawmzgcxt+ijvxq0nhbculm/trs9iycrzzzpjh0cx6u/e/r5nh/zlmhuozbmxni/qzpjjq6fu0jzrwlgnlgnfc3kr5kgng0yzussf4iy8ve/+sflx37s5rjesijti5isfklhjkgjtilwksn3ciydn5jw+ocv6cd+dj3lpyipld8gfo5w8dxjcu</latexit> <latexit sha1_base64="wuj3ysvbyptospgvme8/5bfvnju=">aaab8hicbvbns8naen3ur1q/qh69lbbbu0leug9flx4rgftsqtlsp+3szsbstoqs+i+8efdx6s/x5r9x+agrq8ghu/nmdmvsquw6lrftmlldw19o7xzdredr7h88mctthhyeyes3izacgu+cptqtjwwojlqiky3u7/1bnqirn3joiuwzgml+oiztnjjoidjn4gawbdac+vudhszeawpkqlnbvur6cu8i0ehl8yyjuemgozmo+asjpugm5aypmid6fiqwawmzgcxt+ijvxq0nhbculm/trs9iycrzzzpjh0cx6u/e/r5nh/zlmhuozbmxni/qzpjjq6fu0jzrwlgnlgnfc3kr5kgng0yzussf4iy8ve/+sflx37s5rjesijti5isfklhjkgjtilwksn3ciydn5jw+ocv6cd+dj3lpyipld8gfo5w8dxjcu</latexit> New Holographic Constraints Two scalar fields in AdS black hole 1 & Bulk interaction U( 1, ) =g( ) Possible transition from a state with 1 excited to a state with excited (at fixed energy)? 1 D ( 1 ) D ( ) <latexit sha1_base64="wuj3ysvbyptospgvme8/5bfvnju=">aaab8hicbvbns8naen3ur1q/qh69lbbbu0leug9flx4rgftsqtlsp+3szsbstoqs+i+8efdx6s/x5r9x+agrq8ghu/nmdmvsquw6lrftmlldw19o7xzdredr7h88mctthhyeyes3izacgu+cptqtjwwojlqiky3u7/1bnqirn3joiuwzgml+oiztnjjoidjn4gawbdac+vudhszeawpkqlnbvur6cu8i0ehl8yyjuemgozmo+asjpugm5aypmid6fiqwawmzgcxt+ijvxq0nhbculm/trs9iycrzzzpjh0cx6u/e/r5nh/zlmhuozbmxni/qzpjjq6fu0jzrwlgnlgnfc3kr5kgng0yzussf4iy8ve/+sflx37s5rjesijti5isfklhjkgjtilwksn3ciydn5jw+ocv6cd+dj3lpyipld8gfo5w8dxjcu</latexit> 1 Stronger constraint than the second law?

18 New Holographic Constraints Fixed 1 & varying = 1 1 D α =0.9 =0.6 γ = D redundant with second law α second law

19 New Holographic Constraints Fixed 1 & varying = 1 1 D α =0.9 =0.6 γ = α 1 1 D redundant with second law second law

20 New Holographic Constraints Fixed 1 & varying = 1 1 D α =0.9 =0.6 γ = α 1 Transition allowed by the second law but forbidden for some values of ) 1 second law Full range of D gives new constraints!

21 Conclusions & Outlook Quantum thermodynamics provides new constraints for field theory and gravitational dynamics Additional constraints come from varying the reference state D ( ) any equilibrium state [Bernamonti, FG, Myers, Oppenheim 18] More general states and larger range of D Compute directly in gravity? Additional laws for asymptotically flat black holes? Geometric interpretation? [in progress]

22 Thank you!